TableofContentsCoverimageFront-matterCopyrightPrefaceDedicationAcknowledgementsChapter1.CircuitAnalysisChapter2.BasicBuildingBlocksChapter3.DynamicRangeChapter4.ComponentTechnologyChapter5.PowerSuppliesChapter6.ThePowerAmplifierChapter7.ThePre-AmplifierAppendixIndex

Front-matterValveAmplifiersValveAmplifiersFourthEditionMorganJones

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PrefaceAlmost40yearsagotheauthorboughthisfirstvalveamplifier;itcosthim£3,and represented many weeks’ pocket money. Whilst his pocket money hasincreased,sohavehisaspirations,andtheDIYneedwasborn.Although there were many sources of information on circuit design, theelectronics works gave scant regard to audio design, whilst the Hi-Fi booksbarely scratched the surface of the theory. The author, therefore, spent muchtimeinlibrariestryingtolinkthisinformationtogethertoformabasisforaudiodesign. This book is the result of those years of effort and aims to presentthermionic theory in an accessible form without getting too bogged down inmaths. Primarily, it is a book for practical people armed with a calculator orcomputer,apowerdrillanda(temperature-controlled)solderingiron.TheauthorstartedaB.Sc.inAcousticalEngineering,butleftafterayeartojoinBBCEngineeringasaTechnicalAssistant,wherehereceivedexcellent tuitionin electronics and rose to thegiddyheights of aSeniorEngineer beforebeingmaderedundantbyBBCcuts.HehasalsoservedtimeinHigherEducation,andalthoughdevelopingtheUK’sfirstB.Sc.(Hons.)MediaTechnologycourseandwatching students blossom into graduates with successful careers wasimmensely satisfying, education is achieved by class contact – not bycommitteesandpaperchases.Early on, he became a member of the Audio Engineering Society, and hasdesigned and constructed many valve pre-amplifiers and power amplifiers,loudspeakers,pick-uparmsandapairofelectrostaticheadphones.Itisnow18yearssinceworkbeganonthe1steditionofValveAmplifiers,yetmuchhaschangedinthisobsoletetechnologysincethen.The relentless infestation of homes by computers has meant that test andmeasurement has become both cheaper and more easily integrated, eitherbecause it directly uses the processing power of a computer, or because itborrows from the technology needed to make them. Thus, the Fast FourierTransform has become a tool for all to use, from industrial designer to keenamateur – enabling spectrum analysis via a £100 sound card that was theprovinceofworldclasscompaniesonly20yearsago.Asahappyconsequence,this edition benefits from detailed measurements limited primarily by theauthor’s time. Computer modelling is now freely available – exemplified byDuncanMunro’sPSUD2linearpowersupplyfreeware.The spread of Internet trading has made the market for valves truly global.

ExoticasuchasLoctals,European‘SpecialQuality’valves,andfinalgenerationSovietblocvalvesarenowallreadilyavailableworldwidetoanyLudditewiththe patience to access the Internet – we no longer need to be constrained toconservative (but expensive) choices of traditional audio valves. Even better,many of the 1950s engineering books that you thought had gone forever areavailablefromthesecond-handbooksellersontheInternet.Paradoxically, although digital electronics has improved the supply of valves,otheranaloguecomponentsaredying.Capacitorsare theworstaffectedby thelack of raw materials; polycarbonate disappeared in 2001, and silvered-micacapacitors and polystyrene are both endangered species. Controls havesuccumbedtotheubiquitousdigitalencoder,somechanicalswitchrangeshavecontracted and potentiometers face a similar Darwinian fate. It is particularlygallingtodiscoverauseforZenersjustasmajorsemiconductormanufacturersstopmakingthem.Despite,orperhapsbecauseof, theseproblems,valvesandvinylhavebecomedesign icons,both in televisionadverts and thebits inbetween.The relentlesshype frommanufacturers of audio servers that favour convenienceover soundqualityhasforcedmanufacturersofCDplayerstojustifytheirproductsonsoundquality(andconvenience,becausealthoughnobodymentionsit,aCDplayerisunabletowipeyourentiremusiclibraryatthedropofanoperatingsystem).CDandvinylarenowtheonlyreliablesourcesofqualityaudio–whichisperhapsastepforwardfromthe1980swhenitwasFMradioandvinyl.NotefortheMP3generation:Thatshiny120 mmdiscwasinventedforstoringmusic (such as Beethoven’s 9th Symphony) at far higher quality than acompresseddownload.Tryitsometime–youmightevenlikeit.

DedicationThe author would like to dedicate this book to the dwindling band of BBCengineers, particularly at BBC Southampton, and also to those at BBCWoodNorton,ofwhichhehasmanycolourfulmemories.

AcknowledgementsSpecial thanks are due toEuanMcKenziewho undertook the onerous task ofproofreading at long distance on short notice and in record time to anappropriatelylowuncertainty.Thermionicdesigncannotproceedinavacuum,sotheauthorisgratefulfortheperceptive insightsand insults freelyofferedbyStuartYanigerover the recentyears.An annual celebration of awe and wonder has been the European TriodeFestival. This delightfully civilised bacchanalia has humbled the author withsplendidworks of art and engineeringwhilst at the same time reassuring himthathewasnotalone.Thankyou,Christian,forfirstinvitingme,andevenmorethankstosubsequentorganisersforsuccessfullymaintainingthemomentum.Finally, the author would like to thank those readers who took the time andtrouble to breach the publishing citadel and give the author hugely usefulfeedback.

Chapter1.CircuitAnalysisIn order to look at the interesting business of designing and building valveamplifiers,weneed someknowledgeof electronics funmentals.Unfortunately,fundamentalsarenotterriblyinteresting,andtocoverthemfullywouldconsumethe entire book. Ruthless pruning is, therefore, necessary to condensewhat isneededinonechapter.Itisthuswithdeepsorrowthattheauthorhashadtoforsakencomplexnumbersandvectors,whilsttheomissionofdifferentialcalculusisaparticularlypoignantloss.Allthatisleftisordinaryalgebra,andalthoughtherearelotsofequations,theyaretimid,miserablecreaturesandquitedefenceless.If you are comfortablewithbasic electronic terms and techniques, thenpleasefeelfreetogodirectlytoChapter2,wherevalvesappear.

MathematicalSymbolsUnavoidably,anumberofmathematicalsymbolsareused,someofwhichyoumayhaveforgotten,orperhapsnotpreviouslymet:

a≡baistotallyequivalenttob

a=baequalsb

a≈baisapproximatelyequaltob

a∝baisproportionaltob

a≠baisnotequaltob

a>baisgreaterthanb

a<baislessthanb

a≥baisgreaterthan,orequalto,b

a≤baislessthan,orequalto,bAs with the = and ≠ symbols, the four preceding symbols can have a slashthroughthemtonegatetheirmeaning(a ∋ b,aisnotlessthanb).

√athenumberwhichwhenmultipliedbyitselfisequaltoa(squareroot)

an

amultipliedbyitselfntimes.a4=a×a×a×a(atothepowern)

±

plusorminus

∞

infinity

°

degree,eitheroftemperature(°C),orofanangle(360°inacircle)

∣

parallel,eitherparallellines,oranelectricalparallelconnection

Δasmallchangeintheassociatedvalue,suchasΔVgk.

ElectronsandDefinitionsElectrons arecharged particles.Chargedobjects are attracted toother chargedparticlesorobjects.Apracticaldemonstrationofthisistotakeaballoon,rubitbrisklyagainstajumperandthenplacetherubbedfaceagainstawall.Letitgo.The balloon remains stuck to the wall. This is because we have charged theballoon,andsothereisanattractiveforcebetweenitandthewall.(Althoughthe

wallwasinitiallyuncharged,placingtheballoononthewallinducedacharge.)Charged objects come in two forms: negative and positive. Unlike chargesattract,andlikechargesrepel.Electronsarenegativeandpositronsarepositive,butwhilst electrons are stable inouruniverse, positrons encounter an electronalmostimmediatelyafterproduction,resultinginmutualannihilationandapairof511 keVgammarays.If we don’t have ready access to positrons, how can we have a positivelychargedobject?Supposewehadanobjectthatwasnegativelycharged,becauseithad2,000electronsclusteredonitssurface.Ifwehadanother,similar,objectthat only had 1,000 electrons on its surface, then we would say that the firstobjectwasmorenegativelychargedthanthesecond,butaswecan’tcounthowmanyelectronswehave,wemightjustaseasilyhavesaidthatthesecondobjectwasmorepositivelychargedthanthefirst. It’s justamatterofwhichwayyoulookatit.To charge our balloon, we had to do somework and use energy.We had toovercomefrictionwhenrubbingtheballoonagainst thewoollenjumper.Intheprocess, electrons were moved from one surface to the other. Therefore, oneobject (the balloon) has acquired an excess of electrons and is negativelycharged,whilst theotherobject (woollen jumper)has lost thesamenumberofelectronsandispositivelycharged.Theballoonwould,therefore,sticktothejumper.Orwouldit?Certainlyitwillbeattractedtothejumper,butwhathappenswhenweplacethetwoincontact?Theballoondoesnotstick.Thisisbecausethefibresofthejumperwereabletotouch thewholeof the chargedareaon theballoon, and the electronswere soattractedtothejumperthattheymovedbackontothejumper,thusneutralisingthecharge.At this point, we can discard vague talk of balloons and jumpers becausewehavejustobservedelectronflow.Anelectronisverysmall,anddoesn’thavemuchofacharge,soweneedamorepractical unit for defining charge.That practical unit is thecoulomb (C).Wecouldnowsay that1 Cofchargehad flowedbetweenonepoint andanother,which would be equivalent to saying that approximately6,240,000,000,000,000,000electronshadpassed,butmuchhandier.Simply being able to say that a large number of electrons had flowed past agivenpoint is not in itself veryhelpful.Wemight say that abillion carshavetravelled down a particular section ofmotorway since itwas built, but if youwereplanningajourneydownthatmotorway,youwouldwanttoknowtheflowofcarsperhourthroughthatsection.Similarly in electronics,we are not concernedwith the total flowof electrons

sincethedawnoftime,butwedowanttoknowaboutelectronflowatanygiveninstant.Thus,wecoulddefinetheflowasthenumberofcoulombsofchargethatflowedpastapointinonesecond.Thisisstillratherlong-winded,andwewillabbreviateyetfurther.We will call the flow of electrons current, and as the coulomb/second isunwieldy, it will be redefined as a new unit, the ampere ( A). Because theampereissuchausefulunit,thedefinitionlinkingcurrentandchargeisusuallystatedinthefollowingform.

One coulomb is the charge moved by one ampere flowing for onesecond.

Thisisstillratherunwieldy,sosymbolsareassignedtothevariousunits:chargehassymbolQ,currentIandtimet.

This is a very useful equation, and we will meet it again when we look atcapacitors(whichstorecharge).Meanwhile, currenthasbeen flowing,butwhydid it flow? Ifwearegoing tomove electrons from one place to another, we need a force to cause thismovement. This force is known as the electro motive force (EMF). Currentcontinuestoflowwhilstthisforceisapplied,anditflowsfromahigherpotentialtoalowerpotential.Iftwopointsareatthesamepotential,nocurrentcanflowbetweenthem.Whatisimportantisthepotentialdifference(pd).Apotentialdifferencecausesacurrenttoflowbetweentwopoints.Asthisisanew property, we need a unit, a symbol and a definition to describe it. Wementionedworkbeingdoneinchargingtheballoon,andinitsverypreciseandphysicalsense,thisishowwecandefinepotentialdifference,butfirst,wemustdefinework.

Onejouleofworkisdoneifaforceofonenewtonmovesonemetrefromitspointofapplication.

This very physical interpretation of work can be understood easily once werealise that it means that one joule of work would be done by moving onekilogramme a distance of one metre in one second. Since charge is directlyrelated to themassofelectronsmoved, thephysicaldefinitionofworkcanbemodifiedtodefinetheforcethatcausesthemovementofcharge.Unsurprisingly,becauseitcausesthemotionofelectrons,theforceiscalledtheElectro-MotiveForce,anditismeasuredinvolts.

If one joule of work is donemoving one coulomb of charge, then thesystemissaidtohaveapotentialdifferenceofonevolt(V).

The concept of work is important because work can be done only by theexpenditureofenergy,whichis,therefore,alsoexpressedinjoules.

Inourspecialisedsense,doingworkmeansmovingcharge(electrons)tomakecurrentsflow.

BatteriesandLamps

Ifwewanttomakeacurrentflow,weneedacircuit.Acircuitisexactlythatalooporpaththroughwhichacurrentcanflow,fromitsstartingpointallthewayroundthecircuit,toreturntoitsstartingpoint.Breakthecircuit,andthecurrentceasestoflow.The simplest circuit that we might imagine is a battery connected to anincandescent lamp via a switch.We open the switch to stop the current flow(opencircuit)andcloseittolightthelamp.Meanwhile,ourhelpfulfriend(whohasbeenwatchingall this) leansoveranddropsathickpieceofcopperacrossthebatteryterminals,causingashortcircuit.Thelampgoesout.Why?

Ohm’sLaw

To answer the last question, we need some property that defines how muchcurrent flows.Thatproperty isresistance, soweneedanotherdefinition,unitsandasymbol.

If a potential difference of one volt is applied across a resistance,resultinginacurrentofoneampere,thentheresistancehasavalueofoneohm(Ω).

This is actually a simplified statement of Ohm’s law, rather than a strictdefinitionofresistance,butwedon'tneedtoworrytoomuchaboutthat.WecanrearrangethepreviousequationtomakeIorRthesubject.

Theseareincrediblypowerfulequationsandshouldbecommittedtomemory.ThecircuitshowninFigure1.1isswitchedon,andacurrentof0.25 Aflows.Whatistheresistanceofthelamp?

Figure1.1UseofOhm’slawtodeterminetheresistanceofahotlamp.

Nowthismightseemlikeatrivialexample,sincewecouldeasilyhavemeasuredtheresistanceofthelampto3½significantfiguresusingourshiny,new,digitalmultimeter.But couldwe?Thehot resistanceof an incandescent lamp isverydifferentfromitscoldresistance;intheexampleabove,thecoldresistancewas80 Ω.We could now work the other way and ask how much current would flowthroughan80 Ωresistorconnectedto240 V.

Incidentally,thisiswhyincandescentlampsaremostlikelytofailatswitch-on.The high initial current that flows before the filament has warmed up andincreaseditsresistancestressestheweakestpartsofthefilament,theybecomesohotthattheyvaporise,andthelampblows.

Power

Inthepreviousexample,welookedatanincandescentlampandrateditbythecurrent that flowed through itwhenconnected to a240 Vbattery.Butweallknowthat lampsareratedinwatts,so theremustbesomeconnectionbetweenthetwo.

Onewatt(W)ofpowerisexpendedifonejouleofworkisdoneinonesecond.

Thismaynotseemtobethemostusefulofdefinitions,and,indeed,itisnot,butbycombiningitwithsomeearlierequations:

So:

But:

So:

Weobtain:

ThisisafundamentalequationofequalimportancetoOhm’slaw.SubstitutingtheOhm’slawequationsintothisyields:

Wecannowusetheseequationstocalculatethepowerratingofourlamp.Sinceitdrew0.25 Awhenfedfrom240 V,andhadahotresistanceof960 Ω,wecanuseanyofthethreeequations.Using:

Itwillprobablynothaveescapedyournotice that this lamplookssuspiciouslylikeanACmainslamp,andthatthebatterywasratherlarge.Wewillreturntothislater.

Kirchhoff’sLaws

There are two of these: a current law and a voltage law. They are both verysimpleand,atthesametime,verypowerful.Thecurrentlawstates:

The algebraic sum of the currents flowing into, and out of, a node isequaltozero.

Whatitsaysinamorerelaxedformisthatwhatgoesin,comesout.Ifwehave10 Agoingintoanode,orjunction,thenthatmuchcurrentmustalsoleavethatjunction – itmight not all comeout on onewire, but itmust all comeout.Aconservationofcurrent,ifyoulike(seeFigure1.2).

Figure1.2Currentsatanode(Kirchhoff’scurrentlaw).

Fromthepointofviewofthenode,thecurrentsleavingthenodeareflowingintheoppositedirectiontothecurrentflowingintothenode,sowemustgivethemaminussignbeforepluggingthemintotheequation.

Thismayhaveseemedpedantic,sinceitwasobviousfromthediagramthattheincoming currents equalled the outgoing currents, but youmay need to find acurrentwhenyoudonotevenknowthedirectioninwhichitisflowing.Usingthisconventionforcesthecorrectanswer!Itisvitaltomakesurethatyoursignsarecorrect.Thevoltagelawstates:

ThealgebraicsumoftheEMFsandpotentialdifferencesactingaroundanyloopisequaltozero.

This law draws a very definite distinction between EMFs and potentialdifferences. EMFs are the sources of electrical energy (such as batteries),whereas potential differences are the voltages dropped across components.AnotherwayofstatingthelawistosaythatthealgebraicsumoftheEMFsmustequalthealgebraicsumofthepotentialdropsaroundtheloop.Again,youcouldconsiderthistobeaconservationofvoltage(seeFigure1.3).

Figure1.3Summationofpotentialswithinaloop(Kirchhoff’svoltagelaw).

ResistorsinSeriesandParallel

Ifwehadanetworkofresistors,wemightwanttoknowwhatthetotalresistancewasbetweenterminalsAandB(seeFigure1.4).

Figure1.4Series/parallelresistornetwork.

We have three resistors:R1 is in parallel withR2, and this combination is inserieswithR3.Aswithallproblems,thethingtodoistobreakitdownintoitssimplestparts.Ifwehadsomemeansofdeterminingthevalueofresistorsinseries,wecoulduseittocalculatethevalueofR3inserieswiththecombinationofR1andR2,butaswedonotyetknowthevalueoftheparallelcombination,wemustfindthisfirst.Thisquestionoforderismostimportant,andwewillreturntoitlater.Ifthetworesistors(oranyothercomponent,forthatmatter)areinparallel,thentheymusthavethesamevoltagedropacrossthem.Ohm’slawmighttherefore,beausefulstartingpoint.

UsingKirchhoff’scurrentlaw,wecanstatethat:

So:

DividingbyV:

Thereciprocalofthetotalparallelresistanceisequaltothesumofthereciprocalsoftheindividualresistors.

Forthespecialcaseofonlytworesistors,wecanderivetheequation:

This is often known as ‘product over sum’, andwhilst it is useful formentalarithmetic,itisslowtouseonacalculator(morekeystrokes).Now that we have cracked the parallel problem, we need to crack the seriesproblem.First,wewillsimplify thecircuit.Wecannowcalculate the total resistanceofthe parallel combination and replace it with one resistor of that value – anequivalentresistor(seeFigure1.5).

Figure1.5SimplificationofFig.1.4usinganequivalentresistor.

Using the voltage law, the sum of the potentials across the resistors must beequaltothedrivingEMF:

UsingOhm’slaw:

Butifwearetryingtocreateanequivalentresistor,whosevalueisequaltothecombination,wecouldsay:

Hence:

The totalresistanceofacombinationofseriesresistors isequal to thesumoftheirindividualresistances.

Using the parallel and series equations,we are now able to calculate the totalresistanceofanynetwork(seeFigure1.6).

Figure1.6

Nowthismaylookhorrendous,butitisnotaproblemifweattackitlogically.Thehardest part of theproblem isnotwielding the equationsornumbers, butwheretostart.WewanttoknowtheresistancelookingintotheterminalsAandB,butwedonothaveanyrulesforfindingthisdirectly,sowemustlookforapointwherewecan apply our rules.We can apply only one rule at a time, so we look for acombinationofcomponentsmadeuponlyofseriesorparallelcomponents.Inthisexample,wefindthatbetweennodeAandnodeDthereareonlyparallelcomponents.Wecancalculatethevalueofanequivalentresistorandsubstitute

itbackintothecircuit:

Weredrawthecircuit(seeFigure1.7).

Figure1.7

Looking again,we find that now the only combinationsmade up of series orparallel components are betweennodeA andnodeC, butwehave a choice –eithertheseriescombinationofthe2 Ωand4 Ω,ortheparallelcombinationofthe3 Ωand6 Ω.Theonetogoforistheseriescombination.Thisisbecauseitwillresultinasingleresistorthatwillthenbeinparallelwiththe3 Ωand6 Ωresistors.Wecancopewiththethreeparallelresistorslater:

Weredrawthecircuit(seeFigure1.8).

Figure1.8

Wenowseethatwehavethreeresistorsinparallel:

Hence:

We have reduced the circuit to two 1.5 Ω resistors in series, and so the totalresistanceis3 Ω.This tooka little time,but it demonstrated someusefulpoints thatwill enableyoutoanalysenetworksmuchfasterthesecondtimearound:•Thecriticalstageischoosingthestartingpoint.•Thestartingpointisgenerallyasfarawayfromtheterminalsasitispossibletobe.• The starting point ismade up of a combination of only series or parallelcomponents.• Analysis tends to proceed outwards from the starting point towards theterminals.• Redrawing the circuit helps. You may even need to redraw the originalcircuit if it does not make sense to you. Redrawing as analysis progressesreducesconfusionanderrors–doit!

PotentialDividers

PotentialDividersFigure 1.9 shows a potential divider. This could be made up of two discreteresistors,oritcouldbethemovingwiperofavolumecontrol.Asbefore,wewillsuppose thatacurrent I flows through the tworesistors.Wewant toknow theratiooftheoutputvoltagetotheinputvoltage(seeFigure1.9).

Figure1.9Potentialdivider.

Hence:

This is a very important result and, used intelligently, can solve virtuallyanything.

EquivalentCircuits

Wehave lookedatnetworksof resistorsandcalculatedequivalentresistances.Now we will extend the idea to equivalent circuits. This is a tremendouslypowerfulconceptforcircuitanalysis.Itshouldbenotedthatthisisnottheonlymethod,butitisusuallythequickestandkills99%ofallknownproblems.Othermethods includeKirchhoff’s lawscombined with lots of simultaneous equations and the superposition theorem.

Thesemethodsmaybefoundinstandardtexts,buttheytendtobecumbersome,sowewillnotdiscussthemhere.

TheThéveninEquivalentCircuit

Whenwelookedat thepotentialdivider,wewereabletocalculatetheratioofoutputvoltagetoinputvoltage.Ifwewerenowtoconnectabatteryacrosstheinput terminals,we could calculate theoutput voltage.Usingour earlier tools,wecouldalsocalculatethetotalresistancelookingintotheoutputterminals.Asbefore,wecouldthenredrawthecircuit,andtheresultisknownastheThéveninequivalent circuit. If two black boxesweremade, one containing the originalcircuitand theother theThéveninequivalentcircuit,youwouldnotbeable totellfromtheoutputterminalswhichwaswhich.Theconceptissimpletouseandcanbreakdowncomplexnetworksquicklyandefficiently(seeFigure1.10).

Figure1.10A‘blackbox’networkanditsThéveninequivalentcircuit.

This is a simple example to demonstrate the concept. First, we find theequivalentresistance,oftenknownastheoutputresistance.Now,intheworldofequivalentcircuits,batteriesareperfectvoltagesources;theyhavezerointernalresistance and look like a short circuit when we consider their resistance.Therefore,wecanignorethebattery,orreplaceitwithapieceofwirewhilstwecalculatetheresistanceofthetotalcircuit:

Next, we need to find the output voltage. We will use the potential dividerequation:

So:

Now for a much more complex example. This will use all the previoustechniquesandreallydemonstratethepowerofThévenin(seeFigure1.11).

Figure1.11

For some obscure reason, we want to know the current flowing in the 1 Ωresistor.Thefirstthingtodoistoredrawthecircuit.Beforewedothiswecanobservethatthe5 Ωresistorinparallelwiththe12 Vbatteryisirrelevant.Yes,itwilldrawcurrentfromthebattery,but itdoesnotaffect theoperationof therestofthecircuit.Ashortcircuitinparallelwith5 Ωisstillashortcircuit,sowewillthrowitaway(seeFigure1.12).

Figure1.12

Despite our best efforts, this is still a complex circuit, sowe need to break itdown intomodules thatwerecognise.Lookingat the left-handside,wefindabatterywith a4Ωand12Ω resistorwhich looks suspiciously like the simpleproblem that we saw earlier, so let us break the circuit there and make anequivalentcircuit(seeFigure1.13).

Figure1.13

Usingthepotentialdividerrule:

Using‘productoversum’:

Lookingattheright-handside,wecanperformasimilaroperationtotherightofthedashedline.First,wefindtheresistanceoftheparallelcombinationofthe36 Ωand12 Ωresistors, which is 9 Ω. We now have a potential divider, whose outputresistanceis6 ΩandtheThéveninvoltageis2 V.Nowweredrawthecircuit(seeFigure1.14).

Figure1.14

Wecanmakeafewobservationsat thispoint.First,wehavethreebatteries inseries, why not combine them into one battery? There is no reason why weshouldnotdo thisprovided thatwe takenoteof theirpolarities.Similarly,wecancombinesome,orall,oftheresistors(seeFigure1.15).

Figure1.15

Theproblemnowistrivial,andasimpleapplicationofOhm’slawwillsolveit.Wehaveatotalresistanceof10 Ωanda5 Vbattery,sothecurrentmustbe0.5A.Usefulpointstonote:• Look for components that are irrelevant, such as resistors directly acrossbatteryterminals.•Lookforpotentialdividersontheoutputsofbatteriesand‘Thévenise’them.Keepondoingsountilyoumeetthenextbattery.•Workfrombatteryterminalsoutwards.•Keepcalm,andtrytoworkneatly–itwillsavemistakeslater.

Although it is possible to solve most problems using a Thévenin equivalentcircuit,sometimesaNortonequivalentismoreconvenient.

TheNortonEquivalentCircuit

The Thévenin equivalent circuitwas a perfect voltage source in series with aresistance,whereas theNorton equivalent circuit is aperfectcurrent source inparallelwitharesistance(seeFigure1.16).

Figure1.16TheNortonequivalentcircuit.

WecaneasilyconvertfromaNortonsourcetoaThéveninsource,orviceversa,becausetheresistorhasthesamevalueinbothcases.Wefindthevalueofthecurrent source by short circuiting the output of the Thévenin source andcalculatingtheresultingcurrent–thisistheNortoncurrent.ToconvertfromaNortonsourcetoaThéveninsource,weleavethesourceopencircuitandcalculatethevoltagedevelopedacrosstheNortonresistor–thisistheThéveninvoltage.For the vast majority of problems, the Thévenin equivalent will be quicker,mostlybecausewebecomeusedtothinkingintermsofvoltagesthatcaneasilybemeasuredbyameterorviewedonanoscilloscope.Occasionally,aproblemwill arise that is intractable using Thévenin, and converting to a Nortonequivalentcauses theproblem to solve itself.Nortonproblemsusually involvethesummationofanumberofcurrents,whentheonlyothersolutionwouldbetoresorttoKirchhoffandsimultaneousequations.

UnitsandMultipliers

Allthecalculationsuptothispointhavebeenarrangedtouseconvenientvaluesofvoltage,currentandresistance.Intherealworld,wewillnotbesofortunate,andtoavoidhavingtousescientificnotation,whichtakeslongertowriteandisvirtuallyunpronounceable,wewillprefixourunitswithmultipliers[1].

Prefix Abbreviation Multipliesby

yocto y 10−24

zepto z 10−21

atto a 10−18

femto f 10−15

pico p 10−12

nano n 10−9

micro μ 10−6

milli m 10−3

kilo k 103

mega M 106

giga G 109

tera T 1012

peta P 1015

exa E 1018

zetta Z 1021

yotta Y 1024

Notethatthecaseoftheprefixisimportant;thereisalargedifferencebetween1mΩ and 1 MΩ. Electronics uses a very wide range of values; small-signalpentodeshaveanode togridcapacitancesmeasured in fF (F=farad, theunitofcapacitance),andpetabytedatastoresarealreadycommon.Despitethis,forday-to-dayelectronicsuse,weonlyneedtousepicotomega.Electronicsengineerscommonlyabbreviatefurther,andyouwilloftenheara22pF(picofarad)capacitorreferredtoas22‘puff’,whilstthe‘ohm’iscommonlydropped for resistors, and 470 kΩ (kiloohm) would be pronounced as ‘four-seventy-kay’.A rathermore awkward abbreviation that arose before high-resolution printersbecame common (early printers could not print ‘μ’), is the abbreviation of μ(micro)tom.Thisabbreviationpersists,particularlyintheUStext,andyouwilloccasionally see a 10 mF capacitor specified, although the context makes itclear that what is actually meant is 10 μF. For this reason, true 10 mFcapacitorsareinvariablyspecifiedas10,000 μF.Unlessanequationstatesotherwise,assumethatitusesthebasephysicalunits,so an equation involving capacitance and time constantswould expect you toexpresscapacitanceinfaradsandtimeinseconds.Thus,75 μs=75×10−6 s,andthevalueofcapacitancedeterminedbyanequationmightbe2.2×10−10 F=220pF.Veryoccasionally,itishandiertoexpressanequationusingreal-worldunitssuch asmAorMΩ, inwhich case the equation or its accompanying textwillalwaysexplainthisbreakfromconvention.

TheDecibel

The human ear spans a vast dynamic range from the near silence heard in anemptyrecordingstudiotothedeafeningnoiseofanearbypneumaticdrill.Ifweweretoplot thisrangelinearlyonagraph, thequietersoundswouldhardlybeseen, whereas the difference between the noise of the drill and that of a jetenginewouldbegivenadisproportionateamountof roomon thegraph.Whatweneedisagraphthatgivesanequalweightingtorelativechangesinthelevelofbothquietandloudsounds.Bydefinition,thisimpliesalogarithmicscaleon

thegraph,butelectronicsengineerswentonebetterandinventedalogarithmicratio known as thedecibel (dB) thatwas promptly hijackedby the acousticalengineers. (Thefundamentalunit is thebel,but this is inconveniently large,sothedecibelismorecommonlyused.)ThedBisnotanabsolutequantity.It isaratio,andithasoneformulaforusewithcurrentsandvoltagesandanotherforpowers:

The reason for this is thatP∝V2 or I2, and with logarithms, multiplying thelogarithmby 2 is the same as squaring the original number.Using a differentformula tocalculatedBswhenusingpowersensures that the resultingdBsareequivalent,irrespectiveofwhethertheywerederivedfrompowersorvoltages.This might seem complicated when all we wanted to do was to describe thedifferenceintwosignallevels,butthedBisaveryhandyunit.UsefulcommondBvaluesare:

dB V1/V2 P1/P20 1 13 √2 26 2 420 10 100

BecausedBsarederivedfromlogarithms,theyobeyalltherulesoflogarithms,andaddingdBsisthesameasmultiplyingtheratiosthatgeneratedthem.NotethatdBscanbenegative,implyinglossoradropinlevel.Forexample,ifwehadtwocascadedamplifiers,onewithavoltagegainof0.5andtheotherwithavoltagegainof10,thenbymultiplyingtheindividualgains,thecombinedvoltagegainwouldbe5.Alternatively,wecouldfindthegainindBbysayingthatoneamplifierhad−6 dBofgainwhilsttheotherhad20 dB,andaddingthegainsindBtogiveatotalgainof14 dB.Whendesigningamplifiers,wewillnotoftenusetheaboveexample,asabsolutevoltagesareoftenmoreconvenient,butwefrequentlyneeddBstodescribefilterandequalisationcurves.

AlternatingCurrent(AC)Alltheprevioustechniqueshaveuseddirectcurrent(DC),wherethecurrentisconstantandflowsinonedirectiononly.ListeningtoDCisnotveryinteresting,sowenowneedtolookatalternatingcurrents(AC).AlloftheprevioustechniquesofcircuitanalysiscanbeappliedequallywelltoACsignals.

TheSineWave

TheSineWave

Thesinewaveisthesimplestpossiblealternatingsignal,anditsequationis:

wherev=theinstantaneousvalueattimetVpeak=thepeakvalue

ω=angularfrequencyinradians/second(ω=2πf)t=thetimeinsecondsθ=aconstantphaseangle.

Thesemathematicalconceptsareshownonthediagram(seeFigure1.17).

Figure1.17

Equations involving changing quantities use a convention. Upper case lettersdenote DC, or constant values, whereas lower case letters denote theinstantaneousAC,orchanging,value.ItisaformofshorthandtoavoidhavingtospecifyseparatelythataquantityisACorDC.Itwouldbenicetosaythatthisconvention is rigidly applied, but it is often neglected, and the context of thesymbolsusuallymakesitclearwhetherthequantityisACorDC.Inelectronics,theword‘peak’(pk)hasaveryprecisemeaningand,whenusedtodescribeanACwaveform, itmeans thevoltage fromzerovolts to thepeakvoltage reached, either positive or negative. Peak to peak (pk–pk) means thevoltage frompositivepeak tonegativepeak,and fora symmetricalwaveform,Vpk–pk=2 Vpk.Althoughelectronicsengineershabituallyuseω todescribefrequency, theydosoonlybecause calculus requires that theywork in radians.Sinceω=2πf,we

canrewritetheequationas:

Ifwenow inspect this equation,we see that apart from time t,we couldvaryotherconstantsbeforeweallowtimetochangeanddeterminethewaveform.WecanchangeVpeak,andthiswillchangetheamplitudeofthesinewave,orwecanchangef,andthiswillchangethefrequency.Theinverseoffrequencyisperiod,whichisthetimetakenforonefullcycleofthewaveformtooccur:

Ifwe listen toasound that isasinewave,andchange theamplitude, thiswillmakethesoundlouderorsofter,whereasvaryingfrequencychangesthepitch.Ifwevaryθ(phase),itwillsoundthesameifwearelisteningtoit,andunlesswehaveanexternalreference,thesinewavewilllookexactlythesameviewedonanoscilloscope.Phase becomes significant ifwe compare one sinewavewithanother sine wave of the same frequency or a harmonic of that frequency.Attempting to compare phase between waveforms of unrelated frequencies ismeaningless.Now that we have described sinewaves, we can look at them as theywouldappearonthescreenofanoscilloscope.SeeFigure1.18.

Figure1.18

SinewavesAandBareidenticalinamplitude,frequencyandphase.SinewaveChasloweramplitude,butfrequencyandphasearethesame.SinewaveDhasthe same amplitude, but double the frequency. Sine wave E has identicalamplitudeandfrequencytoAandB,butthephaseθhasbeenchanged.SinewaveFhashaditspolarityinverted.Although,forasinewave,wecannotsee the difference between a 180° phase change and a polarity inversion, forasymmetricwaveforms there is a distinct difference.We should, therefore, beverycarefulifwesaythattwowaveformsare180°outofphasewitheachotherthatwedonotactuallymeanthatoneisinvertedwithrespecttotheother.ThesawtoothwaveformGhasbeeninvertedtoproducethewaveformH,anditcanbeseenthatthisiscompletelydifferentfroma180°phasechange.(Strictly,the UK term ‘phase splitter’ is entirely incorrect for this reason, and the USdescription ‘phase inverter’ is much better, but falls short of the technicallycorrectdescription‘polarityinverter’usedbynobody.)

TheTransformer

Whentheelectriclightwasintroducedasanalternativetothegasmantle,therewasagreatdebateas towhether thedistributionsystemshouldbeACorDC.Theoutcomewassettledbytheenormousadvantageofthetransformer,whichcouldstepup,orstepdown,thevoltageofanACsupply.TheDCsupplycouldnotbemanipulatedinthisway,andevolutiontookitscourse.A transformer is essentially a pair of electrically insulated windings that aremagneticallycoupledtoeachother,usuallyonanironcore.Theyvaryfromthesize of a fingernail to that of a large house, depending on power rating andoperating frequency, with high frequency transformers being smaller. Thesymbolforatransformerismodifieddependingonthecorematerial.Solidlinesindicatealaminatedironcoreanddottedlinesdenoteadustcore,whilstanaircorehasnolines(seeFigure1.19).

Figure1.19Transformersymbols.

The perfect transformer changes oneAC voltage to another,more convenientvoltagewithnolosseswhatsoever;allofthepowerattheinputistransferredto

theoutput:

Havingmadethisstatement,wecannowderivesomeusefulequations:

Rearranging:

The new constantn is very important and is the ratio between the number ofturnsontheinputwindingandthenumberofturnsontheoutputwindingofthetransformer.Habitually,whenwe talkabout transformers, the inputwinding isknownastheprimaryandtheoutputwindingisthesecondary.

Occasionally, an audio transformer may have a winding known as a tertiarywinding,whichusuallyreferstoawindingusedforfeedbackormonitoring,butitismoreusualtorefertomultipleprimariesandsecondaries.Whentheperfecttransformerstepsvoltagedown,perhapsfrom240 Vto12 V,thecurrentratioissteppedup,andeachampereofprimarycurrentisdueto20Adrawnfromthesecondary.Thisimpliesthattheresistanceoftheloadonthesecondary isdifferent fromthatseen looking into theprimary. IfwesubstituteOhm’slawintotheconservationofpowerequation:

The transformerchanges resistancesby thesquareof the turns ratio.Thiswillbecome very significant when we use audio transformers that must matchloudspeakerstooutputvalves.Asanexample,anoutputtransformerwithaprimarytosecondaryturnsratioof31.6:1would allow theoutputvalves to see the8 Ω loudspeaker as an8 kΩload,whereastheloudspeakerseestheThéveninoutputresistanceoftheoutputvalvessteppeddownbyanidenticalamount.The concept of looking into a device in one direction, and seeing one thing,whilst looking in the opposite direction, and seeing another, is very powerful,andwewilluseitfrequentlywhenweinvestigatesimpleamplifierstages.

Practicaltransformersarenotperfect,andwewillinvestigatetheirimperfectionsingreaterdetailinChapter4.

Capacitors,InductorsandReactance

Previously,whenweanalysedcircuits, theywerecomposedpurelyof resistorsandvoltageorcurrentsources.We now need to introduce two new components: capacitors and inductors.CapacitorshavethesymbolC,andtheunitofcapacitanceisthefarad(F).1 Fisanextremelylargecapacitance,andmorecommonvaluesrangefromafewpFto tens of thousands of μF. Inductors have the symbol L, and the unit ofinductanceisthehenry(H).Thehenryisquitealargeunit,andcommonvaluesrangefromafewμHtotensofH.Althoughthehenry,andparticularlythefarad,isratherlargeforourveryspecialiseduse,itssizederivesfromthefundamentalrequirementforacoherentsystemofunits;acoherentsystemallowsunits(suchasthefarad)tobederivedfrombaseunits(suchastheampere)withanabsoluteminimumofscalingfactors.Thesimplestcapacitorismadeofapairofseparatedplates,whereasaninductoris a coil of wire, and this physical construction is reflected in their graphicalsymbols(seeFigure1.20).

Figure1.20Inductorandcapacitorsymbols.

Resistors had resistance, whereas capacitors and inductors have reactance.ReactanceistheACequivalentofresistance–itisstillmeasuredinohmsandisgiventhesymbolX.Wewilloftenhavecircuitswherethereisacombinationofinductors and capacitors, so it is normal to add a subscript to denote whichreactanceiswhich:

Lookingat theseequations,wefindthatreactancechangeswithfrequencyand

withthevalueofthecomponent.Wecanplottheserelationshipsonagraph(seeFigure1.21).

Figure1.21Reactanceofinductorandcapacitoragainstfrequency.

Aninductorhasa reactanceofzeroatzero frequency.More intuitively, it isashortcircuitatDC.Asweincreasefrequency,itsreactancerises.Acapacitorhasinfinitereactanceatzerofrequency.ItisopencircuitatDC.Asfrequencyrises,reactancefalls.Acircuitmadeupofonlyonecapacitor,oroneinductor,isnotveryinteresting,andwemightwanttodescribethebehaviourofacircuitmadeupofresistanceandreactance,suchasamovingcoilloudspeaker.SeeFigure1.22.

Figure1.22

We have a combination of resistance and inductive reactance, but at theterminalsAandBweseeneitherapurereactance,norapureresistance,butacombinationofthetwofactorsknownasimpedance.Inatraditionalelectronicsbook,wewouldnowlurchintotheworldofvectors,phasorsandcomplexnumberalgebra.WhilstfundamentalACtheoryisessentialforelectronicsengineerswhohave topassexaminations,wecannot justify the

mental trauma needed to cover the topic in depth, sowewill simply pick outusefulresultsthatarerelevanttoourhighlyspecialisedfieldofinterest.

Filters

Wementionedthatreactancevarieswithfrequency.Thispropertycanbeusedtomakeafilter thatallowssomefrequenciestopassunchecked,whilstothersareattenuated(seeFigure1.23).

Figure1.23CRhigh-passfilter.

All filters are based on potential dividers. In this filter, the upper leg of thepotential divider is a capacitor,whereas the lower leg is a resistor.We statedearlierthatacapacitorisanopencircuitatDC.Thisfilter,therefore,hasinfiniteattenuationatDC–itblocksDC.Atinfinitefrequency,thecapacitorisashortcircuit,andthefilterpassesthesignalwithnoattenuation,sothefilterisknownasahigh-passfilter(seeFigure1.24).

Figure1.24FrequencyandphaseresponseoftheCRhigh-passfilter.

Frequency is plotted on a logarithmic scale to encompass the wide range ofvalues without cramping. When we needed a logarithmic unit for amplituderatios,weinventedthedB,butalogarithmicunitforfrequencyalreadyexisted,soengineersstoletheoctavefromthemusicians.Anoctaveissimplyahalvingor doubling of frequency and corresponds to eight ‘white keys’ on a pianokeyboard.Thecurvehasthreedistinctregions:thestop-band,cut-offandthepass-band.Thestop-bandistheregionwheresignalsarestoppedorattenuated.Inthisfilter,theattenuation is inverselyproportional to frequency,andwecansee thatatasufficientlylowfrequency(LF),theshapeofthecurveinthisregionbecomesastraightline.Ifweweretomeasuretheslopeofthisline,wewouldfindthatittendstowards6 dB/octave.Note that the phase of the output signal changes with frequency, with amaximumchangeof90°whenthecurvefinallyreaches6 dB/octave.Thisslopeisverysignificant,andallfilterswithonlyonereactiveelementhavean ultimate slope of 6 dB/octave.Aswe addmore reactive elements,we canachieveahigherslope,sofiltersareoftenreferredtobytheirorder,whichisthenumberofreactiveelementscontributingtotheslope.Athird-orderfilterwouldhave three reactive elements, and its ultimate slope would, therefore, be 18dB/octave.Although the curve reaches an ultimate slope, the behaviour at cut-off is ofinterest,notleastbecauseitallowsustosayatwhatfrequencythefilterbeginstotakeeffect.Onthediagram,alinewasdrawntodeterminetheultimateslope.Ifthisisextendeduntilitintersectswithasimilarlinedrawncontinuedfromthe

pass-band attenuation, the point of intersection is the filter cut-off frequency.(Youwilloccasionallyseeidealisedfilterresponsesdrawninthisway,butthisdoesnotimplythatthefilterresponseactuallychangesabruptlyfrompass-bandtostop-band.)Ifwenowdropalinedowntothefrequencyaxisfromthecut-offpoint,itpassesthroughthecurve,andthefilterresponseatthispointis3 dBdownonthepass-bandvalue.Thecut-offfrequencyis,therefore,alsoknownasf−3 dB,orthe−3dBpoint,andatthispointthephasecurveisatitssteepest,withaphasechangeof45°.Second-orderfilters,andabove,haveconsiderablefreedomin thewaythat thetransitionfrompass-bandtostop-bandismade,andsotheclassoffilterisoftenmentionedinconjunctionwithnameslikeBessel,ButterworthandChebychev,inhonouroftheiroriginators.Althoughweinitiallyinvestigatedahigh-passCapacitor-Resistance(CR)filter,other combinations can bemade using one reactive component and a resistor(seeFigure1.25).

Figure1.25

Wenowhaveapairofhigh-passfiltersandapairof low-passfilters;thelow-pass filters have the same slope, and cut-off frequency can be found from the

graphinthesameway.Now thatwe are familiarwith the shape of the curves of these simple filters,referring to themby their cut-off frequency and slope ismore convenient (theword ‘ultimate’ is commonly neglected). For these simple filters, the equationforcut-offfrequencyisthesamewhetherthefilterishigh-passorlow-pass.ForaCRfilter:

AndforanLRfilter:

TimeConstants

Inaudio,simplefiltersorequalisationnetworksareoftendescribedintermsoftheir timeconstants.Thesehaveaveryspecialisedmeaning thatwewill touchupon later, but in this context they are simply used as a shorthand form ofdescribing a first-order filter that allows component values to be calculatedquickly.ForaCRnetwork,thetimeconstantτ(tau)is:

ForanLRnetwork:

Because it isa timeconstant, theunitofτ isseconds,butaudio timeconstantsarehabituallygiveninμs.Wecaneasilycalculate thecut-offfrequencyof thefilterfromitstimeconstantτ:

Notethatτisquitedistinctfromperiod,whichisgiventhesymbolT.Examplesofaudiotimeconstants:•FManaloguebroadcastHighFrequencyde-emphasis:UK50 μsandUSA75 μs•RIAAvinylrecordcharacteristic:3,180 μs,318 μsand75 μs.

A 75 μsHigh Frequency de-emphasis circuit needs a low-pass filter, usuallyCR, soapairofcomponentvalueswhoseproductequals75 μs,1 nFand75kΩwoulddonicely(seeFigure1.26).

Figure1.26A75 μsde-emphasisnetwork.

Resonance

Sofar,wehavemadefiltersusingonlyonereactivecomponent,butifwemakeanetworkusing a capacitorand an inductor,we find thatwehave a resonantcircuit.Resonanceoccurseverywhereinthenaturalworld,fromthesoundofatuningforktothebuckingandtwistingoftheTacomaNarrowsbridge.(Abridgethat finally collapsed during a storm on 7 November 1940 because the windexcitedastructuralresonance.)AresonantelectroniccircuitisshowninFigure1.27.

Figure1.27Seriesresonantcircuit.

Ifwewere to sweep the frequencyof thesource,whilstmeasuring thecurrentdrawn,wewouldfindthatattheresonantfrequency,thecurrentwouldrisetoamaximumdeterminedpurelybytheresistanceoftheresistor.Thecircuitwouldappearasifthereactivecomponentswerenotthere.Wecouldthenplotagraph

ofcurrentagainstfrequency(seeFigure1.28).

Figure1.28Currentagainstfrequencyforseriesresonantcircuit.

The sharpness and the height of this peak are determined by the Q ormagnificationfactorofthecircuit:

ThisshowsusthatasmallresistancecancauseahighQ,andthiswillbeverysignificantlater.Thefrequencyofresonanceis:

Our first resonant circuitwas a series resonant circuit, butparallel resonance,where the total current falls to aminimum at resonance, is also possible (seeFigure1.29).

Figure1.29Parallelresonantcircuit.

IfQ>5,theaboveequationsarereasonablyaccurateforparallelresonance.Wewill not fret about the accuracy of resonant calculations, sincewe rarelywantresonancesinaudio,andsodoourbesttoremoveordampthem.

RMSandPower

Wementionedpowerearlier,whenweinvestigatedtheflowofcurrentthroughalamp using a 240 V battery. Mains electricity is AC and has recently beenrespecified in theUKtobe230 VAC+10%−6%at50±1 Hz,buthowdowedefinethat230 V?Ifwe had a valve heater filament, itwould bemost useful if it could operateequallywell fromACorDC.As far as thevalve is concerned,ACelectricitywillheatthefilamentequallywell,justsolongasweapplythecorrectvoltage.

The RMS voltage of any waveform is equivalent to the DC voltagehavingthesameheatingeffectastheoriginalwaveform.

RMSisshortforRootoftheMeanoftheSquares,whichreferstothemethodofcalculating the value. Fortunately, the ratios of VRMS to Vpeak have beencalculated for the common waveforms, and in audio design we are mostlyconcernedwiththesinewave,forwhich:

All sinusoidalACvoltages aregiven inVRMS unless specifiedotherwise, so aheaterdesignedtooperateon6.3 VACwouldworkequallywellconnected to6.3 VDC.We have only mentioned RMS voltages, but we can equally well have RMScurrents,inwhichcase:

ThereisnosuchthingasanRMSwatt!PleaserefertothedefinitionofRMS.

TheSquareWave

Untilnow,allofourdealingshavebeenwithsinewaves,whicharepuretones.When we listen to music, we do not hear pure tones, instead we hear afundamental with various proportions of harmonics whose frequencies are

arithmetically related to the frequency of the fundamental. We are able todistinguish between one instrument and another because of the differingproportionsoftheharmonicsandthetransientatthebeginningofeachnote.Ausefulwaveform for testingamplifiersquicklywouldhavemanyharmonicsand a transient component. The square wave has precisely these propertiesbecause it iscomposedofa fundamental frequencyplusoddharmonicswhoseamplitudessteadilydecreasewithfrequency(seeFigure1.30).

Figure1.30Squarewaveviewedintimeandfrequency.

A square wave is thus an infinite series of harmonics, all of which must besummed from the fundamental to the infinite harmonic. We can express thisargument mathematically as a Fourier series, where f is the fundamentalfrequency:

This isashorthandformula,butunderstanding thedistributionofharmonics ismucheasierifweexpresstheminthefollowingform:

Wecannowsee that theharmonicsdieawayverygraduallyandthata1 kHzsquare wave has significant harmonics well beyond 20 kHz. What is notexplicitlystatedbytheseformulaeisthattherelativephaseofthesecomponentsis critical. The square wave thus tests not only amplitude response, but alsophaseresponse.

SquareWavesandTransients

We briefly mentioned earlier that the square wave contained a transientcomponent.OnewayofviewingasquarewaveistotreatitasaDClevelwhosepolarity is invertedat regular intervals.At the instantof inversion, thevoltage

hastochangeinstantaneouslyfromitsnegativeleveltoitspositivelevel,orviceversa.Theabruptchangeattheleadingedgeofthesquarewaveisthetransient,and because it occurs so quickly, it must contain a high proportion of highfrequency components. Although we already knew that the square wavecontainedthesehighfrequencies,itisonlyattheleadingedgethattheyallsumconstructively,soanychangeinhighfrequencyresponseisseenatthisleadingedge.We have considered the square wave in terms of frequency; now we willconsider it as a series of transients in time, and investigate its effect on thebehaviourofCRandLRnetworks.Thebestwayofunderstandingthistopiciswithamixtureofintuitivereasoningcoupledtoafewgraphs.Equationsareavailable,butweveryrarelyneedtousethem.Inelectronics,astepisaninstantaneouschangeinaquantitysuchascurrentorvoltage, so it isaveryuseful theoreticalconcept forexploring the responseofcircuits to transients.Wewillstartby lookingat thevoltageacrossacapacitorwhenavoltagestepisappliedviaaseriesresistor(seeFigure1.31).

Figure1.31

Thecapacitor is initiallydischarged (VC=0).The step is applied and switchesfrom0 Vto+V,aninstantaneouschangeofvoltagecomposedmostlyofhighfrequencies. The capacitor has a reactance that is inversely proportional tofrequencyand,therefore,appearsasashortcircuittothesehighfrequencies.Ifitisashortcircuit,wecannotdevelopavoltageacrossit.Theresistor,therefore,hasthefullappliedvoltageacrossitandpassesacurrentdeterminedbyOhm’slaw.Thiscurrentthenflowsthroughthecapacitorandstartschargingit.Asthecapacitor charges, its voltage rises, until eventually it is fully charged, and nomore current flows. If nomore current flows into the capacitor ( IC=0), thenIR=0, and so VR=0. We can plot this argument as a pair of graphs showing

capacitorandresistorvoltage(seeFigure1.32).

Figure1.32ExponentialresponseofCRcircuittovoltagestep.

Thefirstpointtonoteaboutthesetwographsisthattheshapeofthecurveisanexponential (this termwillbeexplainedfurther later).Thesecondpoint is thatwhenwe apply a step to aCR circuit (and even anLR circuit), the current orvoltage curvewillalways beoneof these curves.Knowing that the curve canonlybeoneofthesetwopossibilities,allweneedtobeabletodoistochoosetheappropriatecurve.ThetransientedgecanbeconsideredtobeofinfinitelyHighFrequency,andthecapacitoris,therefore,ashortcircuit.Developingavoltageacrossashortcircuitrequiresinfinitecurrent.

Infinitecurrentisrequiredtoinstantaneouslychangethevoltageacrossacapacitor.

Aninductoristhedualorinverseofacapacitor,andsoaninductorhasasimilarrule.

An instantaneous change of current through an inductor creates aninfinitevoltage.

We can now draw graphs for each of the four combinations of CR and LRcircuitswhenthesamestepinvoltageisapplied(seeFigure1.33).

Figure1.33

Havingstatedthattheshapeofthecurvesineachofthefourcasesisidentical,wecannowexaminethefundamentalcurvesinalittlemoredetail.UsingtheoriginalCRcircuitasanexample,thecapacitorwilleventuallychargetotheinputvoltage,sowecandrawadashedlinetorepresentthisvoltage.Thevoltage across the capacitor has an initial slope, and ifwe continue this slopewithanotherdashedline,wewillfindthatitintersectsthefirstlineatatimethatcorrespondstoCR,whichisthetimeconstantthatwemetearlier.TheCRtimeconstant isdefinedas the timetakenfor thecapacitorvoltagetoreachitsfinalvaluehadtheinitialrateofchargebeenmaintained(seeFigure1.34).

Figure1.34τanditssignificancetotheexponentialcurve.

Theequationforthefallingcurveis:

Theequationfortherisingcurveis:

where‘e’isthebaseofnaturallogarithmsandisthekeymarked‘ex’or‘exp’onyourscientificcalculator.Thesecurvesderive theirnamesbecause theyarebasedonanexponentialfunction.We could now find what voltage the capacitor actually achieved at varioustimes.Usingtheequationfortherisingcurve:1τ 63%3τ 95%5τ 99%

Becausethecurvesareallthesameshape,theseratiosapplytoallfouroftheCRandLRcombinations.Thebestwaytousetheratiosistofirstdecidewhichwaythecurveisheading;theratiosthendeterminehowmuchofthechangewillbeachieved,andinwhattime.Notethatafter5τ,thecircuithasverynearlyreacheditsfinalpositionorsteadystate.Thisisausefulpointtorememberwhenconsideringwhatwillhappenatswitch-ontohighvoltagesemiconductorcircuits.When we considered the response to a single step, the circuit eventuallyachieved a steady state because there was sufficient time for the capacitor tochargeorfortheinductortochangeitsmagneticfield.Withasquarewave,thismaynolongerbetrue.Aswasmentionedbefore,thesquarewaveisanexcellentwaveform for testing audio amplifiers, not least because oscillators that cangeneratebothsineandsquarewavesarefairlycheaplyavailable.Ifweapplyasquarewavetoanamplifier,weareeffectivelytestingaCRcircuitmadeupof a series resistance and a capacitance to ground (often known as ashunt capacitance).We should, therefore, expect to see some rounding of theleadingedges,becausesomeofthehighfrequenciesarebeingattenuated.If the amplifier is only marginally stable (because it contains an unwantedresonant circuit), thehigh frequencies at the leadingedgesof the squarewavewill excite the resonance, and we may see a damped train of oscillationsfollowingeachtransition.We can also test low frequency responsewith a squarewave. If the couplingcapacitors between stages are small enough to change their charge noticeablywithinonehalf-cycleofthesquarewave,thenwewillseetiltonthetopofthe

square wave. Downward tilt, more commonly called sag, indicates lowfrequencyloss,whilstupwardtilt indicateslowfrequencyboost.Thisisaverysensitivetestoflowfrequencyresponse,andifitisknownthatthecircuitbeingmeasuredincludesasinglehigh-passfilter,butwithacut-offfrequencytoolowto bemeasured directlywith sinewaves, then a squarewavemay be used toinferthesinewavef−3 dBpoint.Thefullderivationoftheequationthatproducedthefollowingtable isgivenintheAppendix,but ifweapplyasquarewaveoffrequencyf(Table1.1).

Table1.1RelatingSquareWaveSagtoLowFrequencyCut-OffFrequencySagobservedusingasquarewaveoffrequencyf

(%)Ratioofappliedsquarewavefrequency(f)tolowfrequencycut-off(f−3

dB)

10 305 601 300

Mostanalogueaudiooscillators arebasedon theWienbridgeand,becauseofamplitudestabilisationproblems,rarelyproducefrequencieslowerthan≈10 Hz.10% and 5% square wave sag may be measured relatively easily on anoscilloscope and can, therefore, be used to infer sine wave performance atfrequenciesbelow10 Hz.Anotherusefultestistoapplyahigh-level,HighFrequencysinewave.Ifatalllevelsandfrequencies,theoutputisstillasinewave,thentheamplifierislikelyto be free of slewing distortion. If the output begins to look like a triangularwaveform, this is because one, or more, of the stages within the amplifier isunabletofullychargeoranddischargeashuntcapacitancesufficientlyquickly.Thedistortionisknownasslewingdistortionbecausethewaveformisunabletoslewcorrectly fromonevoltage toanother.The solution isusually to increasethe anode current of the offending stage, thereby enabling it to charge ordischargethecapacitance.

RandomNoise

Thesignalsthatwehavepreviouslyconsideredhavebeenrepetitivesignals–wecould always predict precisely what the voltage level would be at any giventime.Besidesthesecoherentsignals,weshallnowconsidernoise.Noiseisallaroundus,fromthesoundofwavesbreakingonaseashore,andtheradio noise of stars, to the daily fluctuations of the stock markets. Electricalnoisecangenerallybesplit intooneof twocategories:whitenoise,whichhasconstantlevelwithfrequency(likewhitelight),and1/fnoise,whoseamplitudeisinverselyproportionaltofrequency.

White noise is often known as Johnson or thermal noise and is caused by therandom thermal movement of atoms knocking the free electrons within aconductor. Because it is generated by a thermal mechanism, cooling criticaldevices reduces noise, so the input transistor associated with a High PurityGermanium (HPGe) detector used for gamma radiation spectroscopy is alsocooledby the liquidnitrogen (77 K)needed to reduce leakagecurrents in thecrystal,butsomeradiotelescopesneedthemuchcolderliquidhelium(4 K)fortheir head amplifiers. All resistors produce white noise and generate a noisevoltage:

where

k=Boltzmann’sconstant≈1.381×10−23 J/KT=absolutetemperatureoftheconductor≈°C+273.16B=bandwidthofthefollowingmeasuringdeviceR=resistanceoftheconductor.

Fromthisequation,wecanseethatifweweretocooltheconductorto0 Kor−273.16 °C, therewould be no noise because thiswould be absolute zero, atwhichtemperaturethereisnothermalvibrationoftheatomstoproducenoise.Thebandwidth of themeasuring system is important too because the noise isproportional to the square root of bandwidth. Bandwidth is the differencebetweentheupperandthelowerf−3 dBlimitsofmeasurement.Itisimportanttorealise that in audiowork, thenoisemeasurementbandwidth is always that ofthe human ear (20 Hz to 20 kHz), and although one amplifiermight have awiderbandwidththananother,thisdoesnotnecessarilymeanthatitwillproduceanymorenoise.In audio, we cannot alter the noise bandwidth or the value of Boltzmann’sconstant and reducing the temperature is expensive, so our main weapon forreducingnoise is to reduce resistance.Wewill look into this inmoredetail inChapter3andChapter7.1/ fnoiseisalsoknownas flickernoiseorexcessnoise,andit isaparticularlyinsidious formofnoisebecause it is not predictable. It could almostbe called‘imperfection’ noise because it is generally caused by imperfections such asimperfectly ‘clean rooms’ used for making semiconductors or valves, ‘dry’solderedjoints,poormetal-to-metalcontacts inconnectors–thelist isendless.Semiconductormanufacturersusuallyspecifythe1/fnoisecorner,wherethe1/fnoisebecomesdominantoverwhitenoise,fortheirdevices,butequivalentdata

donotexistforvalves.Because noise is random, or uncorrelated, we cannot add noise voltages orcurrents, but must add noise powers, and some initially surprising resultsemerge.Noisecanbeconsideredstatisticallyasadeviationfromameanvalue.Whenanopinionpollorganisationusesaslargeasampleaspossibletoreduceerror,itisactuallyaveragingthenoisetofindthemeanvalue.Ifwe paralleln input devices in a low-noise amplifier, the uncorrelated noisesourcesbegintocancel,butthewantedsignalremainsatconstantlevel,resultinginanimprovementinsignaltonoiseratioof√ndB.Thistechniqueisfeasiblefor semiconductors where it is possible to make 100 matched parallelledtransistorsonasinglechip(LM394,MAT-01,etc.),butweareluckytofindapairofmatchedtriodesinoneenvelope,letalonemorethanthat!

ActiveDevicesWehaveinvestigatedresistors,capacitors,inductorsandtransformers,butthesewere all passive components.Wewill now look at active devices, which canamplifyasignal.Allactivedevicesneedapowersupplybecauseamplificationisachievedbythesourcecontrollingtheflowofenergyfromapowersupplyintoaloadviatheactivedevice.We will conclude this chapter by looking briefly at semiconductors. It mightseem odd that we should pay any attention at all to semiconductors, but amodern valve amplifier generally contains rather more semiconductors thanvalves,soweneedsomeknowledgeofthesedevicestoassistthedesignofthe(valve)amplifier.

ConventionalCurrentFlowandElectronFlow

Whenelectricitywasfirstinvestigated,theelectronhadnotbeendiscovered,andso an arbitrary direction for the flow of electricitywas assumed.Therewas a50/50chanceofguessingcorrectly,andtheearlyresearcherswereunlucky.Bythetimethemistakewasdiscoveredanditwasrealisedthatelectronsflowedintheoppositedirectiontothewaythatelectricityhadbeenthoughttoflow,itwastoolatetochangetheconvention.Weare,therefore,saddledwithaconventionalcurrentthatflowsintheoppositedirectiontothatoftheelectrons.Mostly,thisisoflittleconsequence,butwhenweconsidertheinternalworkingsofthetransistorandthevalve,wemustbearthisdistinctioninmind.

SiliconDiodes

SemiconductordevicesaremadebydopingregionsofcrystallinesilicontoformareasknownasN-typeorP-type.Theseregionsarepermanentlychargedandattheirjunctionthischargeformsapotentialbarrierthatmustbeovercomebeforeforwardconductioncanoccur.Reversepolaritystrengthensthepotentialbarrier,sonoconductionoccurs.Thediode is a device that allows current to flow in onedirection, but not theother.Itsmostbasicuseis,therefore,torectifyACintoDC.Thearrow-headonthediodedenotesthedirectionofconventionalcurrentflow,andRListheloadresistance(seeFigure1.35).

Figure1.35UseofadiodetorectifyAC.

Practical silicon diodes are not perfect rectifiers and require a forward biasvoltagebeforetheyconductanyappreciablecurrent.Atroomtemperature, thisbiasvoltageisbetween0.6 Vand0.7 V(seeFigure1.36).

Figure1.36Silicondiodecurrentagainstforwardbiasvoltage.

Thisforwardbiasvoltageisalwayspresent,sotheoutputvoltageisalwaysless

thantheinputvoltagebytheamountofthediodedrop.Becausethereisalwaysavoltagedropacrossthediode,currentflowmustcreateheat,andsufficientheatwillmeltthesilicon.Alldiodes,therefore,haveamaximumcurrentrating.In addition, if the reverse voltage is too high, the diodewill break down andconduct;ifthisreversecurrentisnotlimited,thediodewillbedestroyed.Unlikevalves,themechanismforconductionthroughthemostcommon(bipolarjunction) type of silicon diode is complex and results in a charge beingtemporarily stored within the diode. When the diode is switched off by theexternalvoltage,thechargewithinthediodeisquicklydischargedandproducesa brief current overshoot that can excite external resonances. Fortunately,Schottky diodes do not exhibit this phenomenon, and soft recovery types arefabricatedtominimiseit.

VoltageReferences

The forward voltage drop across a diode junction is determined by theEbers/Moll equation involving absolute temperature and current, whilst thereverse breakdown voltage is determined by the physical construction of theindividual diode. This means that we can use the diode as a rectifier or as avoltagereference.Voltagereferencesarealsocharacterisedbytheirsloperesistance,whichistheThéveninresistanceofthevoltagereferencewhenoperatedcorrectly.Itdoesnotimplythatlargecurrentscanbedrawn,merelythatforsmallcurrentchangesinthelinearregionofoperation,thevoltagechangewillbecorrespondinglysmall.Voltage references based on the forward voltage drop are known as bandgapdevices,whilstreferencesbasedonthereversebreakdownvoltageareknownasZenerdiodes.Allvoltagereferencesshouldpassonlyalimitedcurrenttoavoiddestruction,andideallyaconstantcurrentshouldbepassed.Zenerdiodesarecommonlyavailableinpowerratingsupto75 W,althoughthemostcommonratingis400 mW,andvoltageratingsarefrom2.7 Vto270 V.Inreality,trueZeneractionoccursat≤5 V,soa‘Zener’diodewitharating≥5Vactuallyusestheavalancheeffect[2].Thisisfortuitousbecauseproducinga6.2 Vdevicerequiresbotheffectstobeusedinproportionsthatcausethetwodifferentmechanisms to cancel the temperature coefficient almost to zero andreducesloperesistance.Diodessuchasthe1N82*seriesdeliberatelyexploitthisphenomenon to produce a 6.2 V reference with vanishingly low temperaturecoefficient (0.0005%/°C for the 1N829A), but note that this performanceonlyobtains if a Zener current of 7.5 ± 0.01 mA is used. Slope resistance risessharplybelow6 V,andmoregraduallyabove6 V,butistypically≈10 Ωat5

mAfora6.2 VZener.Bandgap referencesareoftenactuallyacomplex integratedcircuit andusuallyhaveanoutputvoltageof1.2 V,butinternalamplifiersmayincreasethisto10Vormore.Becausetheyarecomplexinternally,bandgapreferencestendtobemoreexpensive thanZeners,andwemayoccasionallyneedacheap low-noisereference.LightEmittingDiodes (LEDs) and small-signal diodes are operatedforwardbiassed,sotheyarequietandreasonablycheap(Table1.2).

Table1.2ComparisonofForwardDropsandSlopeResistancesforVariousDiodesDiodetype Typicalforwarddropat10 mA(V) Typicalrslopeat10 mA(Ω)

Small-signalsilicondiode(1N4148) 0.75 6.0InfraredLED(950 nm) 1.2 5.4CheapredLED 1.7 4.3Cheapyellow,yellow/greenLED ≈2 10TruegreenLED(525 nm) 3.6 30BlueLED(426 nm) 3.7 26

TheAgilentHLMP6000 redLED isparticularlyuseful as a low-noisevoltagereference(seeFigure1.37).

Figure1.37HLMP6000redLEDforwarddropagainstappliedcurrent.

Astraightlineonalogarithmicscaleimpliesalogarithmicequation:

Moresignificantly,differentiatingtheequationgivesusdV/dI,whichweknowassloperesistance:

Thus, a typical HLMP6000 passing 10 mA has a slope resistance of 3.8 Ω.Notethatthisisanexampleofanequationwhereitwasmoreusefultousethe

scaledunit(mA)thanthebaseunit(A).Bandgap references usually incorporate an internal amplifier, so their outputresistanceismuchlower, typicallystatedas≈0.2 Ωor less,but thisriseswithfrequency. So if low resistance must be maintained to high frequencies (>1MHz),theHLMP6000maybeabetterchoice.

BipolarJunctionTransistors(BJTs)BJTs are themost common type of transistor; they are available inNPN andPNPtypesandcanbeused toamplifyasignal.Thenametransistor isderivedfrom transferred res istor. Before the appellation ‘transistor’ becamecommonplace,theywererathercharminglyknownascrystaltriodes(seeFigure1.38).

Figure1.38TheGET1–oneoftheveryfirsttransistors.

Wecan imagineanNPNtransistorasasandwichof twothickslabsofN-typematerial separated by an extremely thin layer of P-type material. The P-typematerialisthebase,whilstoneoftheN-typesistheemitterandemitselectrons,whicharethencollectedbytheotherN-type,whichisknownasthecollector.Ifwesimplyconnect thecollector to thepositive terminalofabatteryand theemittertothenegative,nocurrentwillflowbecausethenegativelychargedbaserepelselectrons.Ifwenowapplyapositivevoltagetothebasetoneutralisethischarge,theelectronswillnolongerberepelled,butbecausethebaseissothin,the attraction of the strongly positively charged collector pulls most of theelectronsstraightthroughthebasetothecollector,andcollectorcurrentflows.Thebase/emitterjunctionisnowaforwardbiasseddiode,soitshouldcomeasno surprise to learn that 0.7 V is required across the base/emitter junction tocause the transistor toconductelectrons fromemitter tocollector.Because the

baseissothinandtheattractionofthecollectorissogreat,veryfewelectronsemerge from the base as base current, so the ratio of collector current to baseleakage current is high. The transistor, therefore, has current gain, which issometimesknownasβ(beta)butmorecommonlyashFEforDCcurrentgainorhfeforACcurrentgain,althoughforallpracticalpurposes,hFE=hfe,makingtheAC distinction trivial. ( hFE: hybrid model, forward current transfer ratio andemitterascommonterminal.Don’tyouwishyouhadn’tasked?)Realistically,hFEisadefect,notaparameter,andshouldbetreatedassuch.Itisnot constant between samples and varies as device parameters change (seeFigure1.39).

Figure1.39Variationofthedefecthfe.

Ascanbeseen,thereisageneraltrendforhFEtorisewithincreasingcollectorcurrentbut fall sharplyas IC(max) is approached.TheMJ802 isa special audiopower transistor thathasbeenengineeredtomaintainhFEathighcurrents,andthisaccountsforthekinkat40 mA.Afarmore importantandpredictableparameter is the transconductance (moreusefully called mutual conductance in valves) gm, which is the change incollectorcurrentcausedbyachangeinbase/emittervoltage:

Whenwe look at valves,wewill see thatwemust alwaysmeasuregm at theoperating point, perhaps from a graph. For transistors, transconductance isdefinedby theEbers/Moll [3]equation,and for small currents (less than≈100mA),gmcanbeestimatedforanyBJTusing:

TheCommonEmitterAmplifier

NowthatwehaveameansofpredictingthechangeincollectorcurrentcausedbyachangeinVBE,wecouldconnectaresistorRL inserieswith thecollectorand thesupply toconvert thecurrentchange intoavoltagechange.ByOhm’slaw:

ButΔIC=gm·ΔVBE,so:

Wearenowable to find thevoltageamplificationAv (alsoknownasgain) forthiscircuit,whichisknownasacommonemitteramplifierbecausetheemitteriscommontoboththeinputandtheoutputcircuitsorports.Notethattheoutputpolarityof theamplifier is invertedwithrespect to the inputsignal(seeFigure1.40).

Figure1.40Commonemittertransistoramplifier.

Asthecircuitstands,itisnotveryusefulbecauseanyinputvoltagebelow+0.7Vwillnotbeamplified,sotheamplifiercreatesconsiderabledistortion.

Tocircumventthis,weassumethatthecollectorvoltageissettohalfthesupplyvoltage because this allows the collector to swing an equal voltage bothpositivelyandnegatively.BecauseweknowthevoltageacrossthecollectorloadRLanditsresistance,wecanuseOhm’slawtodeterminethecurrentthroughit–which is the same as the transistor collector current. We could then use therelationshipbetweenIBandICtosetthisoptimumcollectorcurrent.Aswesawearlier, the value of hFE for a transistor is not guaranteed and varies widelybetweendevices.For a small-signal transistor, it could range from50 tomorethan400.Thewayaroundthisistoaddaresistorintheemitterandtosetabasevoltage(seeFigure1.41).

Figure1.41Stabilisedcommonemitteramplifier.

The amplifier now has input and output coupling capacitors and an emitterdecouplingcapacitor.Theentirecircuitisknownasastabilisedcommonemitteramplifierandisthebasisofmostlineartransistorcircuitry.

ConsideringDCConditions

Thepotentialdividerchainpassesacurrentthatisatleast10timestheexpectedbase current and therefore sets a fixed voltage at the base of the transistorindependentofbasecurrent.Becauseofdiodedrop,thevoltageattheemitteristhus0.7 Vlower.Theemitterresistorhasafixedvoltageacrossit,anditmust,therefore, pass a fixed current from the emitter. IE= IC− IB, but since IB is sosmall,IE≈IC,andifwehaveafixedemittercurrent,thencollectorcurrentisalsofixed.

The emitter is decoupled to prevent negative feedback from reducing the ACgainofthecircuit.Wewillconsidernegativefeedbacklaterinthischapter.Briefly, if theemitter resistorwasnotdecoupled, thenanychange incollectorcurrent(whichisthesameasemittercurrent)wouldcausethevoltageacrosstheemitter resistor to change with the applied AC. The emitter voltage wouldchange, and vbe would effectively be reduced, causing AC gain to fall. Thedecoupling capacitor is a short circuit to AC and, therefore, prevents thisreductionofgain.Thisprinciplewillbe repeated in thenext chapterwhenwelookatthecathodebypasscapacitorinavalvecircuit.

InputandOutputResistances

Inavalveamplifier,wewillfrequentlyusetransistorsaspartofabiasnetworkor as part of a power supply, and being able to determine input and outputresistances is, therefore, important. The followingAC resistances looking intothe transistor do not take account of any external parallel resistance from theviewedterminaltoground.Theoutput resistance1/hoe looking into thecollector ishigh, typically tensofkΩatIC≈1 mA,whichsuggeststhatthetransistorwouldmakeagoodconstantcurrent source (hoe:hybridmodel,output admittance and emitter as commonterminal).Intheory,ifallthecollectorcurvesofabipolarjunctiontransistorareextendednegatively,theyintersectatavoltageknownastheEarly[4]voltage.Sadly, the real world is not so tidy, and attempts by the author to determineEarlyvoltagesresembledtheresultofdroppingahandfulofuncookedspaghettionthegraphpaper.Nevertheless,theconceptofEarlyeffectisusefulbecauseitindicatesthat1/hoefallsasICrises(seeFigure1.42).

Figure1.42CollectorcurvesforBC558BPNPtransistor.

TheEarlyeffectiscausedbythedepletionregionstraddlingthereverse-biassedbase/collector junction. AsVCB rises, the depletion region widens, effectivelymaking thebasenarrower and less able to capture electrons; this increaseshfeandresultsinincreasedcollectorcurrentathighercollectorvoltages.Theresistancelookingintotheemitterislow,re=1/gm,so≈20 Ωistypical.Ifthe base is not driven by a source of zero resistance ( Rb≠0), there is anadditionalseriesterm,andreisfoundfrom:

whereRb is theThéveninresistanceofall thepaths togroundandsupplyseenfromthebaseofthetransistor.Notethateventhoughwearenolongerexplicitlyincludingabatteryasthesupply,thesupplyisstillassumedtohavezerooutputresistancefromDCtolightfrequencies.Looking into the base, the path to ground is via the base emitter junction inserieswiththeemitterresistor.Iftheemitterresistorisnotdecoupled,thentheresistancewillbe:

Iftheemitterresistorisdecoupled,thenRe=0,andtheequationreducesto:

The AC input resistance owing purely to the base/emitter junction is oftenknown as hie and is generally quite low, <10 kΩ ( hie: hybrid model, inputresistanceandemitterascommonterminal).Ifwenowconsidertheeffectoftheexternalparallelresistances,weseethattheinputresistanceoftheamplifierislow,typically<5 kΩ.Theoutputresistanceseen at the emitter is low, typically <100 Ω (even if the source resistance isquitehigh),andtheoutputresistanceatthecollectoris≈RL.

TheEmitterFollower

Very occasionally, you will see this amplifier called a common collectoramplifier, although this phraseology is rarebecause it doesnot convey clearlywhatthecircuitdoes.Ifwereducethecollectorloadtozeroandtakeouroutputfromtheemitter,thenwe have an amplifier with Av≈1. The voltage gainmust be ≈1 because VE=VB−0.7 V; the emitter follows the base voltage, and the amplifier is non-inverting.AlthoughAv=1,thecurrentgainismuchgreater,andwecancalculateinput and output resistances using the equations presented for the commonemitteramplifier(seeFigure1.43).

Figure1.43Emitterfollower.

Because of its lowoutput resistance andmoderately high input resistance, theemitter follower isoftenusedasabuffer tomatchhigh-impedancecircuitry to

low-resistanceloads.

TheDarlingtonPair

Sometimes,evenanemitter followermaynothavesufficientcurrentgain,andthe solution is to use aDarlington pair; this is effectively two transistors incascade,withoneformingtheemitterloadfortheother(seeFigure1.44).

Figure1.44Darlingtonpair.

ThetwotransistorsformacompositetransistorwithVBE=1.4 VandhFE(total)=hFE1×hFE2.ADarlingtonpaircanreplaceasingletransistorinanyconfigurationifitseemsuseful.Commonusesareintheoutputstageofapoweramplifierandin linear power supplies. Darlingtons can be bought in a single package, butmakingyourownoutoftwodiscretetransistorsusuallygivesbetterperformanceandischeaperintermsofcomponentcost,althoughputtingtwopartsinsteadofoneonaPrintedCircuitBoard(PCB)ismoreexpensive.

GeneralObservationsonBJTsWementionedearlierthattheBJTcouldbeconsideredtobeasandwichwiththebase separating the collector and the emitter.We can nowdevelop thismodeland use it to make some useful generalisations, particularly about the defectknownashFE.As the base becomes thicker, it becomes more and more probable that anelectronpassing from the emitter to the collectorwill be capturedby thebaseandflowoutofthebaseasbasecurrent;hFEis,therefore,inverselyproportionaltobasethickness.When a transistor passes a high collector current, its base current must beproportionately high. In order for the base not tomelt due to this current, thebasemustbethickened.ThethickerbasereduceshFE,andrequiredbasecurrentmustriseyetfurther,requiringaneventhickerbase.hFEis,therefore,inverselyproportionaltothesquareofmaximumpermissiblecollectorcurrent,andhigh-

currenttransistorshavelowhFE.High-voltage transistors need a thick base to allow for the widened depletionregioncausedbyahighcollectortobasevoltage,sohigh-voltagetransistorsalsohavelowhFE.High-current transistors must have a large silicon die area in order for thecollectornot tomelt– this largearea increasescollector/basecapacitance.Thesignificanceof capacitance in amplifyingdeviceswill bemade clearwhenweconsider theMillereffect inChapter2,but for themomentwecansimplysaythathigh-currenttransistorswillbeslow.We have barely scratched the surface of semiconductor devices and circuits.Othersemiconductorcircuitswillbepresentedasandwhentheyareneeded.

FeedbackFeedback isaprocesswherebywetakeafractionoftheoutputofanamplifierandsumitwiththeinput.If,whenwesumitwiththeinput,itcausesthegainoftheamplifier to increase, then it isknownaspositive feedback, and this is thebasis of oscillators. If it causes the gain to fall, then it is known as negativefeedback,andthistechniqueiswidelyusedinaudioamplifiers.

TheFeedbackEquation

The description of feedback was deliberately rather vague because there aremanyways that feedbackcanbeapplied,and theyeachhavedifferingeffects.Before we can look at these effects, we need a few definitions and a simpleequation:

whereA=amplificationwithfeedbackA0=amplificationwithzero(0)feedback

β=feedbackfraction.

Thisisthegeneralfeedbackequationthatdefineshowthegainofanamplifierwillbemodifiedbytheapplicationoffeedback.βisthefeedbackfractionandistheproportionoftheoutputthatisfed,orlooped,backtotheinput.ItisbecauseβissocommonlyusedinthefeedbackequationthattheapparentlyclumsytermhFEismorepopularforbipolartransistorcurrentgain.

If βA0 is very large and positive (causing negative feedback – a reduction ofgain),thenβA0≈βA0+1,andthegainoftheamplifierbecomes:

A0no longeraffectsA,and theclosed loopgainof theamplifier isdeterminedsolelybythenetworkthatprovidesthefeedbacksignal.Thisresultisverysignificantbecauseitimpliesmanythings:• Distortion is produced by variations in gain from one voltage level toanother. If open loop gain is no longer part of the equation, then smallvariationsinthisgainareirrelevant,andtheamplifierproducesnodistortion.• If the feedback acts tomaintain the correct gainunder all circumstances,thenitmustchangetheapparentinputandoutputresistancesoftheamplifier.•Ifthefeedbackfractionβissetbypureresistors,thentheequationforclosedloop gain does not contain any term including frequency.Theoretically, theoutputamplitudeis,therefore,independentoffrequency.

Inthelate1970s,whencheapgainbecamereadilyavailable,designersbecameveryexcitedbythepossibilitiesandimplicationsofthefeedbackequation,andsetouttoexploititbydesigningamplifiersthatwerethoughttohaveveryhighlevels of feedback. In practice, these amplifiers did not have high levels offeedbackatallfrequenciesandpowerlevels,anditwasthelackoffeedbacktolinearise these fundamentally flawed circuits that caused their poor soundquality.Before we explore the expected benefits of feedback, we should, therefore,examinehowthefeedbackequationcouldbreakdown.

PracticalLimitationsoftheFeedbackEquation

ThefeedbackequationimpliesimprovedperformanceprovidedthatβA0>>1.If,foranyreason,theopenloopgainoftheamplifierislessthaninfinite,thenβA0willnotbemuchgreaterthan1,andtheapproximationwillnolongerbetrue.Practical amplifiers always have finite gain; moreover, this gain falls withfrequency.Apracticalamplifierwillalwaysdistorttheinputsignal,andbecausethe distortion-reducing ability of negative feedback falls with frequency, theclosedloopdistortionmustrisewithfrequency.Crossover distortion in Class B amplifiers can be considered to be a severereductionofgainastheamplifiertraversestheswitchingpointofthetransistors

or valves. Because of the drastically reduced open loop gain in this region,negativefeedbackisnotveryeffectiveatreducingcrossoverdistortion.Although not explicitly stated by the feedback equation, the phase of thefeedbacksignaliscruciallyimportant.Ifthephaseshouldchangeby180°,thenthefeedbackwillnolongerbenegative,butpositive,andouramplifiermayturnintoanoscillator.WewillexplorethepracticallimitationsoffeedbackinChapter6,butweshouldrealisethat,aswithanyweaponwieldedcarelessly,itispossibletoshootoneselfinthefoot.

FeedbackTerminologyandInputandOutputImpedances

Wecanmakeanumberofgeneralstatementsaboutfeedbackthatenableus toquicklypredicteffectsateitherinputoroutput:• The way in which the feedback is derived affects the output impedance,whereasthewaythatitisappliedaffectsinputimpedance.• If we make a parallel, or shunt, connection, then we are dealing with avoltage,butifwemakeaseriesconnection,wearedealingwithacurrent.• Feedback confined to one stage is known as local feedback, whereas afeedbackloopenclosinganumberofstagesisknownasglobal.•Wemayhavemorethanoneglobalfeedbackloop,withoneloopenclosedbyanother,inwhichcasetheloopsaresaidtobenested.•Oncewehavedefinedhowthefeedbackisconnected,wecanstatethatfornegative feedback, voltage feedback reduces impedances, but currentfeedbackincreasesimpedances.•Alltheprecedingstatementsapplytonegativefeedbackandarereversedifthefeedbackbecomespositive(thusanincreasebecomesadecrease,andviceversa).

As an example, we can now combine these statements to describe the globalnegative feedback loop of a typical power amplifier as being parallel-derived,series-applied, butwe could equallywell describe it as being voltage-derived,current-applied.Almostallpoweramplifiersusethisparticularfeedbackstrategybecauseitensures:•Lowoutputimpedance(neededtodriveelectromagneticloudspeakersastheloudspeakerdesignerintended)•Highinputimpedance(toavoidexcessiveloadingofpre-amplifiers)

•Non-invertinggain(outputisthesamepolarityastheinput).

Notingthatpositivefeedbackreverseseffects,positivevoltagefeedbackwouldincreaseimpedances,whilstpositivecurrentfeedbackwouldreduceimpedances.Usingacombinationofpositiveandnegativefeedbacks,itispossibletomakeapower amplifier with zero, or even negative, output impedance, and this idearesurfacesatroughly10-yearintervals.Unfortunately,amplifierswithnegativeoutputimpedanceareliabletooscillatebecause they reduce the total series damping resistance of the external(invariably resonant) load to zero. Nevertheless, some early valve poweramplifiershadthefacilitytoadjustoutputimpedancethroughzerotoanegativevalue, in an effort to improve the bass performance of the accompanyingloudspeaker.Asmentioned,thisidearesurfacesperiodically,butitisreallyonlyof use for the dedicated amplifiers in a loudspeaker system with an activecrossover.(Active,orlow-level,crossoversareusedbeforethepoweramplifiersso that eachdriveunit has adedicatedpower amplifier.Although this schememay seem profligate with expensive power amplifiers, it has much torecommendtheuseofactive,orlow-level,crossovers.)Althoughwehavedescribed thevariousmodesof feedbackand their trendonimpedances,wenowneedtoquantifytheeffect.Impedancesarechangedbytheratioofthefeedbackfactor:

ThisisalsothefactorbywhichthegainoftheamplifierhasbeenreducedandisoftenexpressedindBs.Anamplifierwith20 dBofglobalfeedbackhashaditstotalgain reducedbya factorof20 dB,and if thiswasaconventionalpoweramplifierwithshunt-derivedfeedback,itsoutputimpedancewouldthereforebereducedbyafactorof10.

TheOperationalAmplifierConventionally,whenwethinkofcomputers,wethinkofdigitalcomputers,butonceuponatimetherewerealsoanaloguecomputers,whichwerehardwiredtomodelcomplexdifferentialequations,suchasthoserequiredforcalculatingtheballisticsofanti-aircraftshells.Theseanaloguecomputersusedabasicbuildingblockthatbecameknownastheoperationalamplifier.Itwasasmalldeviceforitstime(smallerthanabrick)andusedvalvecircuitsthatoperatedfrom±300 Vsupplies.Withsuitableexternalcomponents, theseoperationalamplifierscouldbe made to perform the mathematical operations of inversion, summation,multiplication,integrationanddifferentiation.Thankfully, the valve analogue computer is no longer with us, but the term‘operational amplifier’, usually shortened toop-amp, is stillwithus, even if it

nowreferstoeight-leggedsiliconbeetles.Op-amps attempt to define the performance of the final amplifier purely byfeedback,andtodothissuccessfullytheop-ampmusthaveenormousgain;120dB gain at DC is not uncommon, although AC gain invariably falls withfrequency.In the following discussions, we always make two fundamental assumptionsaboutop-amps:•Gainisinfinite.•Inputresistanceisinfinite.

Theseassumptionsspecifyidealop-amps.Real-worldop-ampshavelimitationsandwillnot achieve this ideal at all frequencies, voltage levels, etc. Providedthatwerememberthisimportantcaveatatalltimes,wewillnotrunintotrouble.It is habitual in op-amp circuit diagrams to omit the (typically±15 V) powersupply lines to the op-amp to aid clarity; nevertheless, the op-amp still needspower!

TheInverterandVirtualEarthAdder

The op-amp inverter has parallel-derived, parallel-applied, negative feedback,and since op-ampgain is infinite, the point of both derivation and applicationmusthave zero resistance; the amplifier has zerooutput resistance (seeFigure1.45).

Figure1.45Invertingamplifier.

The inverting input of the op-amp also has zero resistance to earth (0 V)because of the feedback. Since the gain of the op-amp is infinite, if the non-invertinginputisatearthpotential,thentheinvertinginputmustalsobeatearthpotential. In this configuration, the inverting input is, therefore, known as avirtualearth.Althoughitisavirtualearthbyvirtueoffeedback,theinvertinginputoftheop-

amp itselfhas infinite resistance, andnosignalcurrent flows into theop-amp.InputsignalcurrentfromRScan,therefore,onlyflowtogroundviaRFandthezero output resistance of the op-amp. The signal currents in RS and RF are,therefore,equal,andusingOhm’slaw:

Since the inverting input is a virtual earth, VS= Vin, VF=− Vout (the op-ampinverts)andthevoltagegainoftheamplifieris:

NotethatthisamplifiercanachieveAv<1andcanattenuatetheinputsignal.Thisis useful because it provides an attenuated output from an almost zero sourceresistance,whereasapotentialdividerwouldhavesignificantoutputresistance.Theminussignremindsusthattheamplifierinvertspolarity.Becausetheinvertingnodeoftheamplifierisavirtualearth,inputresistanceisequaltoRS.Whenweanalysedthisamplifier,weconsideredtheinputsignalcurrent.Thereisnoreasonwhy this inputcurrentshouldcomefromonlyonesourceviaoneresistor, and we can sum currents at the inverting node in accordance withKirchhoff’slaw(seeFigure1.46).

Figure1.46Virtualearthadder.

Thiscircuitisknownasthevirtualearthaddersandismostusefulinbiasservocircuitswherewemayneedtoaddanumberofcorrectionsignals.Voltagegainfor each inputmay be determined using the inverter equation.Whenmultipleinputsaredriven,itisoftenbesttodeterminetheoutputvoltagebysummingthe

signalcurrentsusingKirchhoff’scurrentlaw,findingtheresultantcurrentinRFandusingOhm’slawtodeterminetheoutputvoltage.Thisisnotastediousasitsounds.

TheNon-InvertingAmplifierandVoltageFollower

Frequently,weneedanon-invertingamplifier(seeFigure1.47).

Figure1.47Non-invertingamplifier.

Inthisconfiguration,westillhaveRFandRS,buttheamplifierhasbeenturnedupsidedown,andthefarendofRSisnowconnecteddirectlytoground.Liketheinverterwesawearlier,theamplifierhasparallel-derivednegativefeedback,soits output resistance remains zero, but the feedback is now series-applied,makinginputresistanceinfinite.RFandRSnowformapotentialdivideracrosstheoutputoftheamplifier,andthevoltageattheinvertinginputis:

Sincetheop-amphasinfinitegain,thevoltageattheinvertinginputisequaltothatatthenon-invertinginput,whichisVin,sothegainoftheamplifieris:

IfwenowreducethevalueofRFtozeroanddiscardRS,thegainreducesto1,andtheamplifierisknownasthevoltagefollower(seeFigure1.48).

Figure1.48Voltagefollower.

The voltage follower is an excellentbuffer stage for isolating high-impedancecircuits from low-impedance loads, and because it applies more negativefeedback it is far superior to the single-transistor emitter follower thatwe sawearlier. (A very useful analytical technique is to treat an emitter follower as acommoncollectoramplifierwith100%feedbackandusethefeedbackequationtodetermineinputandoutputresistances.)Ifweneedmorecurrentthantheop-ampcanprovide,wecanaddanemitterfollower,orevenaDarlingtonpair,totheoutputandenclosethiswithinthefeedbackloop(seeFigure1.49).

Figure1.49Additionofemitterfollowertoincreaseoutputcurrent.

TheIntegrator

This circuit is essentially an inverter with RF parallelled byCF, but if RF isomitted, itbecomesan integrator andaccumulatescharge.Thecircuitmaybeconsidered to be a low-pass filter, in which case the cut-off frequency of thefilteris:

We can now see that ifRF=∞, the cut-off frequency=0, and the amplifier hasinfinitegainatDC.AnyDCoffsetswillgraduallyaccumulatesufficientchargeon thecapacitor to cause theoutputof theop-amp to rise tomaximumoutputvoltage(±Vsupply),andtheop-ampisthensaidtobesaturated.Forthisreason,practicalintegratorsareusuallyenclosedbyaservocontrolloop.Theservoerrorsignal chargesCF, but the loopaims tominimise the error, and so thevoltageacrossCFtendstozero.Again,wecouldsumseveralinputcurrentsifwewished,andonepossibleuseofthiscircuitwouldbeformonitoringthevoltagesacrossthecathoderesistorsof several output valves because the integrating function would remove theaudio signal and provide aDC output voltage proportional to the total outputvalveDCcurrent.

TheChargeAmplifier

Noting that the voltage gain of the inverting amplifier was the ratio ofresistances, there isnoreasonwhy thoseresistancesshouldnotbe replacedbyreactances. Although an amplifier with gain defined by inductances is neitherpractical nor useful, replacing the resistors with capacitors is useful and isknownasachargeamplifier.Chargeamplifiersarecommonlyassociatedwithtransducerssuchascondensermicrophonesandradiationdetectors thatchangeorproduce a chargebetween theplatesof a capacitor.Such sources thus looklikeaNortonsource(purecurrentsource inparallelwithcapacitance)andcanbeconvertedintoaThéveninsourcehavingapurevoltagesourceinserieswiththesourcecapacitance.Connectingsuchasourcedirectlytotheinvertinginputof the amplifier produces a circuit very similar to the previously analysedresistiveinvertingamplifier(seeFigure1.50).

Figure1.50Chargeamplifier.

Thesignificanceof thisarrangementis that thevoltagegainis theratiooftworeactances and is independent of frequency. It is initially surprising that anamplifieremployingcapacitorsshouldrespondtoDCbutiseasilyprovedbytheassumption that the op-amp draws zero input current. If the op-amp does notdrawinputcurrent,thenanyDCinputcurrenttotheamplifiermustpassthroughthe feedback capacitor, causing the output to respond. Charge amplifiers aretypically associatedwith small source capacitances (30 pF for a large-capsulecondenser microphone) and require small feedback capacitances (2–3 pF istypical)toprovideusefulgain.Like the integrator, practical charge amplifiers require ameans of dischargingthe feedback capacitor to prevent amplifier saturation, and this is commonlyachievedbyaparalleldischargeresistor(seeFigure1.51).

Figure1.51Practicalchargeamplifier.

Unfortunately,theeffectofaddingthedischargeresistoristoturntheamplifierintoadifferentiator.Inaudioterms,wehaveaddedahigh-passfilterandwouldliketoplaceitsf−3 dBfrequencyaslowaspossible,certainly20 Hz.

Astheequationshows,chargeamplifiersinvariablyrequireverylargedischargeresistances. Nevertheless, such resistors are readily available, even if they dorequire the wearing of clean cotton gloves when handling to avoid addingsurfaceleakagecurrents.Interestingly,becausethechargeamplifierrespondstocharge(orovertheshortterm,currents),itisthenoisecurrentproducedbythedischargeresistorthatisimportant, not its voltage. Remembering that the thermal noise voltage of a

resistoris:

substitutingintoOhm’slawgives:

Thus, for lowestnoise, thedischarge resistorof a charge amplifiermustbe aslargeaspossible.

DCOffsets

WebrieflymentionedDCoffsetswhenconsideringtheintegrator.Op-ampsarenotmagical;theycontainrealtransistors,andbase,orleakage,current,knownasbiascurrent,willflowoutoftheinputs.Thebiascurrentswillnotbeperfectlymatched,andtheimbalanceisknownasoffsetcurrent.Theinputtransistorswillnot be perfectlymatched for voltage either, so therewill be an offset voltagebetween the inputs. These imperfections are detailed in the manufacturer’sdatasheetsandshouldbeinvestigatedduringcircuitdesign.

References[1]Kaye,GWC;Laby,TH,Tablesofphysicalandchemicalconstants.16thed.

(1995)Longman.[2]Parker,G,Introductorysemiconductordevicephysics.(1994)PrenticeHall,

UK,UK.[3]Ebers,JJ;Moll,JL,Large-signalbehaviorofjunctiontransistors,ProcIRE

December(1954)1761–1772.[4]Early,JM,Effectsofspace-chargelayerwideninginjunctiontransistors,

ProcIRENovember(1952)1401–1406.

RecommendedFurtherReading•GrayPR,HurstPJ,SH,MeyerRG.Analysisanddesignofanalogintegrated

circuits.5thed.JohnWiley.Donotbeputoffbythetitle–thisisasuperbbookthatgoesintothedetailof(semiconductor)circuitbuildingblocksatindividualtransistorlevel.

•JungWGG,editor.Opampapplications.Analogdevices,US;2002.Aswouldbeexpected,thisiscircuit/systemdesignfromanICmanufacturer’sperspectiveandincludesplentyofhintsandtipsabouthowtobestusereal-world(asopposedtoidealised)op-amps.

Chapter2.BasicBuildingBlocksInthischapter,wewilllookmainlyatthetriodevalve,howtochooseoperatingconditions and what effect these choices have on the AC performance of thestage.Theanalysiswilluseacombinationofgraphicalandalgebraictechniques,whichhastheadvantageofbeingquicktouse,andtheresultsofthetheoryagreewellwithpractice.Thislastpointmightseemtobeanobviousrequirement,butitisonethatissometimesoverlooked.

TheCommonCathodeTriodeAmplifierThemostcommonuseofavalveisamplification.Therefore,weneedtoknowhowtoconfigureandbiasthevalvesothatitcanamplifyinalinearmannerandminimisedistortion.WewillbeginbyinvestigatingtheanodecharacteristicsofanECC83/12AX7(seeFigure2.1).

Figure2.1Triodeanodecharacteristics.

Theanodecharacteristicsare themostusefulsetofcurvesforavalve,andtheplotshowsanodecurrentIaagainstanodevoltageVa,fordifferingvaluesofgridto cathodevoltage (Vgk).The first point tonote is thatvalvesoperate athighvoltages (typicallya factorof10greater than transistorcircuits)andquite lowcurrents.Thesecondpointisthatifthereisnobiasvoltage(Vgk=0),thenalargeanode current flows.This is known as the space-charge-limited condition andmeansthattheflowofcurrentislimitedonlybythenumberofelectronsthatcan

be released from the cathode. In contrast to the bipolar junction transistor,wehavetoturnthetriodeoff,ratherthanon,inordertobiasitcorrectly.ThebasicamplifierstagehasananodeloadresistorRL,connectedbetweentheanodeandtheHTsupply(thisisthehistoricalphraseology,andstandsforhightension)(seeFigure2.2).

Figure2.2Commoncathodeamplifier.

TheHTsupplyisassumedtohavezerooutputresistanceatallfrequenciesfromDC to light (you may wish to consider whether this is in fact the case in apractical amplifier). By applying our input voltage between the grid and thecathode,wemodulateVgk, and thereby control anode conditions. This iswhythisgridisoftenknownasthecontrolgridinmulti-gridvalvessuchastetrodesandpentodes.Wewillnowuse the techniqueof loadlines to link theamplifier circuit to theanodecharacteristics,andtoextractusefulinformationfromthem.UsingOhm’s law, it isapparent that if there isnocurrent flowing through theresistor(andthereforethevalve),theremustbenovoltageacrosstheresistor.Ifthere is no voltage across the resistor, then all of the HTmust be across thevalve,sowecouldmarkthatasapointonthegraphoftheanodecharacteristics(Va=HT=350 V;Ia=IR=0).Similarly,wecanargue that if there isnovoltage

acrossthevalve,thentheHTmustallbeacrosstheresistor;wecancalculatethecurrent through the resistor, and therefore the valve. In this case,RL=175 kΩandHT=350 V,sotheanodecurrentIa=2 mA,andwecanplotthispointtoo.BecauseOhm’slawisanequationthatdescribesastraightline,ifweknowtwopoints we have completely defined that straight line. Thismeans that we cannowdrawastraight linebetweenour twoplottedpoints,asshown(seeFigure2.3).

Figure2.3Theloadline.

Thisisourloadline.Thisisperhapsthesinglemostusefulpieceofanalysisthatcanbeperformedonavalvestage.Wehavedefinedtheanodecurrentforanyanodevoltage,usinganHTof350 Vandanodeloadof175 kΩ.Ifwewanttochangeouranodeload,orHT,wemustrecalculateandredrawourloadline.Ifwelookalongtheloadline,weseethatitisintersectedatvariouspointsbytheIa/VacurvesfordifferingvaluesofVgk.Whatthismeansisthatthosedifferingvalues ofVgk will cause predictable changes in anode voltage, andwe could,therefore,calculatethegainofthestage.Letussupposethatweapplyan8 Vpk–pksinewavetotheinputofthestage.Ifwestartfrom0 V,andlooktofindwherethe0 Vgridbiaslineintersectstheloadline,thisoccursatVa=72 V.Wethenletthesinewaveswingnegativeto−4V,andseethatitresultsinVa=332 V.Foranappliedvoltageof−4 Vonthe

input, we produced a positive change of voltage at the anode of 260 V. Theamplifier inverts. Since gain is defined as the ratio of output voltage to inputvoltage,wehavejustproducedanamplifierwithagainof−65(theminussignmerelyremindsusthatthisisaninvertingamplifier).Unfortunately, it isn’t very linear. If we now allow the input sine wave tocontinuerisingpast0 V,wesoonfind that theanodevoltage isunable to fallanyfurther,andsotheoutputsignalnolongerlooksliketheinputsignal.Wemustchooseabiasoroperatingpointatwhichwewillsetthequiescent(nosignal) conditions such that the stage can accommodate both negative andpositiveexcursionsofthesignalwithoutgrossdistortion.

LimitationsonChoiceoftheOperatingPoint

Not only did the previous circuit distort, but the anode DC voltage wassuperimposedon theoutput signal, soweadda capacitor anda resistor at theoutputtoblocktheDC(seeFigure2.4).

Figure2.4Gridbiasusingbattery.

ThevalveisbiassedbysuperimposingabiasvoltageontothegridviaRg,whichprevents the battery from short circuiting the oscillator. Cg is the couplingcapacitor that prevents the oscillator from shorting the battery, and rs is theoutputresistanceoftheoscillator.

Returning to the loadline, we find that as Va rises, the grid curves becomeprogressivelybunchedtogether,whichindicatesnon-linearity,andisparticularlysevere when Va is close to the HT voltage. This region is known as cut-off(because the flow of current is being cut off). Operation near cut-off is notadvisable if good linearity is required, although we will meet this mode ofoperationlaterwhenlookingatsomepowerstages.Movingintheoppositedirectionalongtheloadline,weturnthevalveonharderandharder,untilfinallythereisnovoltageacrossit.Thisisextreme,however,andwewillencountertheproblemofpositivegridcurrentlongbeforethat.Aswemakethegridlessandlessnegative,therecomesapointwhentheelectronsleaving the cathode are no longer repelled and controlled by the grid, but areactuallyattractedtothegridandflowoutthroughthegridtoground.Thiscausestheinputresistanceofthevalve,whichcouldpreviouslyberegardedasinfinite,to fall sufficiently low that it begins to load the oscillator’s (non-zero) outputresistance.Because this attenuation only happens on the positivepeaks of theinputwaveform,thiscausesdistortionoftheinputsignal,eventhoughthevalveaccuratelyamplifiesthegridvoltage.Theonsetofgridcurrentvarieswithvalvetype (but is generally around −1 V) and is usually specified on the valvedatasheet.Forinstance,MullardspecifiesVgk(max)(Ig=+0.3 μA)as−0.9 VfortheECC83usedinourexample.Ifwehaveavoltageacrossthevalve,andacurrentflowingthroughit,wemustbedissipatingpowerwithin thatvalve,and therewillbea limitbeyondwhichweareindangerofmeltingtheinternalstructureofthevalve.Thisisknownasthemaximumanodedissipationandisgivenonthedatasheetasbeing1 WfortheECC83.Forpowervalves,thecurvethatcorrespondstothisisoftendrawnon the anode characteristic curves, but, if we wish, we can easily add itourselves.Allweneedtodoistocalculatethecurrentdrawnfor1 Wat0 V,50V,100 V,150 Vand soon.Weplot these resultson thegraph, anddrawacurvethroughthepointstoformahyperbola.The valve datasheet also specifies two more, interlinked, restrictions on thechoice of bias point: maximum Va and maximum Va(b). Maximum Va is themaximum DC voltage at which the anode may be continuously operated,whereasVa(b) is themaximumvoltage towhich the anodemay be allowed toswingundersignalorcoldconditions,andiseffectivelythemaximumallowableHT voltage for that valve. Ignoring these limits usually results in prematuredestruction of the valve to the accompaniment of blue flashes and bangs asresidualgasinthevalveisionisedandbreaksdown.Thisinitselfmaynotcauseirreversibledamage,but ifapath is formedbetween theanodeand thecontrol

grid, then a large anode current will flow, and this may damage the valvepermanently.Youhavebeenwarned.ThefinallimitationisthemaximumallowablecathodecurrentIk(max).Usually,one of the other limitations comes into effect first, but input stages mayminimiseVaandmaximiseIa inorder tomaximisegm,andminimisenoise,soIk(max) should be checked if possible. (Neither Mullard nor Brimar specifiedIk(max)fortheECC83.)Wecannowdraw these limitationsonto the anode characteristics, and chooseouroperatingpointfromwithinthecleararea(seeFigure2.5).

Figure2.5Determinationofsafeoperatingarea.

ConditionsattheOperatingPoint

Althoughthechoiceofoperatingpointhasnowbeenconsiderablyrestricted,wecanstilloptimisevariousaspectsofperformance.In general, there are two main (and usually conflicting) factors: maximumvoltageswingandlinearity.Ifwewanttobiasformaximumvoltageswing,thenwewouldsetthebiaspointatVa=225 V,toallowtheanodetoswingupto300Vanddownto150 V;thiswouldbedonebysettingthegridbiasto−2.1 V.However,itmightbethatwearemoreinterestedinlinearitythaninmaximumvoltageswing.

Triodesproducemainly secondharmonicdistortion,which isgeneratedby theamplifier having unequal gain on the positive half-cycle of the waveformcomparedtothenegativehalf-cycle,andthedistortionisdirectlyproportionaltoamplitude.Tomaximiselinearity,weshouldlookforanoperatingpointwherethedistancetothefirstgridlineoneithersideoftheoperatingpointis,asnearlyaspossible, equal. In this case,wemightbias the anodevoltage to182 Vbyapplying−1.5 Vtothegrid.Supposing we have chosen the linearity approach, we will now want todetermine thedynamic orAC conditionsof the stage to see if they satisfyourneeds.Thefirst,andmostobvious,parametertodetermineisthevoltageamplification(Av),orgain,ofthestage.Wedothisbylookinganequaldistanceoneithersideoftheoperatingpointtothefirstintersectionwithagridline,notingtheanodevoltage. Referring to Figure 2.5, if we move from the operating point to theright, we meet the 2 V grid line, which intersects at a voltage of 220 V;similarly,the1 Vgridlineintersectsat148 V.

Theminussign remindsus that theamplifier is inverting,butyouwillusuallyfind this dropped, in the interests of clarity, sincemost stages invert, and theabsolutepolarityofanyparticularstageisoftenoflittleconsequence.Thenextimportantfactoristhemaximumundistortedvoltageswing.Again,welooksymmetricallyoneithersideof theoperatingpoint,but this timewe lookfor thefirst limitingvalue. In this instance,we look to the leftandfind thatat148 Vweare approachingpositivegrid current.Thiswouldnotmatter if oursourcehadzerooutputresistance,butthisisunlikelytobethecase,andsowemust regard this as a limit. If we look to the right, we find that there is nopracticallimituntilVa=HT.Unfortunately,whilstthismeansthatthevalvecanswingalargevoltagepositively,itcannotswingasfarnegatively.Itisthefirstlimit to be reached that is important. We can now see that the maximumundistortedpeak-to-peakswingattheoutputisdoublethatofthedistancefromthebiaspointtothefirst limit.Inthisexamplethiscorrespondsto72 Vpk–pk,butrememberingthatACsignalsarespecifiedastheRMSvalueofasinewave,weshoulddividethisfigurebyafactorof2√2,whichresultsinavalueof25 VRMS as the maximum undistorted sine wave output, which is perhaps not so

impressive.Itmaybethatthisvalueofmaximumoutputswingisinsufficient,sowewouldgo back and reselect our operating point. If we are still unable to achieve asatisfactoryvalue, thenwemayneed tochooseadifferentvalueofRL,HTorboth. It will now be apparent that designing valve stages requires a pencil, aclearruler,aneraserandplentyofcopiesofanodecharacteristicscurves.Assumingthatthestagelookspromisingsofar,thenextimportantparameteristhe output resistance. A triode can be modelled as a voltage source coupledthrough a series resistance, known as theanode resistance ra. Remember thatbecausethisisanAC,ordynamic,parameter,itisgivenalowercaseletter,andisquitedistinctfromRL,theanodeload.Thisdynamicanoderesistanceistheninparallelwiththeanodeloadtoformtheoutputresistancerout(seeFigure2.6).

Figure2.6Théveninequivalentoftriodeanodecircuit.

ItshouldbenotedthatthevalueofgainpredictedforthestagebytheloadlinealreadyincludestheattenuationcausedbythepotentialdividerformedbyraandRL.Tofindra,wereturntotheanodecharacteristicsanddrawatangenttothecurvewhereittouchestheoperatingpoint.Whatweareaimingtodoistomeasurethegradient of the curve at that point.This is not as difficult as it sounds.A truetangent will touch, or intersect, the curve at only one point, and only at thecorrectpoint.Agoodqualitytransparentrulerisidealforthispurpose.Havingpositioned the ruler correctly, we draw a line that reaches the edges of thegraduationsonthedatasheet,andreadoffthevaluesatthesepoints.Thepurposeofthisistomaketheresultingtriangle,fromwhichwetakeourfigures,aslargeaspossibleinordertominimiseerrors(seeFigure2.7).

Figure2.7Determinationofdynamicanoderesistancera.

Theanoderesistanceracannowbecalculatedfrom:

YouwillnotethattheunitsofmAwereuseddirectlyintheequation,resultinginananswer inkΩ; this isaconventionalpracticeandsaves time.TheoutputresistanceroutissimplyrainparallelwithRL,whichresultsinavalueof47 kΩ.Thisisquiteahighvalueofoutputresistance,andisaconsequenceofusingahighμ(mu)valve,ashighμ(mu)valvestendtoalsohaveahighvalueofrainoperation.

Dynamic,orAC,Parameters

Sofar,wehaveanalysedthebehaviourofthevalvegraphically,butthisisnotthe only method. There are three AC parameters that define completely thecharacteristics of a valve, provided that they are evaluated at the operatingpoint.Theimportanceofthislastpointissometimesoverlooked.Theseparametersare:μ(mu)=amplificationfactor(nounits)gm=mutualconductance(usuallymA/V)

ra=anoderesistance(kΩ,Ω).

Theamplificationfactorisdefinedby:

Theamplificationfactor(μ)ofavalveistheratioofthechangeinanodevoltageΔVatothechangeingridvoltageΔVg,withanodecurrentheldconstant.

Inamoredigestible form, it is themaximumpossiblevoltageamplificationofthe valve, and can only be achieved ifRL=∞. In practice,we rarely achieve againashighasthis.Valvesarefrequentlyclassifiedbyμasfollows:Lowμ: <8 (6080=2,12B4A=6.5)Mediumμ: 8–30 (Type76=13.8,ECC82=18,6SN7=20)Highμ: >30 (ECC81=65,6SL7=70,ECC83=100,ECC807=150,WE416=250,PD500=1050).

Wecanmeasureμattheoperatingpointbydrawingahorizontallinethroughtheoperatingpoint,whichisequivalenttoRL=∞,andcalculatingthegainasbefore,bynotingtheintersectionswiththegridcurves(seeFigure2.8).

Figure2.8Determinationofμ.

Note that it isusual to ignore the signsof the individualvoltagesmeasured inequationslikethis.Rather thanusing the loadline,we canuse a formula todetermine thevoltagegainAvoftheamplifierstage:

which is ingoodagreementwith thevaluepredictedby the loadline (Av=72).Youwillfindthatμisoneofthemorestablevalveparameters,andvarieslittlewithanodecurrent(afactthatwillbeexploitedlater).However,thismethodisnotideal,sincetheaccuracyofthefinalanswerisdependentonhowaccuratelyyoucandrawtangents. It is,however, thoroughlyrecommendedasacheckonthegeneralaccuracyofyourpredictions.Thesecondvalveparameter,mutualconductance,isdefinedby:

ThemutualconductancegmofavalveistheratioofthechangeinanodecurrentΔIatothechangeingridvoltageΔVg,withanodevoltageheldconstant.

Finally,wecandefinera:

The anode resistance raof a valve is the ratio of the change in anodevoltageΔVatothechangeinanodecurrentΔIa,withgridvoltageheldconstant.

Thereisaveryusefulequationwhichlinksthesethreeparameterstogether:

Obviously, we can rearrange this equation as necessary to find the thirdparameterifweknowtheothertwo,butitisspecifiedthiswayround,becausealthoughwecanalwayspredictμandra reasonablyaccurately fromtheanode

characteristics, we cannot directly predict an accurate value for gm (yettraditionalvalve testersvery rarelymeasureanyparameterother thangm) (seeFigure2.9).

Figure2.9Determinationofgm.

Intheory,tofindgm,wesimplydrawaverticallinethroughtheoperatingpoint(hold Va constant), and measure the change in anode current. However, it isimmediatelyapparentthatthechangefrom1.5 Vto1 Visconsiderablygreaterthanthechangefrom1.5 Vto2 V,andtakingtheaveragevaluefrom1 Vto2Vdoesnotgiveanaccuratefigureofgmattheoperatingpoint.

Using the equation, however, with accurate values of μ and ra (theymust bebecausetheyagreedwellwiththeloadlinepredictionofgain),wefind:

whichmeansthatthepreviousvaluewasalmost8%low.Wewillreturntousegmlater.Aparameterthatisveryoccasionallymentionedisperveance,whichistheratioof the space-charge-limited anode current to the three-halves power of anodevoltage(Child’slaw):

Thepractical significanceofperveance is that ahigh-perveancevalve requiresless anode voltage for a given anode current. Additionally, high-perveancevalvessuchasthe5687canswingtheiranodescloserto0 V,increasingvoltageswingandefficiency.

CathodeBias

Now that we have chosen our operating point and evaluated the dynamiccharacteristics of our amplifier stage, we need to look at practical ways ofimplementing the stage.Whilst we could bias the stage using a battery, it isinconvenient to disassemble the amplifier just to change a battery. However,lithium batteries having a shelf life of 10 years are now readily available, sobatteryreplacementcouldperhapsbelessfrequentthanvalvereplacement.Another way of providing grid bias would be to have a subsidiary negativepower supply and use potential dividers to determine the bias to individualvalves. This is frequently done on power stages, but could cause noise andstabilityproblemswithsmall-signalstages.An alternativemethod is to insert acathodebias resistor between the cathodeand ground, and connect the grid to ground via a grid-leak resistor.Conveniently, thegrid isnowat0 V,soweno longerneedan inputcouplingcapacitor(seeFigure2.10).

Figure2.10Cathodebias.

Tounderstand theoperationof this stage,wewill assume a perfect valve thatdoesnotpassgridcurrentevenifVgk=0.Initially, thereisnocurrentflowingthroughthevalve.If this is thecase, therewillbenovoltagedropacrossthecathodebiasresistor,andthecathodewillbeat0 V.Thegridistiedto0 V,soVgkmustbe0 V.Thiswillcausethevalvetoconductheavily,butasitdoesso,theanodecurrent(whichinatriodeisequaltothe cathode current) flows through the cathodebias resistor, causing avoltagedropacrossit.Thisvoltagedropcausesthecathodevoltagetorise,Vgkfalls,andanequilibriumanodecurrentisreached.We know our operating point, therefore we know anode and, hence, cathodecurrent.We knowwhat value ofVgkwe need. If the grid is at 0 V, then thecathodemustbeat+Vgk.Ifweknowthevoltageacross,andthecurrentthrough,anunknownresistor,thenitisasimplemattertoapplyOhm’slawandfindthevalueof that resistor. Inourexamplewechose toplaceouroperatingpointat182 V.Wecouldreadofftheanodecurrentdirectly,butitismoreaccurateinthisinstancetocalculatethecurrentusingOhm’slaw.(ThisisbecausewecanreadoffthevalueofVawithgreateraccuracy.)

Weknowthatthecathodevoltageis1.5 V,sothecathodebiasresistorwillbe:

Again,notethattheequationdirectlyusedmA,resultinginaresistanceinkΩ.

TheEffectonACConditionsofanUnbypassedCathodeBias

Resistor

Although the cathode bias resistor stabilised and set theDC conditions of thestage,itdidsobymeansofnegativefeedback,soweshouldexpectittoaffecttheACconditionssuchasgainandoutputresistance.Wecanusetheuniversalfeedbackequationtodeterminetheeffectitwillhave.

ThefeedbackfractionβinthiscaseistheratioRk/RL,so:

Thegainhasbeenconsiderablyreduced.Thefeedbackisseries-derived,series-applied,soitraisestheinputandoutputresistances.Sincetheinputresistanceofa valve is virtually infinite anyway, this won’t be affected, but the anoderesistancerawillberaised.Althoughthefeedbackequationisveryhandyforquicklydeterminingthenewgain,itisnotquitesoeasilyusedforfindingthenewra.Lookingdownthroughtheanode,theonlypathtogroundisthecathode,viatheanoderesistancera.Since,inthisdirection,resistancesaremultipliedby(μ+1),weseeaneffectiveanoderesistanceof:

Thevalueofrarisesfrom65 kto223 k.InparallelwithRL,thisgivesanewoutput resistanceof98 k,asopposed to47 k. Incidentally, there isnoreasonwhy we should not calculate the new rafirst and use that new value in thestandardgainformulatodeterminethenewgain:

It is most important to appreciate that the feedback affected only the valve’sinternal ra. The anode load resistor RL was external to the feedback, and

thereforenotaffected.Havingevaluatedthenewvaluesofgainandoutputresistance,wemaydecidethattheyarenolongersatisfactory.WecouldeitherchooseanewvalueofRL,andtryanewoperatingpoint,orwemightevenchooseanewvalve.However,thereisanotheravenueopentous.

TheCathodeDecouplingCapacitor

Theadditionofthecathodebiasresistorcausednegativefeedback,andreducedgain.Thismaynotalwaysbedesirable,sowewillnowconsiderhowtopreventthisfeedback.Because the output signal is derived fromchanging Ia throughRL, and Ia alsoflows throughRk,wemustalsodevelopasignalvoltageacrossRk.Thesignalvoltage across Rk is in phase with the input signal, but because the valverespondstochangesinVgk,whichisthedifferencebetweenVgandVk,wehaveeffectivelyreducedtheavailabledrivingvoltagetothevalve.To restore full gain, we must suppress the feedback voltage produced at thecathode with a decoupling or bypass capacitor. The capacitor should be ofsufficiently low reactance that it is a short circuit at all AC frequencies ofinterest. In conjunctionwith the output resistance at the cathode, this forms alocallow-passfilter(seeFigure2.11).

Figure2.11Cathodedecoupling.

We now need to know what resistance the capacitor ‘sees’ from its positiveterminal toground.Clearly, it sees the resistorRk,but it also sees thecathoderesistanceofthevalve.Theresistancelookingintothecathodeis:

WecanseetheHTsupply(ACground) throughtheseriesresistanceofraandRL,butthisisdividedbythefactor(μ+1)becauseoftheinternalvoltagegainofthestage.Ifwenowputsomenumbersintotheequation,wehave:

Inparallelwiththe1.56 kΩcathodebiasresistorthisgivesatotalresistanceatthecathodeof946 Ω.In audio, we usually consider frequencies down to 20 Hz (although a 32 ftorgan stopwill produce 16 Hz), and large loudspeakers can reproduce them.Therewillbeanumberofstagestotheamplifier,eachwithfilters,sotheeffectiscumulative.Thefilterwillbemadewithelectrolyticcapacitors,whicharenotknown for their initial tolerance or stability of value, so the filter frequencyshouldbemuchlowerthananyotherfilterfrequencyintheamplifierincaseitchanges.Ithasalsobeenarguedthatagoodlowfrequencyresponseisrequirednotmerelytomaintaincorrectamplituderesponse,buttoensurethattheeffectsonphaseandtransientresponse(whichextendin-bandtoafactorof10timesthefilter cut-off frequency) are kept to a minimum. Bearing all these factors inmind,itisusualtodesignforacut-offfrequencyof1 Hz,so:

Notethat hadtobeenteredusingthebaseunitofohmsandthattheequationproducesavalueforC in farads.Theneareststandardvalue to170 μF is220μF, and this iswhatwewould use.Youwill note that quite a large value ofcapacitanceisneeded;valveswithalowerrkarenotuncommon,andrequireacorrespondinglylargervalueofcapacitor.

ChoiceofValueofGrid-LeakResistor

Althoughwehaveshownthegrid-leakresistorinplacepreviously,wehavenotassigned it a value.Historically, it has generally been 1 MΩ for small-signalstages,but somewhat lower forpowerstages. It is inour interests tomake the

grid-leakresistoraslargeaspossible,fortworeasons:• The grid-leak resistor forms a potential divider in conjunction with theoutput resistanceof thepreceding stage and therefore causes a loss of gain.Thislossisgenerallyquitesmall,butitaccumulates,sothatattheoutputofafour-stageamplifier,thegaincouldbesignificantlylessthanpredictedifthislossisnottakenintoaccount.•Alargevalueofgrid-leakresistorallowstheinter-stagecouplingcapacitortobeassmallaspossibleforagivenlowfrequencycut-off.

Onceagain,ifweconsultthevalvedatasheet,wefindthatthereisalimitonthemaximum value of grid-leak resistor. Usually, two values are given, one forcathodebiasandoneforgridbias;thevalueforgridbiasisinvariablylower(2.2MΩversus22 MΩfor theECC83).The reason that thegridbiasvalue is somuchloweristhatthereisnostabilisationofoperatingconditionsinthismode.We set grid voltage, and the anode current is solely determined by thecharacteristicsofthatparticularvalve.The clue to the interaction between the valve and the resistor is in the name‘grid-leak’. In practice, there is always a very small leakage current flowingfromthegridtoground,partlybecausetherewillalwaysbesomecontaminationof the grid with the oxide coating used to form the nearby cathode emissivesurface,butalsobecauseofgascurrent.Gascurrentoccursbecausethereisalwaysresidualgasinthevalve.Brownianmotion ensures that individual gasmolecules are distributed evenlywithin thevalve, so some must be in the electron path. When a high velocity electronstrikesagasmolecule,itmayhavesufficientenergytodisplaceanelectronfromthemolecule’soutershell.Theresultingtwoelectronsthencontinuetheirpathtotheanode,butthegasmoleculeisnowapositivelychargedion(becauseithaslostanelectron)andis,therefore,repelledbytheanode,soittravelstowardsthegrid/cathode. Statistically, as more electrons flow from cathode to anode,randomcollisionsbetweenelectronsandgasmoleculesbecomemorelikely,sopositiveioncurrent towardsthegrid increaseswithanodecurrent.Aseachionstrikesthegrid,anelectronimmediatelyflowsupthroughthegrid-leakresistortodischargeit.Theflowofion-dischargingelectronsisasignificantpartofgridleakagecurrentandproduces a potential across the grid-leak resistor,making the grid slightlypositive. Vgk is, therefore, reduced, and if the value of grid-leak resistor issufficiently high, this fall inVgk becomes significant, and anode current rises.Theincreaseinanodecurrentincreasesanodedissipation,releasingyetmoregas

from the hot structures, further increasing ion current, soVgk falls further, thecathodeemitsmoreelectrons,andtheprocessbecomesself-sustaininguntilthevalveisdestroyed.However,althoughgridioncurrentreducesVgk,whichincreasesanodecurrent,the increased anode current has a counterbalancing effect because it increasesVgkbecauseofthevoltagedropacrossthecathodebiasresistorRk.Mullard[1]publishedamethodfordeterminingthemaximumpermissiblevaluefor the grid-leak resistor under actual operating conditions. To determine themaximumpermissiblegrid-leakresistanceofourECC83amplifier,weneedtoknowRkandgm(Rk=1.56 kΩ;gm=1.54 mA/V).First,theeffectiveDCcathoderesistanceofthecircuitisfoundusing:

KnowingRk(effective)andgm,werefertothegraphtofindtheratiobywhichthemaximumfixed-biasgrid-leakresistancemaybemultiplied(seeFigure2.12).

Figure2.12Maximumvalueofgrid-leakresistor.(AfterMullard[1]).

Interpolationof the curves suggests that this particular circuitmayuse a grid-leakresistance,afactoroffourtimesgreaterthanthemaximumfixed-biasgrid-leakresistance(2.2 MΩ)=8.8 MΩ.Nevertheless, the author has seen even larger grid-leak resistances in somedesigns.

ChoiceofValueofOutputCouplingCapacitor

Thisisactuallysomethingofamisnomer,sinceitactuallyprotectstheinputofthenextstagefromtheanodevoltageofthefirststage,butbecausetheinputofavalve stage is usuallyDC coupled, the coupling capacitor becomes associatedwiththeprecedingstage.Thefirst,andmostobvious,pointtoobserveisthatthecapacitorshouldbeabletowithstand the anode voltage applied to it.What is not so obvious is that itshould also be able to withstand the maximum likely HT voltage. ModernamplifiersarefrequentlybuiltusingsiliconrectifiersfortheHT.Thismeansthatattheinstantofswitch-on,thecathodesofthevalvesmaybecold,causingzeroanode current. Because the HT is unloaded, it rises to its maximum possiblevalue, and this voltage appears directly across the coupling capacitors. If theyfailcatastrophically,thenasthevalvesbegintowarmup,thelargepositivebiasontheirgridscausesthemtoconductheavily.Thevalvesmaythenbedestroyed.Usinghighervoltagecapacitorsmaybeslightlymoreexpensive,butitismuchcheaperthanhavingtoreplaceanexpensivevalve(orloudspeakers).TheonlyotherwayaroundthisistoensurethattheHTisneverpresentbeforethe heaters arewarm.Usually thismeans leaving the heaters on permanently,which may be practical, and beneficial, for pre-amplifiers, but we would notwish to leavepoweramplifierheatersonpermanently.Adelay isneeded, andvalverectifiersarethetraditionalsolution(seeChapter5).Theotherchoiceisthevalueofcapacitanceofthecapacitor.Sincewewilluseeitherplasticorpapercapacitors,whicharestable invalue,wedonotmind ifthey define the low frequency cut-off of the amplifier.However, all the otherargumentsusedforthecathodedecouplingcapacitorstillapply,andsoachoiceof2 Hz for cut-off frequency isnotunreasonable. Incidentally, the traditionalvaluesof1 MΩgrid-leakand0.1 μF forma filterwhose−3 dBpoint is1.6Hz. Somemodern designs use much larger values, and we will consider therationaleforthislater.

MillerCapacitance

So far, we have looked at the external, wanted, components of our amplifierstage.Wewillnowturntoanunwantedcomponent:Millercapacitance.Therewillalwaysbesomecapacitancebetweentheanodeandthecontrolgrid.Ina tetrodeorpentode it isstill there,butgreatly reduced.Thiscapacitance isreflectedintothegridcircuitandformsalow-passfilterinconjunctionwiththeoutputresistanceoftheprecedingstage(seeFigure2.13).

Figure2.13Millercapacitance.

We now have two identical stages of the type that we have just designed,connectedincascadetoformatwo-stageamplifier.Millercapacitanceactslikethis:Whenthesecondvalveamplifiesthesignal,itschanging anode voltage is forced to charge and discharge the anode to gridcapacitanceCag. That charging current cannot flow into the grid (because thegrid is high resistance), so itmust be sunkor sourcedby the preceding stage.Now,supposethatthiscapacitancerequiresacurrentitochargeitto1 V.Weapplya1 Vsteptotheinputoftheamplifier,andtheanodemovesnegativelyby 1 V×the gain of the amplifier, in this case by −72 V. The total voltagechangeacrossthecapacitoristherefore(A+1)V=73 V.Thetotalcurrentrequiredtobesunkorsourcedbytheprecedingstageisnow(A+1)× ior73 i.Wecouldnowreflect thiscapacitance into thegridbysayingthat exactly the same current would flow from the source if there was acapacitancebetweenthegridandgroundthatwas(A+1)Cag;hence,theMillerequation:

It is clear that a quite small value of anode to grid capacitance can have analarmingeffectonthehighfrequencyresponseofanamplifiercombination.Inour particular case, we find that we have a Miller capacitance of 115 pF (Cag=1.6 pF for ECC83/12AX7). In combinationwith the output resistance ofthe previous stage, this gives a high frequency f−3 dB point of 29 kHz. Straycapacitancewillreducethisfrequencyevenfurther.Therearevariouswaystocombatthisproblem.

•Reducetheoutputresistanceoftheprecedingstage.•ReducesignificantlyCagbyscreeningthegridsupportrodsfromtheanode.

•DramaticallyreduceCagbyscreeningtheentiregridfromtheanode(tetrodeorpentode).•Reducethegaintotheoffendinganode(cascodeorcathodefollower).

This problem of High Frequency response is so important that we willinvestigate all four of these methods of improving the performance of thecommoncathodetriodestage.

ReducingOutputResistanceofthePreviousStage

Choosing an E88CC/6922 and operating it correctly reduces the outputresistance to a typical value of 10 kΩ. Ifwe also change the second stage toE88CC/6922, theMillercapacitance is then lower, typically50 pF(due to thegainfallingto30),givinganf−3 dBpointofapproximately300 kHz.However,wehavereducedthecombinedgainofthetwo-stageamplifierfrom5,184(72²)to900(30²).Asanalternative,wecouldplaceacathodefollower(whichwewillinvestigatelaterinthischapter)betweenthetwostages.Acathodefollowereasilyachievesrout≈1 kΩ,soevendriving115 pFofMillercapacitancegivesanf−3 dBpointof1.4 MHz.

Guided-Grid,orBeam,Triodes

Intheefforttoobtainhighμandgmsimultaneously,thespacingbetweenanodeandgridmustbe reduced, forcingCag to rise, and theMiller effect causes thestagetohavehighinputcapacitance.Althoughwemightthinkofthegridasbeingameshoffinewiresbetweenthecathodeandtheanode,ithastobesupportedbyrigidverticalmetalrodswhichmustbeofamuchgreaterdiameterthanthegridwiresinordertodeterminethecathode/gridspacingprecisely.Asanexample,thegridwireofthe417 Atriodeisspecified[2]tobe7.4 μmindiameterandwoundwithapitchof0.065 mmper turn. On dissection, 80 grid wires were counted under a travellingmicroscope.Thewidthoftheanodeneartothegridis≈3 mm,sothetotalgridwire area is 80×3×0.0074=1.78 mm 2.The support rodsweremeasured to be0.875 mmdiameter,thelengthoftheanodeneartotherodsis5 mm,andthereare tworods, so the total rodarea is2×0.875×5=8.75 mm2.Thegridsupport

rodshaveasurfaceareafivetimesthatofthegridwires,andconsequentlyfivetimesthecapacitancetoaflatanode.Valves for use at high frequencies seek to minimise capacitance between theanodeandthesupportrods,hencethebath-tubanodeonthe417A,whichbringstheanodeclosetothegridwiresandavoidstherods,butthisstillmeansthatasubstantial proportion of Cag is due to a structure that has no effect on thepassage of electrons, and could, therefore, be screened from the anode withimpunity. Logically, these should be called screened-grid valves, but the termhadalreadybeenusedfortetrodes,sotheratherlesssatisfactorytermsguided-gridtriodeorbeamtriodewereused(seeFigure2.14).

Figure2.14Dissected417A:Notethesizeandshapeoftheremaininganodesectionrelativetotheactiveareaofthegrid.

Valves such as thePC97,PC900 and6GK5have internal support rod screensand bath-tub anodes, causing Cag to fall to <0.5 pF – a very worthwhileimprovement. Sadly, most of these Ultra High Frequency (UHF) valves weredesignedtobevariable-μvalves,toallowAutomaticGainControl(AGC),andwewillseelaterthatthiscausesdistortion(seeFigure2.15).

Figure2.15Dissected417A:Notetherelativesizeofthecontrolgridsupportstructurecomparedtothegridwires.

TheTetrodeAs described by the patent, the tetrode [3] was invented to overcome thereduction ingain causedby the electric fieldof the anode interactingwith theelectricfieldofthegrid.Anauxiliary,orscreengrid,g2,isplacedbetweentheanode and the grid to screen the changing anode potential from the grid. Tomaintain electron flow to the anode, g 2 is connected to a positive potentialslightly lower than that of the anode so that electrons are attracted to g 2, butmost pass through the (coarse) mesh to be captured by the anode as anodecurrent(seeFigure2.16).

Figure2.16Thetetrode.

Although originally devised to increase voltage gain, the far more importanteffectofaddingg2isthatitscreenstheanodefromthegridatACandgreatlyreduces Miller capacitance, allowing useful amplification at much higherfrequencies. It will come as no surprise to learn that this tinkering with theinternalstructuretoincreasegainchangestheanodecharacteristicsofthevalve(seeFigure2.17).

Figure2.17Anodecharacteristicsofthetetrode.

The kink in the curves is caused by secondary emission. At very low anodevoltages,electronsareemittedby thecathode in thenormalwayandcollected

by theanode.Atslightlyhigheranodevoltages,anelectronmayhit theanodewith such velocity that instead of merely being absorbed by the anode, itdislodges two low velocity electrons, which are easily attracted to the higherpotentialofthescreengrid.Theanodehaseffectivelyemittedoneelectron,andanodecurrenthasfallen.Asanodevoltagerisesstillfurther,althoughelectronsaredislodgedfromtheanode,theyswiftlyreturntotheanodebecausethescreengrid is at a lowpotential relative to the anode, andnot so attractive, so anodecurrentrisesoncemore.Notonlydoesthekinkintheanodecurvescausedistortionofthesignal,butitalso implies negative anode resistance,which can cause stability problems, sothepuretetrodewassoonsuperseded.

TheBeamTetrodeandthePentodeThese two valves sought to keep the advantages of the tetrode (high gain andlow Cag) without the disadvantage of the kinked anode characteristic. Thepentodeworksbyplacingaverycoarsegrid,thesuppressorgridg3,connectedtothecathode,betweeng2andtheanode,inordertoscreeng2fromtheanode.The result of this is that the high velocity electrons emitted from the cathodepass straight through the suppressor grid, but the low velocity secondaryelectronsemittedfromtheanodearescreenedfromg2,andreturntotheanode.Becausesecondaryemissionelectronsfromtheanodearenolongerattractedtog2,thekinkintheanodecharacteristicsofthetetrodeisavoided.Operationof thebeam tetrode isdifferent from thatof thepentode inorder toavoid infringement of the 1928 Philips pentode patent [4]. Instead of theelectronsleavingthecathodefromallpointsofthecompassandflowingtotheanode,theelectronsaredirectedintotwonarrowbeamsofhighelectrondensitybythebeamformingplates,whichareconnectedtothecathode.Eachbeamisfurtherfocussedanddividedintothinhorizontalsheetsbecausetheg1andg2windings are vertically aligned, which increases electron density still further.Electronsattemptingtoleavetheanodebysecondaryemissionarenowrepelledby the incoming flood of electrons and are quickly returned to the anode.Because the dynamics of this space are very similar to the space-charge-stabilised emission from the cathode, it is known as a virtual cathode.Interestingly, the pentode patent hints at a virtual cathode as a means ofsuppressionofsecondaryemission.Some electrons may succeed in leaving the anode and travelling a limiteddistance, and to avoid them reaching g 2, the anode-to-g 2 distance is rather

greater than in the pentode, which is why the anode of the beam tetrode(KinklessTetrode)KT66 is larger than thatof thepentodeEL34,despite theirverysimilarratings.Thenecessaryalignmentoftheg1andg2windingsinabeamtetrodefocussesthestreamsofelectronssuchthattheymostlypassbetweenthewiresofg2,thusreducing g 2 current compared to the pentode,which improves efficiency in apower valve, although there is no reasonwhy a pentode should not adopt thesamestrategy.Inpractice,whenweuseabeamtetrodeorapentode,weseesolittledifference in theirelectricalcharacteristics thatwecan treat thembothaspentodes.(Thorn-AEIclassifiedthePCL82asatriode/beamtetrode,yetMullardclassifieditasatriode/pentode.)The beam tetrode offers some interesting possibilities. For instance, ifwe hadtwo anodes and individually connected beam anodes, we could modulate thevoltagebetweenthebeamanodestocontroltheratioofcurrentsplitbetweenthetwoanodes.The6AR8 is suchavalve, and itwasdesignedmainly forcolourdecoding of video in televisions, but its characteristicswere also exploited byaudiotunersintheRFmixerstageandinthestereodecoder.

TheSignificanceofthePentodeCurves

IfweinvestigatetheanodecharacteristicsoftheEF86small-signalpentodefor,weseethattheanodecurvesarenearlyhorizontal(seeFigure2.15).

Wecanmakesomeusefulobservationsfromthesecurves.Firstly, pentode characteristics arevery similar to transistor characteristics andindicate an anode resistance that is sufficiently high that for most practicalpurposes,itmaybetakentobeinfinite.Theoutputresistanceofapentodestageistherefore≈RL.Secondly,theanodeisabletoswingmuchcloserto0 Vthanthetriode,andsowe can obtain a greater peak-to-peak output voltage. This has significantimplications for efficiency, and makes the pentode a good choice for highvoltagestages.Thirdly, the shape of theVa and Ia curves for the pentode (and transistor) isexponentialsothat:

This relationship not only results in the pentode producing significant oddharmonicdistortion,butalsotheharmonicsextendfurtherupthespectrumthanforatriode.Asanexample,anE55LpentodewasbiassedtoIa=50 mAwitha

4.7kΩanodeloadfroma410 Vsupply.Thestageclippedat≈73 VRMS,soitwas tested for distortion at an output of ≈50 V RMS, whereupon the stageproduced 1.3%TotalHarmonicDistortion (THD), but note that the distortionspectrumcontainssignificantharmonicsuptothe12th(seeFigure2.18).

Figure2.18E55Lpentodedistortionspectrum.

Bycontrast,theshapeofthetriodeanodecurveisapowerlaw:

This equation can be approximated using a binomial series, and although itcontainsbothodd(x3,x5,…)andeven(x2,x4,…)terms, indicatingoddandevenharmonics, the termsdie awayvery rapidly (the author hasnot normallyneeded to look beyond the sixth harmonic when testing triodes). We can,therefore, expect the triode to produce predominantly second harmonicdistortion.Thetypeofdistortionproducedissignificantbecausetheearisfarmoretolerantofevenharmonicdistortionthanofodd,notonlybecausetheearitselfproduceseven harmonic distortion, but also because the higher odd harmonics are nolongermusicallyrelatedtothefundamentalandsounddiscordant.Themeasureddistortionofapentodeamplifier,therefore,needstobemuchlowerthanthatofofa triodeamplifierbecausethesubjectiveeffect issomuchgreater,andsuchamplifiersgenerallyuseplentyofnegativefeedback.

UsingtheEF86Small-SignalPentode

WecannowconsiderhowwewouldusetheEF86.RLischoseninthenormalway,inconjunctionwithloadlinesandthe210 V HT;inthisexample,RL=47kΩandtheoperatingpointisat108 V(seeFigure2.19).

Figure2.19Asmall-signalpentodeamplifier.

Whenwecometocalculatethegain,wefindthattheanodecharacteristicbeginstocurveaswereachitsintersectionwiththeloadline.Itisperfectlyvalidtotreatthe anode curve as a straight line, and toproject this lineontoour loadline inordertofindthesmall-signalgain,thusgivingagaininthisexampleof90(seeFigure2.20).

Figure2.20Anodecharacteristicsanddeterminationofgainofthepentode.

ischoseneitherbyadetailedperusalofthefulldatasheets,orbyobservingthatg2current isgenerallyafixedproportionofanodecurrent.For theEF86,thisproportionis≈1:4.Therefore,iftheanodevoltageandtheg2voltagearetobe similar, theg 2 resistor shouldbe equal to4RL, and180 kΩ is, therefore,appropriate.Theproportionatemethodisquicker,butforpowervalveswemustresorttothedatasheet.Althoughtermedagrid,g2behavesasananodeinthatitreceiveselectrons,anditmust,therefore,havean‘anode’resistance.Weneedtoknowthisresistanceinorder to calculate the value of capacitor required to hold g 2 at AC groundpotential.Unfortunately, thedatasheets forpentodesdonotalwaysgive ,

or , but these can be deduced from triode-connected valve data (g 2connectedtoanode):

Remembering that gm describes the controlling effect of Vgk on Ik, once theelectronshaveleftthecontrolgrid/cathoderegion,theirnumbersarefixed,andthedensityof theg2meshsimplydetermineshow thecathodecurrent is splitbetweenanodeandg2.Thus:

Using the triodecurves for theEF86,atVa=108 V,Vg=1.5 Vandra≈14 kΩ,.This70 kΩisinparallelwith (180 kΩ),givingafinalresistance

of≈50 kΩ,andsofora1 Hzcut-off, =3.3 μF.Forapentode,Ik≠Ia,andwemustsumIa(2.17 mA)and (0.54 mA)tofindIk (2.71 mA), before we can calculate Rk. Vgk=1.5 V, so the cathode biasresistormustbe560 Ω.Evaluatinggmfromtheanodecharacteristics,byholdinganodevoltageconstant,andmeasuringthechangeinanodecurrentforgridvoltageproduceavalueofabout1.95 mA/V.Forthepentode,thecathoderesistancerk=1/gm,andasthisisinparallelwiththe560 ΩRk,wewouldneeda680 μFdecouplingcapacitorfora1 Hzcut-off.Wecanalsousethisvalueofgminanalternativemethodofcalculatingthegain,whichisgivenbythefollowingequation:

Theloadlinegaveagainof90,sotheagreementisgood.Notethatthisequationdoesnotworkfortriodesbecauseitassumesinfinitera.CagfortheEF86isgivenas<50 mpF,whichisaratherquaintwayofwriting50 fF (femtofarads, 10 −15 F). You might wish to consider how Mullardmeasuredavalueofcapacitancethissmallin1955.Clue:Youprobablywouldnotmeasureitdirectly.

Thisisadramaticallyreducedvaluecomparedtothetriode,butbecauseitissosmall, we must now consider stray capacitances that were previouslyinsignificant.Since the control grid g 1 is near to the cathode, it must have significantcapacitancetothecathode,which,sincewehavebypasseditwithacapacitor,isat ground potential. In the datasheet, a value for Cin is given, which is thecapacitance from the grid to all other electrodes except the anode and is,therefore, thevalueof straycapacitancewithin thevalve.For theEF86,Cin is3.8 pF, which gives a total input capacitance (due to the valve) of 8.4 pF.Realistically,weoughttoaddafewpFforwiringcapacitance,soavalueof11.5pFwouldbeareasonabletotalfigure.TheECC83triodegaveavalueof115 pF,sointhisrespectthepentodeis10

times better. In summary, the pentode has greater gain, greater output voltageswinganddramaticallyreducedinputcapacitancecomparedtoatriode.Sowhydon’tweusethemallthetime?We have already seen the undesirable distribution of harmonics in pentodedistortion,buttherealkillerforsmall-signalpentodesisnoise.MullarddescribedtheEF86asa‘low-noisepentode’,andinaverystrictsensethisistruebecauseitislownoisebypentodestandards.Bytriodestandards,itreallyisn’tverygoodbecauseofpartitionnoise.This is the additional noise, compared to the triode, that is generated by theelectron stream splitting to pass either to the anode, or to g 2. This additionalnoise is related to the ratio of anode to screen grid current and to themutualconductanceofthescreengrid;typically,thismakesagivenpentode6–14 dBnoisierthanthepentodeconnectedasatriode.(Connectedasatriode,theEF86isactuallyquiteagoodtriode.)Evenworse,partitionnoisehasa1/ffrequencydistribution,whichmeans that itsamplituderisesasfrequencyfalls,whichhasbeenfoundtobeparticularlyirritatingtotheear.

TheCascodeWhat we would like is a valve, or a compound device, that gives all theadvantages of the pentode with none of its disadvantages – this compounddevice, known as the cascode[5], was invented for use as a high-gain erroramplifier in power supply regulators but quickly became very popular as apentodesubstitute(seeFigure2.21).

Figure2.21Thecascode.

The cascode bears considerable similarity to the pentode in that there is anarrangementofcomponents(R1,R2andC1)thatlooksverymuchlikeascreengridbias supply,and, indeed, this iswhat it is.Thedevicehasaveryhighra,approximately equal to the ra of the lower valve,multiplied by ( μ+1) of theuppervalve.Operation is as follows: The upper valve has an anode loadRL, as usual, butinsteadofmodulatingVgkbyvaryingthegridvoltage,andholdingthecathodeconstant,wevarythecathodevoltage,butholdthegridconstant.Theuppergridis biassed towhatever voltagewe feel is necessary for linear operation of theupper valve and is held at AC ground by the capacitor. This is significantbecause it means that the cathode is screened from the anode by the grid, soMillercapacitanceisnotaproblem.Becausewearechangingthecathoderatherthanthegridvoltage,thispartofthestageisnon-inverting.Althoughtheuppervalvehasagridinthewayoftheelectronstream,itdoesnotdrawcurrent,sopartitionnoisedoesnotoccur.Thelowervalveoperatesasanormalcommoncathodestage,exceptthatithasasitsanodeloadthecathodeoftheuppervalve.Becausethedynamicresistancelookingintothecathodeislow,thegainofthelowervalvetoitsanodeislow,soits Miller capacitance is also low. Another way to view the cascode is to

consider that both the cascode and the pentode seek to screen the changingvoltageacrossRL from thesensitive inputcircuit, and thereby reduceCin.Thepentodedoes this by adding an internal screenbetween the input grid and theanode and directly reducesCag, whereas the cascode grounds the grid of theuppervalve(whichthenactsasascreen)anddrivestheuppercathodefromthelowervalve.Because the lower valvehas a lowvalueof load resistance, itwouldgenerateconsiderabledistortionifitwereallowedtoswingverymanyvolts.Fortunately,mostof thegain isprovidedby theupperstage,andsodistortionof the lowerstageshouldnotbeasignificantproblem.AnimportantpointtonotewithcascodesisthattheonlygeneralpurposevalvethatwasdesignedtoworkwellinacascodeistheECC88/6DJ8orE88CC/6922(specialqualityversion).Tryothervalves,byallmeans,butdonotexpect theperformancetobeasgood.Wewillnowseehowtodesignacascode.Itisusualtooperatetheloweranodeatabout75 V,soifwehavea285 VHT,thisleaves210 Vacrosstheuppervalve.We can choose an anode load for the upper valve and draw a loadline in theusualway.InthiscaseRL=100 kΩandVg=−2.5 V,causingVa=−76.5 V,whichgivesaparticularlylinearoperatingpoint.Theanodecurrentis, therefore,1.34mA(seeFigure2.22).

Figure2.22Choiceofoperatingpointoftheuppervalveofacascode.

Iftheanodeofthelowervalveistobeoperatedat75 VandtheuppervalvehasaVgkof−2.5 V,thenthegridoftheuppervalvemustbeat72.5 V.Sincethegrid of the upper valve does not draw any current, its voltage is set by thepotentialdivider, andcompletelydetermines theconditionsof theupper stage,whichisworkingingridor fixed-biasmode.Westillhavetobecarefulnot toexceedthemaximumpermissiblegrid-leakresistanceoftheuppervalve,whichforanE88CC/6922is1 MΩ,buttheThéveninresistanceofthepotentialdivideris 560 kΩ, so we are well within limits. (We have assumed that the DCresistanceofthepowersupplyiszeroinmakingthiscalculation.)Weonlyneeda0.33 μFcapacitor tomake thegrida shortcircuit togroundas farasAC isconcerned(f−3 dB=1 Hz)comparedto3.3 μFfortheEF86 g2capacitor.Attemptingtoinvestigatethelowerstageusinganodecharacteristiccurvesisnotvery helpful. Instead, wewill use themutual characteristics of anode currentagainstgridvoltage(seeFigure2.23).

Figure2.23Triodemutualcharacteristics.

WeknowthatVaofthelowervalveis75 V,sowecanlookalongthecurveforVa=75 VuntilwecometothepointwhereIa=1.34 mA(upperandloweranodecurrentsareequal);thisistheoperatingpointofthelowervalveandgivesaVgkof about 2.6 V. Plotting the point Va=75 V and Ia=1.34 mA on the anodecharacteristicsgivesVgk=2.4 V,sotheagreementisnottoobad.Fromthis,wecouldtakeanaveragevalueof2.5 V,andcalculatethevalueofRkat1.8 kΩ.Becausethecascodeismadeupofonestagethatisnon-invertingandonethatinverts, theoutput is invertedwith respect to the input.Thegainofacascode,whereV1isthelowervalveandV2istheuppervalve,withequalanodecurrentsis:

This unwieldy equation is commonly approximated to . From theequation,weseethatweneedtofindgmforthelowervalve.Thisiseasilydoneusing the mutual characteristics, by measuring the gradient at the operatingpoint.

Weneedrafortheuppervalve,butwearenotsittingconvenientlyonagridline,sowemustinterpolate(guess).Wecoulddothiseitherbytakinganaverageofthevalueseither sideof theoperatingpoint (if theyare symmetricalabout theoperatingpoint),orwecoulduseaFrenchcurvetodrawanewgridcurvewhereweneedit(quiteagoodmethod).Inthisinstance,wewilltakeanaveragevalue(seeFigure2.24).

Figure2.24Averagingtwovaluesofratofindintermediatevalue.

Therefore,wewillsaythatatVg=2.5 V,ra≈6 kΩ.Attheoperatingpointofbothvalves,μ=32.5.Putting all these values into the equation yields a gain of 214.Using gwould have given a gain of 270, which is 2 dB high; nevertheless, theapproximationisusefulbecauseitquicklytellsyouwhetheritisworthpursuingthedesignanyfurther.Wecannowusethisvalueoftotalgaintocalculatethegainofthelowerstage(ifwewish).This is auseful exercisebecause it allowsus to find thevoltageswingon the lower anode.From this,we can check linearity (whichmight beproblematic) andMiller capacitance.We can read the gain of the upper stagefrom the loadline,whichgivesus againof 30, so thegainof the lower stagemustbe7.1.SinceCag=1.4 pFforE88CC,theMillercapacitancemustbe:

Aswith thepentode,weshouldadd the strays,3.3 pF for the internal (valve)straysand3 pFforexternalstrays, togivea totalvalueof18 pF.This isnotquiteasgoodasthepentodethatwesawearlier,but if thepentodehaduseda100 kΩanodeload,itsgainandMillercapacitancewouldhavedoubledandtheanswerswouldthenhavebeencomparable.

Thevalueofcathodebias resistor iscalculated in thenormalwayfora triode,buttheloadresistanceseenbytheloweranodeissolowastobenegligible,solookingintothelowercathode,wefind:

whichisthesameasforthepentode.Inourexample,weassumedra≈6 kΩandμ=32.5,sork≈185 Ω,andthisisinparallelwithRk=1.8 kΩ,soforourusual1Hzcut-off,werequire950 μF–theneareststandardvalueof1,000 μFwillbefine.Weneednotuseequalvaluesofanodecurrent in theupperand lowervalves.Addinga resistor from theHT to the loweranodeallowsadditional current toflowintothelowervalve.Thisisusefulbecauseincreasedloweranodecurrentincreasesgain(byincreasing )andimproveslinearity(seeFigure2.25).

Figure2.25IncreasingIaofthelowervalveinacascode.

As an extreme example, we might need a low noise, low distortion cascodeusinghalfofa6SN7dual triodeas theuppervalve,sowemightset itsanodecurrentto8 mA(goodlinearityatthiscurrent).However,ifthelowervalvewasa triode-strapped E810F, passing 45 mA, an additional 37 mA would be

required.IfVa=100 VfortheE810FandtheHT=400 V,then:

Ratherthanapplyingfixedbiastotheuppervalve,self-biascanbeimplementedby adding a conventional cathode bias network to the upper valve, plus thenormalgrid-leakresistor,butbypassingthegridtogroundwithacapacitor(seeFigure2.26).

Figure2.26Self-biassedcascode.

The self-biassed cascode reduces sensitivity to power supply noise at theexpenseoflesstightlydefinedDCoperatingconditionscomparedtothefixed-biasvariant.CascodeshavesuchahighoutputresistancethattheyarealmostinvariablyDCcoupled to a cathode follower (whosedetaileddesignwewill investigate veryshortly), and a very elegant modification [6] is to derive the upper grid’s

required bias voltage from a tapping in the cathode follower’s load resistance(seeFigure2.27).

Figure2.27Cascodebiassedfromcathodefollower.

TheadvantageofthisconnectionisthatnotonlydoesitsupplytherequiredDCbiaswithanabsoluteminimumofcomponents(andassociatedtimeconstants),butitalsoappliesnegativefeedbacktotheuppervalveallthewaydowntoDC,reducing its distortion and further lowering the cathode follower’s outputresistance. As pointed out in the patent, the feedback reduces the gain of theuppervalveand,therefore,increasestheresistanceseenlookingintoitscathode,whichincreasesthegainofthelowervalve,makingnoiseintheuppervalvelesssignificant.However, thepricepaidfor this improvementis that increasingthelowervalve’sgaininevitablyincreasesitsMillercapacitance.All topologies that involve operating cathodes at voltages significantly aboveground have problems because of heater/cathode leakage currents and themaximum allowable heater to cathode voltage Vhk (see Chapter 4). It is notuncommon for the cathode of a valve to be unbypassed and, therefore, havesignalvoltagesonit,butinthecascode,thegaintotheuppervalve’scathodeislow,andweareusingthedevicebecauseofitsgoodnoiseperformance,soitislikely that thesignalvoltageon thatcathode isverysmall,perhapsonlya few

millivolts.Leakagecurrentsvia theheater/cathode insulationbecomeworseasVhkrises,sothecombinationofVhk=75 Vandasmall-signalvoltagemeansthattheeffectscanbesignificant.Theauthoroncemadeacircuitusingvalves thatwere ratedatVhk(max)=150 V,operated thevalvesatVhk=120 Vand sufferedlow-frequencynoise,whichwasonlycuredbysittingtherelevantheatersona150 VDCsupply.There isanunderstandable reluctance todo thisbecause itmeans thatwe need two ormore heater supplies, one connected to ground asnormal and the other connected to an elevated voltage.Wewill return to thispracticalproblemlater.

TheChargeAmplifierThepentodeandcascodesoughttominimiseCagbyscreeninginordertoavoidHigh Frequency losses. But a more subtle approach when dealing with anawkward parasitic component is to see if it can be persuaded to perform adifferent function. The charge amplifier was introduced in Chapter 1 as aninverting op-amp configuration, but a triode can be configured to become achargeamplifier(seeFigure2.28).

Figure2.28Triodechargeamplifier.

Thesignificanceofusingatriodeasachargeamplifier is thatCagbecomesanintentional feedback component, making gain independent of frequency.Becausetheamplifierisafeedbackamplifier,wemustfirstdeterminethegainof thecommoncathodeamplifierwithin thefeedback loop,and thenapply thefeedback equation to determine the final gain. In this example, the open-loopgainA0is73.Rememberingthatcapacitivereactanceisinverselyproportionalto

frequency,weinverttheequationfordeterminingthefeedbackfraction:

Gainafterfeedbackbecomes:

Thismaynotseemveryexciting,butthecircuitisparticularlyusefulastheinputamplifier following a condensermicrophone. 30 pF is a typical large capsulecapacitance, and it is this capacitance that is used as Cinput – so a builtmicrophone charge amplifier looks for all theworld like an ordinary commoncathodeamplifier.Notingthatthefeedbackisshunt-derivedandshunt-applied,itactstoreduceimpedancesatthepointofderivationandapplication,soitreducesanode impedance (making the amplifier better able to drive cables) and gridimpedance(makingitlesssusceptibletoleakagecurrents).Stray capacitance to ground attenuates the signal from the capsule, directlydegradingthesignal-to-noiseratioofthemicrophone,butbecausethisamplifiercauses the grid to become a virtual earth, the effect of stray capacitance fromgrid to earth is proportionately reduced by the feedback factor,minimising itseffectonsignal-to-noiseratio.Large capsule microphones are popular for saxophones and singers, both ofwhicharequite loudandmayneedattenuation toavoidoverloadingeither thecapsuleamplifieror themixingdesk.Aswitchedcapacitor fromanode togridincreases feedback, reducinggainwithoutdegradingnoise,and this ishowthecommon‘−10 dB’switchworks.Somedesignersmaypermanentlyincorporatean additional anode to grid capacitor to optimise the amplifier’s gain andfeedback, so please don’t incense Tim de Paravacini by removing them anddestroyingthatdelicatedesignbalance.The condenser microphone is the ideal audio application for the chargeamplifier,yetthereisaverysmallflyintheointment.Thegridstillneedsagrid-leakresistortodefineDCconditions,buttoavoiditcausinglow-frequencylossitmustbeverylarge,and500 MΩisnotuncommon.Wesawearlierthatgridcurrent limits the maximum permissible value of grid-leak resistor to avoidanode current runaway, so valves intended for use as microphone chargeamplifiermustbe selected for lowgrid current.Fortunately, this tends tobe anaturalconsequenceoftheinevitableselectionforlowgridcurrentnoise.

TheCathodeFollowerThe circuits that we have considered up until now have been concerned

exclusivelywithprovidingvoltagegain.Sometimesweneedabufferstagethatprovides high input and lowoutput resistance.The cathode follower [7] has avoltagegainofslightlylessthan1,alowoutputresistance,typically≤1 kΩ,ahigh input resistance (≈500 MΩ in condenser microphones) and is non-inverting.Wewill consider the fixed-biasversionof thecathode follower first(seeFigure2.29).

Figure2.29Fixed-biascathodefollower.

Compared to the common cathode amplifier,wehave changed the position oftheloadresistorsothattheoutputisnowtakenfromthecathode,butthecircuitcan still be analysed in the same way as before, using loadlines (see Figure2.30).

Figure2.30Operatingpointoffixed-biascathodefollower.

RL=100 kΩ,andsowedrawtheappropriateloadline,Vg=−2.5 V,withVa=−81V, because of the excellent linearity in this region. Remembering that Va isactuallytheanode-to-cathodevoltage,thecathodeisnowat285−81 V=204 V,andbecauseVgk=−2.5 V,thegridmustbeat201.5 Vtobiasthevalvetothiscondition.ThisvoltageissetbythepotentialdividersR1andR2.Thecathodefollowerissimplyaspecialcaseofthecommoncathodeamplifierwith100%negativefeedback(parallel-derived,series-applied).Tofindthegainafter feedback, we use our normal technique of measuring the gain from theloadline(Av=28.5),andapplythefeedbackequation:

Since we have 100% feedback, β=1, and the gain of our example becomes28.5/29.5=0.97.Alternatively,we can combine the common cathode amplifier’s gain equationwiththefeedbackequationtocalculatecathodefollowergaindirectly:

Thisequationshowsexplicitly that thegainofan idealcathode follower tendstowardsunityandthatthisisbestachievedifμandRkareaslargeaspossible.WesawearlierthattheACresistanceatthecathodewas:

Butforacathodefollower,RLfromtheanodetotheHTis0,sothisequationisfrequentlyapproximatedto1/gm.Fromtheanodecharacteristics,gm≈5 mA/V;this gives an output resistance of ≈200 Ω. This is not a particularly accurateanswer,sincethemethodofdetermininggmwascrude,butthisdoesnotmatter,since it is usual to operate an audio cathode followerwith ≈1 kΩ resistor inserieswithitsoutputtoensureHighFrequencystabilityintocapacitiveloads–so this swamps the slight inaccuracy. Nevertheless, 1.2 kΩ is a low outputresistanceforavalvestage.Asshown, thestagedoesnothaveaparticularlyhigh input resistancebecausethefixed-biasnetworkisinparallelwiththeinput,althoughthisconfigurationisusefulformakingSallen&Keyactivefilters.Ifweneedahighinputresistance,wemustchangeourbiasarrangements(seeFigure2.31).

Figure2.31Cathodebiascathodefollower.

Wenowhavecathodeorself-biasprovidedbythe1.3 kΩresistor,whosevalueiscalculated in thenormalway.Youwillnote thatbyadding this resistor,wehaveslightlyincreasedthevalueofRLand,indeed,thiswasalsothecaseinthecommoncathodeamplifier,butthis≈1%increasehasanegligibleeffectonDCconditions.At first sight, this configuration is very little better than the fixed-biasconfiguration,astheinputresistanceappearstobeonly1.1 MΩ.However,the

1 MΩgrid-leak resistorhasbeenbootstrapped,which is tosay that theentireinputsignaldoesnotappearacrossit.Itworks like this:Wehave just calculated thegainAv to thecathodeasbeing0.97.We can calculate the attenuation of the potential divider formed by thecathode bias resistor andRL as being 0.987, so the proportion of input-signalvoltage at the lower endof thegrid-leak resistor is 0.96 V in.Now, since theoutputofacathodefollowerisnon-inverting,thismeansthatthereisonly0.04V inacross the grid-leak resistor.The signal current through this resistorwill,therefore,beonly4%ofwhatitwouldhavebeenhadthegrid-leakresistorbeenconnected directly to ground. It presents an input resistance equivalent to 1MΩ/0.04=25 MΩ.Formalisingthisargument:

NotethatAisthegainofthecathodefollower,nottheoriginalloadlinegain.Asimilarargumentcanbeusedtodeterminetheinputcapacitanceofthecathodefollower:

Note that this is anapproximatevaluebecause therewillbe significant strays.UsingourexamplewiththeE88CC:

Weshouldadda fewpF forwiringstrays,aswedidbefore,whichbrings thelikelyinputcapacitanceof thecathodefollowerto4.5 pF,whichisrather lessthanhalfthevalueofthecascodeorpentode.Althoughtheself-biascathodefollowerhasthehighestinputimpedance,itsDCconditions are less stable than the fixed-bias cathode follower that has its gridvoltage defined by an external network. This means that fixed-bias cathodefollowerstendtobeusedinsituationswheretheirlowoutputresistanceandDCstabilityareimportant,suchasdirectlydrivingoutputvalves.Ithasbeensuggestedthatthelinearityofthecathodefollowerisquestionable.Itishardtoseehowthisaccusationcanbetrue,particularlyiftheoperatingpointhasbeenchosencarefully,as in thepreviousexample,since thestageoperatesunder 100% negative feedback. This means that any non-linearity will bereduced in proportion to the feedback factor (1+ βA0), which in our examplegivesareductionof30:1.Nevertheless, it ispossible todoevenbetter.Wementionedearlier thatμwasone of themore stable valve parameters, whereas ra varies considerably with

anode current. This is significant because it is mostly the variation of ra thatcausesdistortion,andwecanseewhythisisifwelookattheequationforthegainofacommoncathodeamplifier:

IfwecouldmakeRLverylarge,ideallyinfinite,rawouldbecomeinsignificantby comparison and could no longer cause distortion. Provided that we havechosen a sensible operating pointwhereμ does not vary greatly,wewill thenhave a very low-distortion buffer. Unfortunately, if we simply makeRL verylarge,wefindthatthereissuchavoltagedropacrossitthatweneedanHTofmorethan2 kV!(seeFigure2.32).

Figure2.32EffectofincreasingRLinacathodefollower.

WeneedawayaroundtheproblemofexcessivelylargevaluesofRL,andtodothisweneedtoexaminesomedefinitions.

SourcesandSinks:DefinitionsAcurrentorvoltagesourceisasupplyofenergy(suchasabattery)capableofsupplying energy into a load whose other terminal is connected to ground,whereasasinkmaycontrol thecharacteristicsofanexternalsourceofenergy,butprovidesnoneofitsown.There are three important aspects that describe the performance of a constantcurrentsourceorsink:•DCaccuracy:Insomeapplications,thedefiningaspectistheaccuracywithwhichaDCcurrentmaybesetandheldunderchangingcircumstances.DCapplicationstendtoinvolvechemistry,suchaselectroplating,wherethemassdeposited is assumed to be directly proportional to the total charge. Thus,provided thatacurrentappropriate to theplatingareacanbeaccuratelyandreliablyset,platingthicknessbecomesafunctionoftimeandcurrent.(Current

wasoncedefinedintermsofthemassofsilverplatedinagiventime.)•Voltagecompliance:This is the rangeofvoltageoverwhich thesourceorsinkisable tomaintainitsdesignedperformance.Theuppervoltagelimit isusuallydeterminedbythemaximumworkingvoltageofthedevicecontrollingthe load, but it may be that power dissipation in that device limits safeoperation before the explicit voltage limit is reached. Thus, a sink mightemployatransistorratedat400 Vand15 W,butifconfiguredasa75 mAsink,only200 Vcouldbeallowedbeforethe15 Wlimitwouldbereached.Thelowerlimit ismoreinsidiousanddefinestheminimumvoltagerequiredacross the source or sink to ensure correct operation. The voltage across asourceorsinkcanbeincreasedfromzerowhilstmonitoringcurrentandatacertainvoltage,thecurrentwillbeseentojumptoitsdesignvalue,andit isverytemptingtotakethisasbeingtheminimumvoltagerequired.However,amore careful investigation monitoring output resistance against appliedvoltagewouldalmost certainlydiscover that ahigherminimumvoltagewasrequiredthanthatsuggestedbythesimplecurrenttest.•Outputresistance:Theoutputresistanceofaconstantcurrentsourceorsinkisideallyinfinite.However,asalreadynoted,thiscannotbemaintainedatallvoltages or power dissipations, so it is a small-signal parameter, eitherdescribedasasloperesistancerslope,orsimplyasanACresistancer.

Audio electronics often needs real-world approximations to constant currentsources and sinks inorder to improve theACperformanceof the surroundingcircuit,sothefollowingdefinitionsarecouchedintermsoftheircommoneffectsonACperformance,eventhoughpracticalimplementationsusingactivedevicesmaybeequallyeffectiveatDC.Aperfectconstantvoltagesource/sinkisashortcircuit(zeroresistance)toAC,and Ohm’s law, therefore, ensures that even an infinite AC current passingthroughitdevelopszeroACvoltageacross it.Althoughactivedevicessuchasvoltage regulators are frequently better, suitably sized capacitors are ofteninescapably used as AC approximations to constant voltage sources/sinks.Common audio examples include the reservoir capacitor in a capacitor inputpowersupply(source),orthecathodebypasscapacitor(sink).Conversely, a perfect constant current source/sink is an open circuit (infiniteresistance) to AC, and even an infinite AC voltage across it is incapable ofdriving any AC current through it. Active constant current sources/sinks arebecomingmorecommon,butinductorswerethetraditionalACapproximationstoconstantcurrentsources/sinks, themainaudioexamplebeingthechokeina

choke input power supply (source) or the primary inductance of an outputtransformer(sink).Although it has been suggested that capacitors and inductorsmay be used asapproximations to perfect sources or sinks, the implication is that topologiestraditionally using these approximations may be replaced by active devices,which can bemore nearly perfect. It is probably true to say that the primarydifferencebetweenavalveamplifierdesignedinthe‘GoldenAge’andamoderndesign is that themodern design is likely to replace passive componentswithactivedevicestoapproximateperfectsourcesandsinksmoreclosely.

TheCommonCathodeAmplifierasaConstantCurrentSink(CCS)Wesawearlier that leaving a common cathode; amplifierwithRk unbypassedcausedratoriseduetonegativefeedback.WecanexploitthiseffectdeliberatelytocreateaCCS(seeFigure2.33).

Figure2.33Constantcurrentsink.

Letussupposethatweneedtosinkacurrentof2 mAusinganE88CCvalveandthatwehave204 VofHTavailableforthesink.WecantreatVa=204 V,Ia=0 mAasoneendofaloadline,andplotthispointonthegraph(seeFigure2.34).

Figure2.34Operatingconditionsofconstantcurrentsink.

PlottingVa=204 V,Ia=0 mAiseasy,butwedon’tyetknowwheretheotherendoftheloadlinewillbe.However,wedoknowapointontheline;weknowthatIa=2 mAattheoperatingpoint,althoughwedonotknowthevoltage.Itisuptoustochooseavoltage,andVa=81 Visagoodchoiceforlinearity.LinearityisstillimportantinaCCSbecausethecompletecircuitwillprobablymodulatethesink’sanodevoltagewithanaudiosignal.Iflinearityispoor,thisindicatesnon-constant ra,which is part of the term that governs theoutput resistanceof thesink.Iftheoutputresistancevarieswithappliedvoltagewhilstitisbeingusedasanactiveloadforanothervalve,itwillcausedistortioninthatvalve.Ifwenowdrawourloadline,wecanfindthecurrentthroughRLwhenVa=0.Fromthis,wecancalculatethevalueofRL,whichisthen60 kΩ.Thenearestvaluetothisis62 kΩ,andthisiswhatwewoulduse.Since Ia=2 mA, we know that the cathode of the valve will be at 124 V.Vgk=−2.5 V,sothegridneedstobeat121.5 V.Thisvoltageissetinthenormalwayusingthepotentialdividerandcapacitorcombination.TheACresistance,lookingintotheanodeofthiscircuit,is:

Forourdesign, thisgivesavalueofslightlymore than2 MΩ.Achieving thisresult with a pure resistance would require a 4 kV HT supply. The ACresistance is inparallelwithCout, andCag causes sinkgain to fall, so the sink

impedance falls as frequency rises. (Cout is the capacitance fromanode to allotherelectrodesexceptthegrid.)

PentodeConstantCurrentSinks[8]

Pentodesare evenbetter asCCSsbecauseof theirhighμ, andareparticularlyusefulwhentheallowablevoltagedropacrossthesinkisquitelow.IfweneededaCCSof10 mA,butwereonlyalloweda100 Vdropacrossit,anE88CCcouldachieveanoutputresistanceofonly≈100 kΩ,whichisstilla10-foldimprovementovera10 kΩresistor,butapentodecandoratherbetter.Ifweleaveevena2 kΩcathoderesistorunbypassed,apentodecanincreaseitsoutputresistance to>10 MΩ.This isastunninglygoodCCS,but itshouldberememberedthatpentodestendtobenoisy,sothiswouldnotbeagoodchoiceinthefirststageofasensitivepre-amplifier(seeFigure2.35).

Figure2.35Pentodeasconstantcurrentsink.

WhenusingapentodeasaCCS,itisvitaltorememberthatthecathoderesistorpassesnotonlythedesiredconstantcurrent,butalso theg2current.Notealsothattheg2decouplingcapacitormustbetakentothecathode,andnottoground.Thisisbecausewewantcathodefeedbacktoincreasera,butwedonotwantthevoltage between g 2 and the cathode to vary, as this would cause positivefeedbackthatwouldreducera.

SomepentodesmakebetterCCSsthanothersbecausetheiranodecharacteristicsare flatter, giving a higher output resistance, or because the flat part of theiranodecharacteristicsswingscloserto0 V.Table2.1showssinglepentodesthatareparticularlysuitableinCCSs.

Table2.1ComparisonofPentodeSuitabilityversusCCSCurrentType Optimumcurrent(mA) Cout(pF) Pa(W)

EF91/6AM6 ≤6 3.1 2.5EF184/6EJ7 8–15 3 2.5EL83/6CK6 15–30 6.6 9EL822 20–45 6 12

Table 2.1 shows optimum currentsmuch lower than Ia(max), partly because athigher currents the anode curves tilt away from the horizontal, indicatingreduced ra, but mostly because the major contribution to output resistanceactuallycomesfromtheunbypassedRk,whosevalueismultipliedbyafactorofgm· ra( μ), which is typically 1,000 or more for a pentode. Higher currentsrequirelessbiasandareducedvalueofRk,thusreducingoutputresistance.Formaximum output resistance, it is better to use a valve with an oversized Pa,requiringalargeRk, thanthatwithaperfectlyratedPa,requiringasmallerRk.Unfortunately, the disadvantage of a CCS operated at very low Ia is thatbecomesasignificantproportionofIk,makingthecircuitinefficient.Asanexample,wemightrequirean8 mACCS.However,thisisthelowerendof efficient operation for an EF184, and the curves show that it is likely torequire , which means that total HT current has been increased by≈38%.Ifthereisonlyonesink,thenthisisn’taproblem,butiftherearemanysuch sinks, this can greatly increase the cost of the HT supply. If we werewillingtoreducethesinkcurrentto6 mA,thiswouldbringitwithinrangeoftheEF91,whichonlyrequires inthisinstance,reducingHTcurrentfrom11 mAto7.55 mA.AlthoughtheEF91doesnothavequitesuchattractivecurvesastheEF184,itisfarcheapertouse,andifHTcurrentislimited,itcanbeworthbendingadesigntoallowitsuse.Optimallybiassed,mostsmall-signalpentodessplitIkbetweenIaand by≈4:1ratio.Thus,8 mAof Ia typically requires2 mAof . It isvery important tocheck that thepentode’sIa,Pa,andespecially arenotexceeded.SuccessfuldesignofpentodeCCSsrequiresfulldatasheetswithcurvesoravalvetester/rigto allowvoltages to be imposed and currents to be determined experimentally(whichismorereliable).IftheCCSistobeusedinastagewithalowsignallevel,itisworthconsidering

hum and screening. The EF184 has an integral metal screen, the EF91 has aconductivepaintscreenontheinsideoftheenvelope,buttheEL83andEL822powervalvesarecompletelyunscreened.

TheCathodeFollowerwithActiveLoadYouprobablyhaverealisedthattherequirementsforthetriodeCCSweresetbythecathode followerdesignedearlier, sowecannowcombine them to formacathodefollowerwithanactiveload(seeFigure2.36).

Figure2.36Cathodefollowerwithactiveload.

BecausethevalueofRLfortheupperstageisnowsolarge,thegainbecomes:

The gain is, therefore, 0.97, which is only a little higher than before, but thedistortion is greatly reduced. It is possible tomake distortion predictions, butthese are of very doubtful value, since real valves do not behave in the nicemathematicalfashionthattheequationsrequiretogeneratesensibleanswers.Gridcurrentcancauseacathode follower tohaveverymuchhigherdistortionthan expected.The author tested a self-biassed cathode follower using a 6S45

with an EF184 CCS active load, and then determined its input resistance bymeasuring the relative loss when driven from a 1 MΩ source resistancecomparedto5 Ω.Sadly,theinputresistancewasnotquiteashighaspredicted,and adjusting the value of grid-leak resistor from 150 kΩ to 1 MΩnot onlychangedtheinputresistanceandslightlychangedIa(indicatinggridcurrent),butalso reduced the distortion at +20dBu from 0.23% to 0.052%. Reducing thesource resistance from 1 MΩ to 24 kΩ further reduced the Total HarmonicDistortion+Noise(THD+N)from0.052%to0.02%.Cathodefollowersareoftenusedasbuffersaftervolumecontrols,sothissensitivitytosourceresistancecanbe significant, particularly because, as we will see in Chapter 7, that somevolumecontrolshavehigheroutputresistancethanothers.Tosumup,acarefullydesignedcathodefollowerwitharesistiveloadproduceslow distortion – replacing this with an active load improves it further, andchallenges test equipment, but for optimum distortion the valve should beselected/testedforlowgridcurrent.

TheWhiteCathodeFollowerNamedafteritsinventor,theWhitecathodefollower[9]isthebasisofalloutputtransformer-less (OTL) power amplifiers because of its low output resistance.The circuit comes in two forms: one self-contained and the other requiring anexternalphasesplitter.

AnalysisoftheSelf-ContainedWhiteCathodeFollower

Thelowervalveisfedwithasignalfromtheuppervalve,which,inturn,itfeedsback into thecathode/gridcircuitof theuppervalve.At the input to the lowervalve,thecircuitmaybeconsideredtobeacascodeamplifier(seeFigure2.37).

Figure2.37Self-containedWhitecathodefollower.

Providedthatμisreasonablylargeandthecathodeisbypassed:

Andtheresistancelookingintothecathodeoftheuppervalveis:

Butthegainofthelowervalveisdevotedtoreducingtheoutputresistanceatthecathodeoftheuppervalve,socombiningthetwoequationsgives:

μisusuallyrathergreaterthan1,evenforpowertriodes,soifwesubstituteμ=gm·ra:

WecannowrecognisetheR·ra termastheinvertedparallelcombinationofRandra.ThisissignificantbecauseitindicatesthatthereisapointbeyondwhichincreasingRhasnoeffectandthatfinaloutputresistanceislimitedbyra:

where

Itshouldbenotedthattworatherdubiousapproximationsweremadetoderivethis result, both of which relied on high μ. The example in Figure 2.36 wasoptimised for low output resistance, and R≈10 ra, beyond which limit nopracticalimprovementispossible.Although superficially completely different, the self-contained White cathodefollowerand the shunt-regulatedpush–pull (SRPP)amplifierdescribed later inthischapterarebothshunt-regulatedamplifiersbecausebothvalvescontributetotheACloadcurrent.RigorousequationsforgainandoutputresistancederivedbyAmosandBirkinshaw[10]areasfollows:

whereV1istheupper(amplifying)valveandV2isthelower(regulating)valve.Using an E88CC as an example, with gm≈5 mA/V and μ≈28, the rigorousequationpredictsrout=6.6 Ω,whereastheapproximateequationisonly4%highat 6.9 Ω despite the two dubious approximations. Experimentation with aspreadsheetrevealsthatthisversionoftheWhitecathodefollowerisunsuitedtolow-μvalves,sincea6080(μ=2)predictsrout≈35 Ω,whichisworsethanwhenused as a standard cathode follower ( rout≈15 Ω).However, a triode-strappedE55L(μ=30)predictsrout<2 Ω,andatriode-strappedD3a(μ=80)shouldeasilyachieve rout<1 Ω. It is easy to become excited about predicted low outputresistances, butwemust always remember that all such equations contain theimplicitassumptionthattheoutputresistanceoftheHTsupplyis0 Ω,whichisnormallyonlyapproximatedbyaregulatedsupply.Since theWhite patent suggested that the circuit was particularly suitable fordrivinganaloguevideocables(whichweretypically75 Ωtransmissionlines),itisnotsurprisingthatthestagemakesanexcellentoutputcabledriverforapre-amplifier.Note that because the feedback that causes the low output resistance is ACcoupled,outputresistancerisesatlowfrequenciesnotto1/gm,butto:

Inthisinstance,routrisesto1.5 kΩ,ratherthan200 Ω,whichiswhatanormalcathodefollowerwouldachieve.Thepracticalimplicationisthatthestagewillnot short circuit low-frequency noise (such as mains hum) induced into theoutputcableaseffectivelyasastagewithatrue6 ΩoutputresistancefromDCtolight.Usually, we do not need to calculate the gain Av precisely, and the generalcathodefollowerapproximationofAv=μ/(μ+1)isperfectlyadequate,butifthestage was to be used as the basis of a Sallen & Key filter, the rigorouscalculationofgainmightbeneeded.

TheWhiteCathodeFollowerasanOutputStage

Theprimary use of theWhite cathode follower is as an output stage forOTLamplifiers.AseriesresistorineitheroftheHTrailsisaseriouswasteofpower,sowemustusetheversionprecededbyaphasesplitter(seeFigure2.38).

Figure2.38Push–pullinputWhitecathodefollower.

Assumingthatneithervalveswitchesoffunderanysignalconditions(ClassA),thegainofthelowervalveis:

Theuppervalvenolongerhasaresistorinitsanodecircuit,sork=1/gm,andthisistheanodeloadofthelowervalve.Substituting:

Multiplyingbygmandsimplifying:

AcathodefollowerwithRk=∞wouldhavethesamegain,andbecausethelowervalvestrivestoproduceexactlythesamesignalasastandardcathodefollowerifitsawRk=∞,thereisnovoltagedifferencebetweenthetwovalves,sotheuppervalvedoes seeRk=∞.However, the input to the lowervalvemustbe inverted,requiringanexternalphasesplitter.Thelowervalvenolongerreducestheoutputresistanceoftheuppervalve,sincewithagainof1itcannotapplyfeedbacktotheuppervalve,whichiswhyOTLamplifiers need considerable global feedback to bring their output resistancedowntoasuitablevaluefordampingmovingcoilloudspeakers.

Theμ-FollowerInventedbyJ.W.Horton[11]in1933,butforgotten,thisisadesignwhichhasattractedconsiderableinterestsinceitsrediscoveryafewyearsago[12].(Thereisnothingnewunderthesun.)Essentially,itisacommoncathodeamplifierwithanactiveload.Unlikethecathodefollower,whereitisarguablewhetherthisisreallynecessary,thecommoncathodeamplifiercandefinitelybenefitfromthissortoftreatment(seeFigure2.39).

Figure2.39μ-Follower.

The topvalve is a self-biassed cathode follower that has its input capacitivelycoupledfromtheanodeofthecommoncathodelowerstage.SincethecathodefollowerhasAv≈1,andisnon-inverting,thesignalat itscathodewillbenearlyequaltothatattheanodeofthelowervalve.Ifthisisthecase,thentherewillbelittle,orno,signalvoltageacrosstheupperresistors.Little,orno,signalcurrentflows, implying a high-resistance active load or constant current source. ThelowervalveachievesvoltagegainAv≈μ,anditproduceslowdistortion(raisnolonger a factor). As a bonus, we have two output terminals, either the directoutput from the lower anode or the low resistance output from the cathodefollower. It should be noted, however, that the high-resistance active loadactually only operates at AC, since the coupling capacitor forms a high-passfilterinconjunctionwiththe(admittedlyhigh)cathodefollowerinputresistance.Iftheuppervalveisaconstantsource(evenifonlyatAC),thenwecanplottheloadlineforthelowervalveasahorizontalline(seeFigure2.40).

Figure2.40Operatingconditionsoflowervalveinμ-follower.

ThisisanexampleofanACloadline,wheretheslopeoftheloadlinedoesnotrelate toDCconditions,although itmustpass through theDCoperatingpoint.Wecanmovethislinetoanyoperatingpointthatwelike.Ifwechooseananodecurrentof2 mA,andbiastheanodevoltageto80 V,thisgivesμ=32.5,andsowewouldexpectagainof≈32.We now have to determine the operating point for the upper stage. We willsupplythecompoundstagefromanHTof285 V,leaving205 Vfortheupperstage.Sincetheanodecurrentsareequal,Iafortheuppervalvemustalsobe2mA.Ifwenowchooseananodevoltagefortheuppervalve(Ihavechosen80V),wecanplot the loadline.AtVa=0,wehavea currentof3.25 mA,whichcorrespondstoa63 kΩtotalcathodeloadfortheuppervalve.Vgkfortheuppervalve is 2.5 V, for Ia=2 mA; we need a 1.25 kΩ cathode bias resistance(1k5//7k5).WehavenowestablishedtheDCconditionsofthestage.Onceweknowthegainofthecathodefollower,wecandeterminethevalueoftheactiveloadthatitpresents,andfinditsinputresistance,whichwillenableustochooseanappropriatevalueforthecouplingcapacitor.From the loadline, the gain before feedback is 29, so the gain of the cathodefolloweris29/30,whichis0.97.Thelowervalveseesananodeloadof:

This gives a value of ≈2 MΩ, so our earlier assumptions about the gain andlinearity of the lower stage were justified.We can use our earlier formula to

determinetheinputresistanceatthegridofthecathodefollower:

Thisgivesaninputresistanceof≈19 MΩ.Ifweneeda1 Hzcut-off, then10nF is perfectly adequate. The cathode bias resistor for the lower valve iscalculatedinthenormalway.Thelowervalve’sraandstraycapacitanceformalow-passfilter,andalthoughthis effect is generally negligible with medium- μ valves such as the 6J5, itbecomessignificantwhenhigh-μvalvessuchasthe7F7areused.Therearetwoways in which we can inadvertently raise ra and cause significant HighFrequencyloss:•Forhigh-μ valves inparticular, thechoiceofoperatingpoint is abalancebetween maximum swing (requiring low Ia, but causing high ra) and HighFrequencyf−3 dBpoint(lowra,butrequireshighIa).

•Althoughthehighvalueofloadresistanceforthelowervalvecausesβtobesosmallthatnotbotheringtobypassthelowercathoderesistorinaμ-followerdoesn’tcausenoticeablelossofgainat1 kHz,itraisesra.

As an example of these points, a μ-follower using a 7F7 as the lower valvesuffered0.9 dBlossat20 kHzduetotheinteractionbetweenexcessiveraandstray capacitances when the cathode bypass was removed (1 kHz gain wasunchanged).An extremely useful secondary advantage of the μ-follower is its excellentimmunitytonoiseontheHTsupply,knownasPowerSupplyRejectionRatio(PSRR).Attheoutputofanycommoncathodeamplifier,PSRRcanbefound:

ThisisquitesimplybecauseraformsapotentialdividerwithRL.FormaximumrejectionofHTnoiseandripple,RLshouldbeashighaspossiblecomparedtora.Apentodehasra>RLand,therefore,hasnorejectionofHTnoise.Cathodefeedbackconsiderablyincreasesra,butdoesnotreducetotalgainbyaproportionate amount and, therefore, destroysHT rejection. In our (bypassed)example,ra for the lowervalve isequal to6 kΩand theactive load≈2 MΩ,resultingin50 dBrejectionofHTnoise,butremovingthebypasswouldraisera

forthelowervalveto47 kΩandreduceHTrejectionto33 dB,despiteleavinggainrelativelyunchanged.Strictly,weshouldincludethelossofthecathodefollowerinanycalculationofgain to the low resistance output (Atotal=μ×Acathode follower), giving a gain of31.5inthisinstance.

TheImportanceoftheACLoadline

Upuntilnowwehavetacitlyassumedthattheinputresistanceofthefollowingstage had little, or no, effect on the performance of the preceding stage. Thiswould not be true if we used the anode output of the μ-follower because thevalue of the following grid-leak (typically ≈1 MΩ) is notmerely comparablewith the value of RL, it is actually less than RL and, therefore, lowers theeffectivevalueofRL from≈2 MΩto670 kΩ.Thishasanegligibleeffectongain,buttreblesthedistortion,sousingtheanodeoutputisnotrecommended.WhilstRg≥10RL,itislegitimatetoignoreitseffectontheprecedingstage,butonceitbecomessmallerthanthis,weshouldconsiderdrawinganACloadlinetoinvestigatewhether itwillcauseaproblem.Stageswithactive loadsmust takeintoaccounttheinputresistanceofthefollowingstage.An accurateAC loadline is easily drawn.Firstwe find theAC load,which isusuallyjusttheanodeloadandthefollowinggrid-leakinparallel.WeknowthattheACloadlinemustpassthroughtheoperatingpoint,soallweneedisasecondpoint.Thesimplestway todo this is tomoveaconvenientnumberof squareshorizontally(changethevoltageby100 Vorso),andcalculatetheincrease,ordecrease, in current through the AC load to give our second point. The linethroughthesepointsisthentheACloadline,soinspectionofthislinegivesthegainandlinearityofthestageincludingtheeffectsofthefollowingloadresistor.

UpperValveChoiceintheμ-Follower

Thereisnoreasonwhytheuppervalveshouldbethesameasthelowervalveinaμ-follower.Asaruleofthumb,theACloadresistanceseenbythelowervalvecanbefoundby:

Maximising rLminimises distortion in the lower valve, but experiment showsthat once rL≥50 ra, there is no further benefit to be gained and it is moreprofitable to investigate thedistortionproducedby theuppervalve.Because acathodefolloweroperateswith100%feedback,increasingμincreasesfeedback

and reduces distortion.However, high- μ valves need a higher value ofVa toavoid grid current, reducing available Va for the lower valve and loweringmaximumvoltageswing.High gm is also useful in the upper valve if the stage is to feed a passiveequalisationnetworkbecausetheresultantlow(butchangeable)routisasmallerproportionofthenetwork’sseriesresistance.The6545Psingletriodehasμ=52andgm≈20 mA/Vatsensibleanodecurrents,butitsmainadvantageastheuppervalveisthatitcanswingVgkcloseto0 Vwithout distortion, allowing a high output voltage swing from a given HTvoltage.When triodestrapped(g2,g3 toa), theD3apentode isalsoagoodchoiceasμ=80, and gm≈20 mA/V is easily achievable even at quite low currents, butsignificantgridcurrentbeginsatVgk≈−1.1 V.TheD3ahasgold-platedpinsandwasproducedintheerawhengoldplatinggenuinelymeantspecialquality.Notonlydoes itmeet itspublishedspecification,but it isveryconsistent fromonesampletoanother.Bycontrast,the(Sovietera)6545Pgenerallyonlyjustmeetsthe lower limits of its specification and is rather variable, although its anodecurvesareextremelylinear.

Limitationsoftheμ-Follower

Althoughtheμ-followerisanexcellentgainstage,itdoeshavelimitations.Wehave seen that it has a low output resistance and low distortion, and it is,therefore, tempting to use it as a line stage to drive long cables or low inputresistancetransistoramplifiers.However, a low-impedance load steepens the AC load line of the cathodefolloweruppervalve.Althoughthisvalvehas100%feedback, thesteeper loadlineslightlyreducesgainand thecathodefollowercanno longerbootstrap thelowerstage’sRLaseffectively,sothelowervalveseesareducedloadresistance,and distortion in the lower valve rises; connection of an external load alwaysincreases distortionwithin aμ-follower.As an extreme example, the rout of a6J5/6J5μ-followerwastestedat0 dBu.At+28 dBu,thestageproduced0.29%THD+N, so itwaspredicted toproduce≈0.01%THDat0 dBu.However, anoutputresistancemeasurementthatdroppedtheoutputfrom0 dButo−6 dBubyloadingitwitha720 ΩresistanceincreasedTHD+Nto0.85%.Ifalow-loadresistancemustbedrivenwithminimumdistortion,theμ-followercanbebufferedbyacathodefollower.Todrivetheloadeffectively,thecathode

followershouldpass≥10 mA,and thevalveshouldbea frame-grid typewithhigh gm and high μ; 6545P and triode-strapped D3a are ideal. The cathodefollowerisahigh-impedanceload,soitcanbedirectcoupledtotheloweroutputof theμ-follower toavoid the inevitabledistortionof theuppervalve in theμ-follower.Forlowestpossibledistortion,thecathodefollowershouldhaveaCCSasitsload.Awell-designedμ-followerentersoverloadverysuddenly.A6J5/6J5μ-followerdrivenfroma51 kΩsourcewasdrivenintogridcurrent,resultinginanoutputof+38.1 dBu(61.6 VRMS)at0.87%distortion.Ahighsourceresistancecauseshardclippingattheonsetofgridcurrent,soweshouldexpectadecayingseriesofoddharmonics.However,becausegridcurrentonlyclipsonehalf-cycleandasymmetry causes even harmonics,we can expect all possible harmonics (seeFigure2.41).

*Figure2.41Distortionspectrumof6J5/6J5μ-followerenteringgridcurrent.

Droppingthelevelby1 dBto+37.1 dBureducedthedistortionto0.54%,andthehigherharmonicsentirelydisappeared(seeFigure2.42).

*Figure2.42Distortionspectrumof6J5/6J5μ-follower1 dBbelowgridcurrent.

Theμ-followerisagainstageandcathodefollowerconnectedinsuchawaythatit provides a CCS load to the gain stage, making it much more linear. Thedownside is that the cathode follower is in series with the gain stage andconsumes excess HT voltage because the (normally triode) cathode followercannotswingtoVa=0,andalsobecauseofthevoltagedroppedacrossRL.Ifwedon’tcombinethetwovalvesinthisway,butinsteaduseasemiconductorCCSload for thegain stageandanother for the (DC-coupled)cathode follower,wecanobtain the samedistortionas theμ-followerbutahighermaximumoutputswing for agivenHTvoltage.Wewill investigate semiconductorCCSsat theendofthischapter.

TheShunt-RegulatedPush–PullAmplifier(SRPP)PatentedbyRCA[13],theSRPPwasdevelopedintheearly1950stobeusedasapoweramplifierormodulatorintelevisiontransmitters,whereitwastypicallyrequired todrive1,100 V pk–pk intoa loadof400 Ω inparallelwith500 pFwith lowdistortion [14]. Farmore distortion can be tolerated in video than inaudio,andthestandardsofvideoatthetimewerecomparativelypoor,so‘lowdistortion’meant≈2%and‘negligibledistortion’meant<1%.AlthoughweareunlikelytousetheSRPPinitsoriginalapplication,itisusefulto understand the problems that the transmitter engineers faced and how they

weresolved.Developing1,100Vpk–pkacross400 Ωwasn’treallyaproblem–itjust needed a large valve, but maintaining that voltage across the 500 pFcapacitance was. The highest frequency produced by the 405 line ‘highdefinition’ system was 3 MHz, and at this frequency, XC≈100 Ω, requiringconsiderablymorecurrentthanthe400 Ωresistance.Theobvioussolutionwastoincreasethestandingcurrentinthestage,butthiswouldhavebeenwastefulofelectricitybecausefullamplitudeHighFrequencysignalsareveryrareinrealpictures(asopposedtotestsignals).Whatwasneededwasameansofsensingwhentheextracurrentwasrequired,andthenallowingasecondvalvetofurnishthat current.A resistor in serieswith the output of the lower valve senses theload current, so the voltage across this is used to drive the regulator (upper)valve. Because the regulator valve could typically quadruple the total signalpower of the stage without requiring any additional standing current, thisstratagem allowed a considerable increase in efficiency – a very importantconsiderationinamplifiersdissipatingkilowattsofheat.Thesametypeofvalveisinvariablyusedforbothupperandlowersections(seeFigure2.43).

Figure2.43Shunt-RegulatedPush–Pull(SRPP)amplifier.

The same current passes through both valves, so the associated cathode biasresistorRk is thesame.FromaDCpointofview, thesectionabove the loweranodeisidenticaltothatbelowit,soeachsectionseeshalftheHTvoltage.Ifwedrawaverticallineontheanodecharacteristicsat285 V/2=142.5 Vandchooseour anode current, this determines the required bias. The −4 V curve crosses142.5 Vat4.5 mA,so4 V/4.5 mA=889 Ω,anda910 Ωresistorisfine(seeFigure2.44).

Figure2.44ChoosingSRPPoperatingcurrent.

Conceivably,differingvalvesordifferingDCconditionscouldbeusedforupper(V2)andlower(V1)valves,inwhichcasethefullequationsderivedbyAmosandBirkinshaw[15]givethegainofthestageas:

Andtheoutputresistancemaybefoundfrom:

TheSRPPisintermediatebetweenthecommoncathodeamplifierwitharesistorasRL,andtheμ-followerwithanactiveRL,butthelowvalueofuppercathoderesistanceRkmeans that thevalueofRL seenby the lowervalve is inevitablyquitelow,implyingthattheSRPPmusthaveAv<μandsignificantlyincreaseddistortioncomparedtoaμ-follower.A pair of typical 6J5GTswhose characteristics had previously beenmeasuredwassetupasanSRPP:μ=21gm=2.95 mA/V

ra=7.11 kΩ.

TheequationspredictedAv=14.3androut=2.3 kΩ.MeasurementfoundAv=13.5

androut=2.3 kΩ.TheSRPPwascomparedwiththeμ-followerbyswappingthesame valves between stages, and testing with identical DC conditions for allvalves. Unsurprisingly, given its heritage, not only did the SRPP deliver asignificantly higher output voltage swing than the μ-follower, but also the μ-followerrequiredahigherHTvoltagebecauseitwastesHTacrossitsadditional10kΩRk(seeFigure2.45).

Figure2.45CircuitsusedforcomparisonofSRPPandμ-follower.

At an output of +28 dBu (19.5 V RMS), the μ-follower produced 0.24%THD+N,buttheSRPPproduced1.32%,anincreaseof15 dB.Aspredicted,theSRPPproducessignificantdistortion,andalthoughthisfallswithlevel,itisstillrather high for use in a pre-amplifier gain stage. The effect ofHT voltage ondistortionat+28 dBuwasalsoinvestigated(seeFigure2.46).

Figure2.46THDversusHTvoltagefor6J5/6J5SRPPat+28 dBu.

Although the SRPP seems a poor choice compared to the μ-follower, it doeshave the advantage that it is DC coupled internally (the μ-follower needs acouplingcapacitortotheuppervalve),andit is, therefore,immunetoblocking(seeChapter3).

Theβ-FollowerTheβ-follower [16] seeks to exploit the advantagesof theμ-followerwith theefficiencyandDCcouplingoftheSRPPstage(seeFigure2.47).

Figure2.47β-Follower.

Replacing the cathode bias resistor with a bipolar transistor allows the large(perhaps10 kΩ)RLtobediscarded,reducingwastageofHT,andallowingthetwovalvestobeDCcoupled.Bipolar transistors are usually treated as if their output characteristics areconstant current, which implies horizontal output curves, but real transistorshavecurvesthatslopeslightly(seeFigure2.48).

Figure2.48ICversusVCEforBC549NPNtransistor.

Lookingintotheanode,avalvemultipliesRkbyμ;similarly,abipolartransistormultipliesanyresistanceintheemittercircuitbyβ,orhfe,sothecurvescanbeflattenedbyaddinganemitterresistor.Sincehfe forasmall-signal transistor islikelytobe≈400,a100 Ωresistorintheemittermakestheoutputresistance1/hoe≈40 kΩ.Thecathodefollowerthenmultipliesthisresistancebyitsμ,perhaps20,togiveRL≈8 MΩ,whichisevenbetterthanaμ-followercanachieve.Theβ-followereasilyachievesrL≥50ra,evenwithalow-μuppervalve,sotheupper valve must be chosen for minimum distortion, otherwise it willcompromisetheexcellentperformanceofthelowervalve.Theβ-followerisanexcellenttestbedfordeterminingirreducibledistortion.Ifthe lower valve is fed from rs≈0, and loaded by rL≈∞, then the remainingdistortionisduetoerrorsinvalvegeometry,suchasunevengridwinding.The6J5/6J5 β-follower shown in Figure 2.47 gave distortion performance thatchallenged the author’s test equipment, with only the second harmonic beingreliablymeasurableat−55 dBbelowthefundamentalatanoutputlevelof+28dBu–allotherharmonicswerebetterthan−100 dB!Intheory,wecouldreplacethebipolartransistoranditsassociatedcomponentsby a depletion-mode junction field-effect transistor (JFET). If the gate isconnecteddirectlytothesource,atypical2SK147becomesa≈9 mAconstantcurrent source. However, rd (the output resistance looking into the drain) istypically<10 kΩ,soitisnotaseffectiveatreducingdistortionastheβ-follower(seeFigure2.49).

Figure2.49μ-Followerwith2SK147JFETconstantcurrentsource.

TheCathode-CoupledAmplifierThe cathode-coupled amplifier was a popular oscilloscope amplifier becausedirectlycouplingacathode follower toagroundedgrid stageproducedanon-inverting amplifier having wide bandwidth; the circuit has recently becomepopularinOTLheadphoneamplifiers(seeFigure2.50).

Figure2.50Thecathode-coupledamplifier.

The amplifier can be considered to be a cathode follower (non-inverting)coupledtogroundedgridamplifier(alsonon-inverting).Thecathodefollowerhas100%negativefeedback,anditsgainbeforefeedbackis:

Feedbackreducesgain:

Combiningthetwotogivethegainafterfeedback:

Lookingintothecathodeofthegroundedgridstage,wesee:

ButthecathodefollowerseesthisrkinparallelwithitsloadresistanceRk,soitsgainbecomes:

Thetotalgainoftheamplifieristheproductofgroundedgridgainandcathodefollowergain:

AsTektronix[17]pointedout,onceRLapproachesra(aswouldbelikelyinanoscilloscope)andμ is large, cathode followergain simplifies to½, implyingatotalgainroughlyhalfthatofacommoncathodestage.Otherwise,providedthatμisreasonablylarge,theRktermbecomesnegligible,andthegainsimplifiesto:

which is slightly lower than the gain we would expect from a conventionalcommoncathodestage,butnon-inverting.Thegroundedgridsectionintrinsicallyhaswidebandwidthbecausethecontrolgrid screens the cathode from the anode, and the cathode follower sectionhaswidebandwidthbecause itdoesnot sufferMillercapacitance fromachanginganodevoltage.Thus,thecombinedamplifierhaswidebandwidth–whichiswhyitwassopopularasanoscilloscopeamplifier.However,thereisapricetobepaidforthisbandwidth.UnlessRLisverylarge,theloadresistanceseenbythecathodefollowerisonlyafewkΩ,whichgreatlyincreasesitssecondharmonicdistortion(H2).Itisfortunatethatthesignallevelat this point is likely to be low, because this load resistance causes very littlegainbefore feedback and, therefore, very little feedback is available to reducedistortion.TheincreasedH2wouldnothavebeenaprobleminanoscilloscopebecause oscilloscope display tubes necessitated push–pull operation, whichcancelsH2.

TheDifferentialPairAllofthecircuitsthatwehavesofarstudiedhavebeensingle-ended,whichistosay that they have only one output. (Theμ-follower-type circuitswere single-endedbecausealthoughtheyhadtwooutputs,theywereofthesamepolarity.)By contrast, the differential pair has two inputs and amplifies the differencebetweenthemtoprovidetwooutputs,oneinvertedwithrespecttotheother;this

makesthedifferentialorlong-tailedpair[18]averyusefulstage.Adifferentialpaircanbemadeusingthebasiccommoncathodetriodeamplifieror with cascodes. (The μ-follower is not suitable because differential pairsattempt toexploit thenormally large ratiobetweenRLandRk.)Forsimplicity,we will analyse the differential pair using the basic common cathode triodeamplifier(seeFigure2.51).

Figure2.51Thedifferentialorlong-tailedpair.

The circuit consists of two identical triodes, often in the same envelope,withtheircathodestiedtogether,passinganodecurrenttogroundviaaCCSandeachdrivingequalvalueanodeloadresistors.SupposethatweapplyaninputsignalsuchthatthevoltageontheanodeofV1risesby1 V.ThecurrentthroughV1must,therefore,havefallen,butsincebothvalves are sitting on aCCS, this can only occur if the current throughV2 hasrisenbyanequalamount.Sincetheanodeloadresistorsareequal,itfollowsthatthevoltageontheanodeofV2musthavefallenby1 V.The outputs of the two anodes are equal in voltage, but one is inverted with

respecttotheother.Returningtotheinputs:ifweshortcircuit toground,andapplyasinewaveto , then the cathode will ‘follow’ that signal because, ignoring the anodeloads, the circuit is a cathode follower. This means that V2 is driven by itscathode,anamplifiedsignalappearson itsanode,and, therefore,anequalandopposite signal appears on the anode ofV1. The argumentworks in the samemannerforasignalappliedto .

GainoftheDifferentialPair

When driven by a signal connected between the two grids, the gain of thedifferentialpairisidenticaltothatofastandardcommoncathodestage,buttheoutputvoltage is foundbetween theanodesof thestage.Therefore, ifwe lookbetweenoneanodeandground,weonlyseehalfoftheoutputvoltage,andthegainappearstobehalved.If we use the differential pair as a phase splitter, and apply the same inputvoltageasbeforebetweenonegridandground,insteadofeachgridseeinghalftheinputvoltage,oneseestheentireinputvoltageandtheothernone.Becausethevoltagedifferencebetween the twogrids is the same, thegain remains thesame.

OutputResistanceoftheDifferentialPair

Providedthattheoutputofthedifferentialpairisnotunbalancedinanyway,routateachterminalisidenticaltothatofasimplecommoncathodeamplifier(ra‖RL).However, ifonlyoneoutputis loaded,theoutputresistancerisesconsiderably.Working backwards from the path to ground (HT supply) via the firstRL,wesee:

ButwenowalsoseeapathRktoground(0 V),whichisinparallelwithrk:

Multiplyingthroughby(μ+1):

Lookingdownthroughthesecondanode,weseerainserieswiththismultipliedbyafactorof(μ+1):

IfwedividebyRk(μ+1),weobtain:

As Rk tends to ∞, the right-hand term on the bottom line reduces to zero,resultinginamaximumvalueof :

ThishighvalueofrawillbecomesignificantwhenweinvestigatethePSRRofthedifferentialpair.IfRL>>ra,thentheoutputresistance(onlyoneterminalloaded)is:

ACBalanceoftheDifferentialPairandSignalattheCathode

Junction

Provided that theanode loadresistorsareperfectlymatched, theonlywaythattherecanbeanACimbalanceat theanodes is ifsomesignalcurrent is lost toground by a finite tail resistance.Thus, an infinite tail resistancewould allowtwo entirely different valves to achieve perfect balance provided their anodeloadswerematched.If the twovalves are perfectlymatched, then theymust have identical gain totheir identical anode loads and there can be no signal at the cathode junction(gridsdrivenbysignalsofequalandoppositepolarity).Iftheyarenotperfectlymatched, their gains must differ, so there must be a signal at the cathodejunction.Ifthetwovalvesarenotdrivenbysignalsofequalandoppositepolarity,theremustbeasignalatthecathodejunction.Thisstatementiseasilyunderstoodbyconsidering the extreme case of a phase splitter (signal at only one grid); theonlywaythevalvewithnosignalonitsgridcanhaveitsVgkmodulatedisby

movingitscathode,requiringasignalatthecathodejunction.The two previous statements show that any imperfection of drive or valvematchingresultsinasignalatthecathodejunction–thereshouldideallybenosignal.Worse, if there isasignal, it implies that thevalvesarebeingforcedtoamplifythatsignalinordertoproducetheiroutputsignal,andanyinterferencesignalatthecathodejunctionwillalsobeamplified.

Common-ModeRejectionRatio(CMRR)

Rather than assuming signals of equal and opposite polarity on each grid,wewillnowconsidertheresponsetoidenticalsignalsoneachgrid.Ifweapply+1V tobothgrids, thecathodevoltagesimply risesby1 V, thecathodecurrentremains constant, and the anodevoltages donot change, becausewehavenotmodulatedVgk.Theamplifieronlyrespondstodifferencesbetweentheinputsordifferential signals. Applying the same signal to both grids is known as acommon-modesignal.Thispropertyof rejectingcommon-modesignals issignificant,since it impliesthatthecircuitcanrejecthumonpowersupplies,orcommon-modehumontheinputsignal,sowewillinvestigateitfurther.ThesignalateachoutputcanbeexpressedintermsofcurrentsusingOhm’slaw:

Eachoutputwillbeanexactinvertedreplicaoftheotherifi1=i2,providedthatthetwoloadresistorsareequal.Therearetwomainwaysinwhichthisnirvanamaybeeroded:•Ifsignalcurrentislostthroughanadditionalpathtoground.Asignalcurrenti1flowingdownV1outofitscathodemustsplit,withsomecurrentbeinglostdownRkandtheremainderflowingupintothecathodeofV2, tobecome i2.However, ifRk=∞, no current can flowdownRk, and i1= i2. Ifμ1=μ2, andRL(1)=RL(2),then:

Thisindicatesthatweshouldusehigh-μvalves,andmaximisetheratioofRktoRL.Asanexample,anEF184constantcurrentsource(rsink=Rk≈1 MΩ)

andE88CCdifferentialpair (μ=32)andRL=47 kΩwouldhaveCMRR≈57dB.•Resultsfromtheaboveequationwillbedegradedifμ1≠μ2,orifRL(1)≠RL(2),oracombinationof thetwo.Withtheeasyavailabilityof low-cost,accuratedigitalmultimeters,mismatchingof loadresistors isavoidable,butmatchingthevalvesisharder.Ifμ1≠μ2,then:

which indicates that high- μ valves are still desirable, but that matching isimportant.

BecausethesimpleequationforCMRRignoresmismatchedvalves,mismatchedloadresistorsandstraycapacitances,anypredictionsofCMRR>60 dBshouldbe treated with caution. Nevertheless, it is handy for checking that your tailresistanceRk issufficientlyhigh toensure thatpredictedCMRR>40 dB,since40 dBisaneasilyachievableCMRRinpractice.

PowerSupplyRejectionRatio(PSRR)

Sincehumandnoiseonthepowersupplylineareacommon-modesignal,theymust also be attenuated by the CMRR. We might also expect the potentialdividerformedbyraandRLtogivesignificantadditionalattenuation.However,ateitherterminal,theonlypathtogroundisviatheotheranodeandRLuptotheHTsupply,whichisexactlythescenarioweinvestigatedwhendeterminingroutwithonlyoneoutputloaded,therefore:

And the attenuation of power supply noise (solely due to potential divideraction)isthus:

IfRL>>ra,weachievethemaximumattenuationof6 dB!Ourpreviousexample(RL=47 kΩandra=4.95 kΩ)attenuatesby5.2 dB, and togetherwith the57dBduetoCMRR,PSRR=62 dB.It is now well worth comparing the PSRR of the common cathode stage, μ-

follower and differential pair (same DC conditions for the amplifying valve)(Table2.2).

Table2.2ComparisonofPSRRforDifferentTopologiesStage PSRR(dB)

Commoncathode(RL=47 kΩ) 20μ-Follower(rL≈742 kΩ) 44Differentialpair(rsink≈1 MΩ) 62

The differential pair is the best, and will remain the best, since an improvedconstant current source for the μ-follower could be adapted to become animprovedCCSforthedifferentialpair.Knowing the PSRR enables us to design power supplies correctly because itgivesanindicationoftheallowablehumontheHTsupply.For example, the second (differential pair) stage of a balanced pre-amplifiermight need the 100 Hz power supply hum to be 100 dB quieter than themaximumexpectedaudiosignal.Atthispoint,thesignalhasnotreceivedRIAA3,180 μs/318 μscorrection, so the level at100 Hz is13 dB lower thanat1kHz.However,peaklevelsfromLPare+12 dBcomparedtothe5 cm/sline-uplevel,sothemaximumaudiosignalat100 Hzis1 dBlowerthanthe1 kHzcalculated signal level at the anode (2.2 V RMS)=2 V. We want 100 dBsignal/hum,butbecause62 dBofthiswillbeprovidedbythedifferentialpair’sPSRR,weonlyneedthehumonthepowersupplytobe38 dBquieter than2V,sowecouldtolerate25 mVofhumonthepowersupply–whichiseasilyachievable.

SemiconductorConstantCurrentSinksThedifferential pair demonstrated the need forCCSs, but the pentodeCCS isprofligatewithHTvoltage (although it is a good sink), and a differential pairwithgridsatgroundpotentialwouldrequireasubsidiarynegativesupplyforthesinkof−100 V.Thisisoftenundesirable,soasolutionisneeded.Unliketheoriginalvalvedesigners,weareinthefortunatepositionofbeingabletousetransistors,andevenop-amps,ifweconsiderthemtobenecessary.Thisisaperfectexampleofwhereatransistorortwocanbeveryhelpful.ThesimplestformofatransistorCCSisverysimilartoourtriodeversion.TheredLEDsetsaconstantpotentialof≈1.7 Vonthebaseofthetransistor.Vbeis≈0.7 V, so the emitter resistor has 1 V held across it – irrespective of itsresistance. We can, therefore, use Ohm’s law to determine the resistancerequiredtoprogrammeaparticularcurrent:

Thus,ifweneedtosink5 mA,wewouldneeda200 Ωprogrammingresistor.TheACresistancelookingintothecollectoris:

In this instance, a BC549C ( hFE guaranteed>420 and 1/ hoe≈12 kΩ) givesrout≈96 kΩ.Note that an expensive 2 W resistor is required to bias theLED(seeFigure2.52a).

Figure2.52Semiconductorconstantcurrentsources.

The simple circuit can easily be improved upon, and since silicon is cheap, itseemsworthwhiletodoso.Therearetwoproblemstobeaddressed.Firstly,thetransistorneedsVCE>0.5 VforittooperateasaCCS,whichisuncomfortablyclosetotypicalbiasvoltagesforhigh-μvalvessuchastheECC83.Secondly,92kΩoutputresistanceisnotespeciallyhigh,andwecandomuchbetter.A transistor cascode is broadly similar to a pentode, but a practical circuitrequires a negative supply, although this may not be a problem in a poweramplifier,becausethereisoftenanegativebiassupplyfortheoutputvalvesthatwecanuse.(Eventhoughthebiaswindingnormallysupplies<1 mA,wireratedfor 1 mA is very fragile, so transformer manufacturers typically use thickerwire, allowing us to draw 10 mA from this winding, and the increase intransformerVAloadingisusuallynegligible.)AcascodeCCShasmuchhigheroutputresistancethanasingletransistorCCS:

TheACoutputresistanceoftheinitialdesignhasbeenmultipliedbythehfeofthe second transistor (assumed tobe400),which improves it from≈96 kΩ to

≈40 MΩ,andthevalueof1/hoe(whichweprobablydon’tknowaccurately)isnownegligible.The qualitieswewant from aCCS are high output resistance and low outputcapacitance–becausecapacitance togroundreducesoutput impedanceathighfrequencies.Alltransistorshaveinternalcapacitancebetweentheircollectorandbase Ccb, and the higher the power and/or voltage rating of a transistor, thehigher Ccb tends to be. Maximising performance at high frequencies meanschoosingthemostfragiletransistorwedareinordertominimiseCcb.However, it is possible to accidentally make Ccb higher than expected (seeFigure2.53).

Figure2.53Collector-to-basecapacitance(Ccb)forBC549.

Ccb is the capacitance across the depletion region between base and collector,anditsthicknessisproportionalto ,soifthere’sachoicebetweenhaving1V and having 10 V across the transistor, choose 10 V – this is anotherjustification for anegative supply.However, amoreobviousadvantage is thatthe negative supply allows the output port to be taken down to 0 Vwithoutlinearityproblems.HighFrequencystabilityofthecascodeCCSisexcellent(seeFigure2.52b).Asshown, thecascodecurrentsink is relativelysensitive tohumandnoiseonthe negative supply because of current changes through the voltage reference.Thecheapestandbestsolutionistoregulatethenegativesupply,perhapsusinga

337three-terminalregulator,butifthereisn’tenoughnegativevoltageavailableforthe4 Vdropneededacrosstheregulator,asecond-bestsolutionistoinsertaconstantcurrentdiodeintothechainthatfeedsthevoltagereference(seeFigure2.52c).ThecascodeCCSiseasilyadaptedtowithstandalargervoltagebyreplacingtheouter transistor (theoneconnected to the load)withahigher-voltage type,butthisgeneratestwonewproblems:•High-voltage transistors inevitably have a lowhfe, and because rout is theproduct of the two current gains and the programming resistor, reduced hfetranslates directly into reduced rout. Don’t over-specify the device – if youonly need to withstand 100 V and dissipate 100 mW, then a 2N5551 (hfe(min)=80) doubles the output resistance compared to an MJE340 (hfe(min)=30).

• If the outer transistor has a significant voltage across it, it probably alsodissipatessignificantpower.Asanexample,120 V×10 mA=1.2 W–whichis too much for a small transistor, forcing an MJE340 and a heatsink.Elsewhere,theauthorhasvilifiedsmallheatsinksontransistors,preferringtousethechassisasaheatsink,butthisistheoneinstancewhereitisessentialtouseanindividualheatsink.Thecollectorofalmostallpowertransistorsisconnected to the case, sowe place an insulatingwasher between it and theheatsink.ForanMJE340,thetransistor,insulatingwasherandheatsinkformacapacitanceof≈8 pF,andoneendofthiscapacitorisconnectedtotheoutputterminalofourCCS.Ifweconnecttheheatsinktoground,weconnect8 pFinparallelwith theoutputofourCCSand reduceoutput impedanceathighfrequencies. Solution: Use an individual heatsink (oriented to lose heatefficiently), do not connect it to ground, and minimise its capacitance toground.

Because we have voltage to spare, some of the lost output resistance can berecoveredbysettingahigherreferencevoltage,allowingahighervalueofRE.The1N4148diodecompensatesforvariationofthelowertransistor’sVbeduetotemperature,butshouldnotbeaddedtoLEDreferencesbecausethetemperaturecoefficientsofVbe andVLED arequite similar, so theyare already temperaturecompensated[19](seeFigure2.52d).It isessential torealise that it isonly theouter transistor(theoneconnectedtothe load) that has to withstand any external high voltage. Not only is itunnecessary to use a high-voltage device for the inner transistor, but itwould

significantlydegradeperformance.High-voltagetransistorsalwayshavelowhfe−40istypicalfortheMJE340–soacascodeCCSrequiredtowithstand+100Vusing apair ofMJE340swouldhave anoutput resistanceone-tenth that ofexactlythesamedesignusingaBC549Castheinnertransistor,simplybecausetheBC549Chas 10 times thehfe of anMJE340.Remember: choose the outertransistor to survive external conditions and the inner transistor to optimiseperformance.TheWilliams[20]‘ring-of-two’circuitworksbyholding0.7 Vacross the120Ω sense resistor. If that voltage rises, due to increased current through theresistor,T1turnsonharder,whichcausesthebasevoltageofT2tofall.T2beginsto turn off, so the current through the 120 Ω resistor and, therefore, the sinkcurrent,isheldconstant(seeFigure2.52e).Beware that because the ring-of-two relies on feedback applied over twotransistors, there is a possibility of oscillation at high frequencies due to straycapacitances. By comparison, the cascode CCS is far less likely to becomeunstable.

UsingTransistorsasActiveLoadsforValves

All the previous sink circuits can bemirrored about 0 V and PNP transistorssubstituted forNPN. If the circuit is then connected to theHT supply, all theprevious sink circuits become constant current sources, allowing a triode toachieveAv=μ.Moresignificantly,theypermitavalvetoachievelowdistortionfromalowHTvoltage.As an example, in common with all high- μ valves, the ECC83 needsconsiderableVabeforeitcanbebiassedoutofgridcurrent;150 Vistypical.Asageneralruleofthumb,RL>2ra,andasra≈75 kΩfortheECC83,wemightuseRL=150 kΩ.IfIa=0.7 mA,wewoulddrop105 VacrossRL,sowewouldneed255 VofHT.Butwemightonlyrequirethestagetoproduceanoutputswingof5 Vpk–pk,somostoftheHTiswasted.Ifwereplacethe150 kΩresistorwithaconstantcurrentsource,thevalveseesamuchhighervalueofRL,andwecansetthe HT voltage independently to accommodate the maximum required outputswing(seeFigure2.54).

Figure2.54Semiconductoranodeloads.

In Figure 2.54, the concept of operating a high- μ valve from a lowHTwastakentotheextremebecausetheauthorneededahighgaindifferentialpairstage(ECC83:μ=100),butonlyhad150 VofpositiveHTavailable.Notethathigh-voltagetransistorsarerequiredtowithstandeitheranodeswingingtowards0 V.At fist sight, thecircuithas twoconstantcurrentsources,both trying todefinethe current in the samewire.The trick is that the cathodeCCS is deliberatelysuperior to the anode constant current sources, enabling it to enforce itsbehaviouruponthem.The anode constant current sources have an output resistance of ≈600 kΩ (hfe=40 andRE=15 k), but the cathode CCS has an output resistance of ≈130MΩ(hfe1=420,hfe2=40andRE=7k5).Thus,fineadjustmentofthecathodeCCSsimply changes the voltage drop across the 600 kΩ output resistance of theanode constant current sources. The output resistance of the anode constantcurrentsourcesdoesn’tchangeappreciablywithtemperature,sothestabilityofthefinalcircuitisdowntothebehaviourofthecathodeCCS.ThecathodeCCS

enforces 0.82 mA, ideally split equally between the anodeCCSs so that eachpasses0.41 mA.ByOhm’slaw,a1 μAchangeincurrentthroughthe600 kΩoutputresistanceofananodeCCSwouldcauseachangeinvoltagedropof0.6V.TheLEDreferencevoltageandordinaryresistorinthecathodeCCScircuitshouldbestableto<1%driftincurrent,resultingin<2.5 Vdriftineachanodevoltage,whichisperfectlyacceptable.Although Zener diodes are normally bypassed to reduce noise, the noisegeneratedbybothdiodes is a commonmodeand is, therefore, rejectedby thenext (differential) stage. On test, the circuit achieved the required differentialswingof7Vpk–pkat1 kHzwithonly0.04%distortion.Acascodegreatlyincreasesrout,flatteningtheloadlineandreducingdistortioninthevalve.Ifwewantedtomaximiseoutputswingandminimisedistortion,wemightoperatea7N7(loctalequivalentto6SN7)atIa=8 mAbecauseμbecomesmorenearlyconstantwhenIa>6 mA.Weassumethatourcascodewillprovideahorizontalloadline,soweplotthisat8 mA(seeFigure2.55).

Figure2.557N7withconstantcurrent8 mAloadline.

Normally,asVarises,wehavetoconsiderthecrampingofcurvesasIafallsandcut-off is approached, but Ia is now a constant, and the only limit to positiveswingisthatthecascoderequiressufficientvoltagetooperatecorrectly.15 Visquiteadequateforthecascode,soa400 VHTwouldallowVatoswingto385V.Looking in theoppositedirectionalong the8 mA loadline,gridcurrent islikelytobeginat≈100 V.Themaximumpossibleswingis,therefore,385−100V=285 Vpk–pk≈100 VRMS.AlthoughthecascodeforcesIa=8 mA,wemustadjustvalvebias tosetVa.At

just over maximum swing, we should clip positive and negative half-cyclesequally, so the operating point should be halfway between themaximum andminimumpermissibleanodevoltages–whichistheiraverage:

Lookingatthecurves,weseethatVgk≈8 VisrequiredtosetVacorrectly,andthiscanbeprovidedbyan8.2 VZenerdiode(seeFigure2.56).

Figure2.56Cascodedsemiconductoranodeload.

Sincethestageisintendedtoswinglargevoltages,noiseisnotaproblem,soitisnotessentialtobypasstheZenerdiodewithacapacitor.If there is 242.5 V across the valve, then there is 147.5 V across the lowertransistor,soitmustdissipate1.18 Wwhenquiescent.WhenVaswingsto100V,thetransistormustwithstand285 Vat8 mA,soitmomentarilydissipates2.28 W, and it might seem that this is the required rating of the transistor.However,theflatloadlinehasreduceddistortionalmosttozero,sothepositiveandnegativeswingsareequal,andtheaveragepowerdissipatedinthetransistoroveronecycleofaudioisequaltothequiescentpower.

As before, it is only the transistor nearest the valve that must be able towithstand high voltages and dissipate significant power, so the additionaltransistorcanbeasfastandfragileaswelike.

OptimisingroutbyChoiceofTransistorType

Table2.3comparestransistorsthatareusefulinsupportcircuitryforvalves.

Table2.3AbbreviatedDataforBipolarTransistorsUsefulinValveSupportCircuitry

VCE(max):Themaximumallowablevoltagebetweencollectorandemitter.(Therearevariouswaysofspecifyingthislimit,sounlessyouknowyourprecisecircuitconditions,itiswisenottoexceed2/3VCE.)

IC(max):Themaximumallowablecollectorcurrent.

Pmax:Themaximumallowablepowerdissipationinthedevice(P=IC×VCE).

hFE(min):MinimumDCcurrentgainfrombasetocollector.(Theauthor’smeasurementssuggestthathFEisgenerallydoublethemanufacturer’sspecifiedminimumvalueatthetypicalcurrentsrequiredbyvalves.)fT:ACcurrentgainhfefallswithfrequency.AtfT,hfe=1;thisisknownasthetransitionfrequency.

1/hoe(typ):ThisisthetypicalACresistance(equivalenttora)seenlookingintothecollector.Itisveryrarelyspecifiedbymanufacturers,sothesefiguresweremeasuredonacurvetraceratVCE=10 VandIC=10 mAtoallowcomparisonbetweenthetypes.PNPtransistorstendtohavealowerEarlyvoltagethantheirNPNcounterparts,so1/hoeislowerandfallsfasterathighercurrents.

VCE(max)(V) IC(max)(mA) Pmax fT hFE(min) 1/hoe(typ)(kΩ)

BFR90 NPN 15 25 300 mW 5 GHz 40 5BC549C NPN

30 100 500 mW300 MHz 420 12

BC558B PNP 200 MHz 220 62N3904 NPN

40 200500 mW

250 MHz 10015

2N3906 PNP 625 mW 52N5551 NPN 160 600 625 mW 100 MHz 80 35MPSA42 NPN

300 500 625 mW 50 MHz 4050

MPSA92 PNP 35MJE340 NPN

300 500 20 W10 MHz

30150

MJE350 PNP 4 MHz 50

Output resistance at low frequencies is partly determined by 1/ hoe, but isdominatedbyhfe,sinceanyresistanceintheemittercircuitismultipliedbyhfe.Impedanceathighfrequenciesisshuntedbythecapacitanceseenatthecollectorof the transistor, which will partly be determined by strays, but also by thetransistor itself. In general, high-voltage/high-power transistors have a largersilicon die area, and greater capacitance, which is reflected in their lower fT.Additionally,fTvariessignificantlywithIC,andoperatingatransistorbelowitsoptimum IC could reduce fT by a factor of five. If in doubt, download thetransistor’s datasheet from the Internet – all the semiconductor manufacturershave excellent websites. As a consequence of these considerations, a smallcascode CCS would ideally use two BC549Cs, or if low output capacitance(≈0.5 pFexcludingstrays)wasessentialandsufficientvoltagewasavailable,a

triple cascode composedof aBFR90with twoBC549Csbeneath it. It is onlycritical for the outer transistor to have low output capacitance because thecapacitancesoftheothertransistorsareatlowerimpedancepoints.AnybipolartransistorneedsaminimumVCEforittooperatelinearly.Foralow-voltage transistor at currents ≤30 mA,≈1 V is sufficient, but higher currentsmayrequire2 V(seeFigure2.57).

Figure2.57ICversusVCEfor2N3904transistorshowingminimumVCErequired.

High-voltagetransistorssuchasMPSA42orMJE340mayrequireVCE>2 V.ACCSinadifferentialpairoperatingasaphasesplitterhashalf theinputsignalacross it, so this point can become significant. In a cascode sink, the lowertransistorhashardlyanyACsignalacrossit,soitcanoperatewithonly2–3 VDC,leavingtheremainingDCfortheuppertransistor,whichsupportsthebulkoftheACsignal.

Field-EffectTransistors(FETs)asConstantCurrentSinks

FETsaredescribedasbeingdepletionorenhancementmode.Anenhancementmodedevice needs bias similar to a bipolar transistor to turn iton,whereas adepletionmodedeviceneedsbias similar toavalve to turn itoff.BothcanbeusedformakingCCSs,butadepletionmodedevicecanbeself-biassed,whereasthe enhancement mode device requires an external voltage, making it morecumbersometouse.‘Constantcurrent’diodesareactuallydepletionmodeFETswith their gate and source tied together. They tend to have a low maximum

voltage,anddisappointinglylowsloperesistancefortheirprice.Asstatedearlier,theoutputcapacitanceofanyconstantcurrentcircuitmustbeminimisedifitistomaintainitsperformanceathighfrequencies,andthatmeanschoosing transistors with low output capacitance. Sadly, many high-voltageFETs simply aren’t suitable for valve electronics because of excessive outputcapacitance. As an example, the 700 mW power rating of the ZVN0545Asuggests that itought tobeusefulbut itactuallyhashigheroutputcapacitancethanthe15 W(TO220)DN2540N5.Thereasonfor this is thatsemiconductormanufacturers make far fewer different devices than you think – they justpackagethediesdifferently.Thus,theDN2540N3isthesamesilicondie,butinaTO92package,reducingitspowerratingto1 W.Happily, the400 V15 WSupertexDN2540N5depletionmode JFET isverynearly ideal for supporting valve audio. Unfortunately, the phrase ‘devicevariation’ was invented for FETs and never more so than for the voltageVGS(ID=0) required to turn the device on (or off); Supertex specify a spread ofVGS(ID=0)from−1.5 Vto−3.5 V.Fortunately,it’seasytomeasureVGSforanindividualdeviceunderanyoperatingconditions,sodevicescanbematchedorothercircuitvaluescanbedeterminedforaspecificdevice(seeFigure2.58).

Figure2.58ThisjigallowseasydeterminationofVGSforanyFETconditions.

Thedrainofthedeviceisconnectedtoapositivesupplyhavingthesamevoltageexpectedinthefinalcircuit.Thegate isconnectedtogroundviaa1 kΩgate-stopper resistor to prevent RF oscillation. The source is connected to aconvenient negative supply via a programmable CCS adjusted to the required

current. A Digital Volt Meter (DVM) connected between ground and sourcemeasuresVGS.Ifwehadmorethanonedevice,wewouldquicklyrunthemallthroughthetestjigtofindeachindividualVGS.DeviceswithsimilarVGSwouldbedeemedtobepairs.

DesigningConstantCurrentSinksUsingtheDN2540N5

TheverysimplestCCSusingtheDN2540N5islittlemorethanthecontentsoftheconstantcurrentdiodevilifiedearlier(seeFigure2.59).

Figure2.59ThesimplestJFETCCS.

The carbon gate-stopper resistor prevents Very High Frequency (VHF)oscillation, and the source resistor programmes the current.Unfortunately, thevalue of the source resistor has to be found empirically for eachDN2540N5,usingthetestjigofFigure2.58.Alternatively,avariableresistorcouldbeusedandAdjustedOnTest(AOT),butwestillneedtoknowtheapproximatevaluerequiredinordertobuythecorrectvalueofvariableresistorandifaccidentallyset to0 Ωatswitch-on, thesaturationcurrentmightcausedamage.Itreallyiseasier(andcheaper)tousethejigandfitafixedresistor.As an example, wemight want to use a DN2540N5 as a CCS shared by thecathodesofapairofEL84s.WeknowthatwhentheEL84sareworking, theircathodeswillbeat≈11 Vandwillpassa totalof80 mA.TheprogrammableCCS probably needs aminimum of 6 V across it to operate correctly, soweconnect it toanegativesupplyofperhaps−9 V.Wethenapply+11 Vto thedrain of our Device Under Test (DUT), and using an ammeter adjust theprogrammable CCS to draw 80 mA through the DN2540N5. Having set therequired current,wemeasure the voltage between 0 V and theFET’s source.(Wedon’tattempttogenuinelymeasureVGSontheFETbecauseconnectingaDVMtoitwillalmostcertainlycauseoscillation,soweassumezerogatecurrent

and measure from 0 V.) Perhaps, we find that for our particular sample,VGS=−1.873 VatIds=80 mA.AllweneedtodototurntheJFETintoa80mACCSforourEL84 is toadda source resistor thatwilldrop1.873 Vwhen80mApassesthroughit(justlikeatriode),1.873 V/0.08 A=23.4 Ω.Theneareststandardvalueof24 Ωwillalmostcertainlydo.LikethepentodeCCSsweinvestigatedearlier,theFETmultipliesthevalueofits programming resistor by μ. Unsurprisingly, μ is not given by themanufacturer,butcanbefoundfromtherelationship:

Thedrainsloperesistancerdscanbefoundfromthedevicecurvesbymeasuringoutput currents on one VGS curve at two widely spaced voltages (see Figure2.60):

Figure2.60DeterminingFETrdsisjustlikedeterminingpentodera.

Themutual conductancegm atVds=100 V can also be found from the devicecurves:

Notethatalthoughthisvalueofgmismuchlowerthangivenonthedatasheet,itisfarhigherthanavalvecouldachieveatthesamecurrent.Combiningthetwovalues,weobtainμ≈4,500,whichisalittlehigherthanwemightexpectfromapentode.More significantly, a 39 Ω programming resistor in this FETwouldproducea≈40 mACCShavinganoutputresistanceof175 kΩ.Toputthisinto

context, a genuine 175 kΩ resistorwould drop 7 kV rather than 100 V anddissipate282 Wratherthan4 W.Thepreviousworked examplewasgivennot to suggest that such aprocess isneeded,buttoshowjusthowgoodaCCScanbemadewiththeDN2540N5.Nevertheless,considerableimprovementispossible,andlikethesimplebipolartransistor,thecascodeisthewaytogo.RememberinghowthesingleBJTCCSevolvedintoacascode,wecouldaddavoltagereferenceandsecondFET(seeFigure2.61aandb).

Figure2.61EvolutionoftheJFETcascodeCCS.

Unfortunately, by adding the voltage reference, we lose the very desirablepropertyofthecircuitbeingatwo-terminaldevice.BecausetheDN2540N5isadepletionmode device, the voltage reference is not strictly necessary, andwecoulduseoneDN2540N5as the reference resistance for theother (seeFigure2.61c).However, there are disadvantages because the lower device in the cascode isforcedtooperatewithaverylowVds,buttheycanbeamelioratedbyreturningtheupperdevice’sgatestoppernotto0 Vbuttothesourceofthelowerdevice(seeFigure2.61d).Thissimplecircuitisdeservedlypopularbecause(beingtwo-terminal)itcanbeused equally well as an anode load or as the cathode tail resistance in adifferentialpair.Theprogrammingresistanceismultipliedbybothamplificationfactors,andeventhoughthelowerdevice’sperformancesuffersduetothelowVds,ourpreviousexampleislikelytoimprovefrom≈175 kΩto≈30 MΩ.However, thingsarenotquiteas rosyas theymight seem.Thehigh resistanceappliesatDC,butnotatACbecauseofoutputcapacitanceCOSS[21](seeFigure2.62).

Figure2.62COSSoutputcapacitanceoftheDN2540.

Ascanbeseenfromthegraph,COSSisalarminglyhighatlowvoltagesanditisnotuntilVds>15 Vthat itfalls toitsasymptoticvalueof≈12 pF.Fortunately,wewould always operate atVds>15 V (preferably 40 V, ormore) because aBJTcascodeisabetterchoiceatlowervoltages.AnEF184pentodeCCScouldachieveanoutputcapacitanceof3 pF,butonceweaddtypicalstraysof3 pFtoboth circuits, the valve advantage degrades to 6 pF against 15 pF. Thissomewhat poorer output capacitance is the price we pay for the undoubtedconvenienceofatwo-terminalCCS.Thedevicehasamaximumcontinuouscurrent ratingof500 mA,so itshouldcomeasnosurprise to learn thatperformancedegradesat lowcurrents. Ifyouneed a current <10 mA, then you owe it to yourself to see if there’s analternativesolutionbecausethedeviceismuchbetter>10 mA,andat25 mAitreallycomesalive(routofacascodeCCSat25 mAwasfourtimesthatat10mA,allotherfactorskeptconstant).

References[1]Mullard.Book2(part1):receivingvalvesandtelevisionpicturetubes.

Generaloperationalrecommendations.Mulland,Londen1969:17.[2]Gewartowski,JW;Watson,HA,Principlesofelectrontubes.(1965)Van

Nostrand;pp.112–21.

[3]Improvedvacuumelectricdischargeapparatushavinganincandescentcathode.Siemens&HalskeAktiengesellschaft.BritishPatent145,421;1921.

[4]ImprovementsinorrelatingtocircuitarrangementsanddischargetubesforamplifyingelectricoscillationsNVPhilips.Gloeilampenfabrieken.BritishPatent287,958;1928.

[5]Hunt,FV;Hickman,RW,Onelectronicvoltagestabilizers,RevSciInstrum10(January)(1939)6–21.

[6]JohnsonWZ.Cascodeamplifier.USPatent4,647,872;1987.[7]BlumleinAD.Improvementsinandrelatingtothermionicvalvecircuits.

BritishPatent448,421;1934.[8]Puckle,OS,Timebases.1sted.(1943)Chapman&Hall;p.92;2nded.

Wiley,NewYork,1951.p.129.[9]WhiteE.Improvementsinorrelatingtothermionicvalveamplifiercircuit

arrangements.UKPatent564,250;1940.[10]Amos,SW;Birkinshaw,DC,Televisionengineering:principlesand

practice.Generalcircuittechniques.Vol.4(1958)Iliffe;p.264.[11]HortonJW,JFranklinInst.Vol.216.December1933.[12]Kimmel,A,Themustage,GlassAudio5(2)(1993)12.[13]BalancedDirectandAlternatingCurrentAmplifier.USPatent2,310,342.9

February1943[filedNovember1940].[14]Cooper,VJ,Shunt-regulatedamplifiers,WirelessEngineerMay(1951)

132–145.[15]Amos,SW;Birkinshaw,DC,Televisionengineering:principlesand

practice.Generalcircuittechniques.Vol.4(1958)Iliffe;p.250.[16]Ignacio,Vilá,Thebetafolloweramplifier,GlassAudio10(4)(1998)1.[17]Typicaloscilloscopecircuitry.Reved.Tektronix.1966.p.7-1.[18]BlumleinAD.Improvementsinorrelatingtothermionicvalveamplifying

circuitarrangements.BritishPatent482,740;1936.[19]Lefferts,PA,LEDusedavoltagereferenceprovidesself-compensating

tempcoefficient,ElectronicDesignFebruary(1975)92.[20]Williams,P,Ring-of-tworeference,WirelessWorldJuly(1967).[21]DN2535,DN2540datasheet.SupertexInc;2001.

RecommendedFurtherReading

•Yarwood,J,Anintroductiontoelectronics.(1950)Chapman&Hall;Quiteasmallbookcoveringmostelectronicprinciplesbutmajoringonthephysicalbackgroundbehindthem.Essentialreading.

•Valley,GE;Wallman,H,Vacuumtubeamplifiers.(1948)McGraw-Hill;NowreprintedbyAudioAmateurPress(2000).Averygeneralbookrangingfromaudiothroughnuclearpulseamplifierstoradioandmodulation.Hasagoodsectiononnoise.

•Terman,FE,Electronicandradioengineering.4thed.(1955)McGraw-Hill;Asimpliedbythetitle,majorsonradiobutcontainsplentyofgeneralelectronicprinciples.

•Reich,HJ,Theoryandapplicationsofelectrontubes.(1939)McGraw-Hill;Asimpliedbythetitle,fundamentalelectronicswithaudioandradioapplications.AnidealcounterparttoTerman.

•Langford-Smith,F,Radiodesignershandbook.4thed.(1953)Iliffe;Generallyconsideredtobethebibleofvalveaudio,especiallyasitcontainsconsiderabledetailonoutputtransformerdesign.However,manyoftheaudiocircuitsarecrudebymodernstandards,andtheunderstandingofloudspeakersisflawed.

•ReichHJ.Principlesofelectrontubes;1941.NowreprintedbyAudioAmateurPressUS.(1995).Readilyavailable,butnotoutstanding.

•Ryder,JD,Electronicfundamentalsandapplications.3rded(1964)Prentice-Hall;Asshouldbeexpectedfromabookwrittenatthetransitionfromvacuumstatetosolidstateelectronics,considerablespaceisgiventoearlytransistors.However,thestrengthofthisbookisthataprincipleexplainedinonetechnologyisthenshowntobegeneral.

•Amos,SW;Birkinshaw,DC,Televisionengineering:principlesandpractice.Video-frequencyamplification,Vol.2.(1956)Iliffe;Ignoretheword‘video’inthetitle.LucidlywrittenaspartoftheBBC’sinternalengineeringtraining,thisbookanalysesanumberofcircuitscommontovideothathavebeenstolenbymodernaudio.

•Alexander,RC,Theinventorofstereo:thelifeandworksofAlanDowerBlumlein.(1999)Focal;Notanengineeringtome,butaveryreadablebiographyofageniuskilledattheageof39havinggenerated128fundamentalpatents.Blumleininventedmostofaudioandvideoand(asifthatwasnotenough),thedifferentialpairandstereo.

•Burns,R,ThelifeandtimesofADBlumlein.(2000)TheInstitutionofElectricalEngineers;TheotherbiographyofBlumlein,thistimewithmore

ofanengineeringbias.Readthetwoasapair.

Chapter3.DynamicRange

DistortionandNoise

In engineering terms, dynamic range is the ratio between the largest and thesmallest signals, and it is primarily wide dynamic range (not bandwidth) thatdistinguishesqualityaudiofromrubbish.Providedthat the largestsignal isnotclipped,maximisingdynamicrangebecomesaproblemofminimisingthethreeunwantedsignalsthatotherwisemaskthesmallestwantedsignal:•Distortion•Randomnoise• Artificial interference, frequently referred to as ElectroMagneticCompatibility(EMC).

EMC is largely a construction issue andwill be considered inBuilding ValveAmplifiers,sothischapterwillinvestigatehowtominimisedistortionandnoise.

DistortionTo investigate and minimise distortion, we must begin by looking at thefundamentals of distortion measurement. Even designers of test equipmentwould probably concede that this is not the sexiest of topics, but unless weunderstandhowerrors can creep into ourmeasurements,wewill not have theconfidence tocompare the resultsofonemeasurementwith thoseof theother,leavingusunabletotestandimproveourdesigns.

DefiningDistortion

Althoughwemaygliblyusetheword‘distortion’whiletalkingaboutamplifiers,thereareactuallytwodistincttypesofdistortion.Linear distortions do not change with amplitude. If we consider the transfercharacteristicofadeviceproducinglineardistortion,itisastraightline–hencethetermlineardistortion(seeFigure3.1a).

Figure3.1Transfercharacteristicsandthedistortiontheyproduce.

Althoughadevicecausinglineardistortionchangestheshapeofthewaveform,therearenoadditionalfrequenciesattheoutputofthedevice.Lineardistortiontypicallycauseserrorsintheamplitudeagainstfrequencyresponse–andthisisthewaythatitisusuallyassessed.However,itisperfectlypossibletochangetheshapeofawaveformwithoutchangingtheamplitudeagainstfrequencyresponseby distorting the time at which frequencies arrive – loudspeaker crossoversystems without delay compensation inevitably generate this distortion. Theshapeofasquarewave’sleadingedgeisparticularlysensitivetotimingerrors,so an oscilloscope quickly reveals problems. Alternatively, timing errorsbetweensinewavesofdifferingfrequenciescanbedeterminedbymeasuringthegradient of a plot of phase against frequency (linear scale for frequency).Deviationsfromtheexpectedstraight line implyphaseerrors–hence the termlinearphaseforanidealdevice.Unsurprisingly, the transfer characteristic for non-linear distortion is not astraight line, and a device causing non-linear distortion has frequencies at theoutputthatwerenotpresentattheinput(seeFigure3.1b–d).

MeasuringNon-LinearDistortion

Wecanassessthelinearityofadeviceintwofundamentalways:•Weplotthetransfercharacteristicdirectly.Sincethedefinitionofnon-lineardistortionwas that the transfer characteristic should deviate from a straightline,wecouldmeasure thedeviations. Inpractice, this isapoormethod for

analogueaudio (althoughgood forconvertersbetweenanalogueanddigital)becausethesmalldeviationsproducedbyhigh-qualityaudiomakeitdifficulttokeepmeasurementuncertaintiesbelowthedeviations.•Welookforfrequenciesattheoutputofthedevicethatwerenotpresentatthe input. This is a very sensitive and easily applied test, so there are twocommonvariationsonthetheme.

Thesimplestexpressionofthesecondtestistoapplyasinglesinewavetothedevice. At the output of the device, we expect to see a single sine wave.However, if the device produces non-linear distortion, there will also beharmonicsof theoriginal sinewave.The test ispopularbecause removing theoriginalsinewaveattheoutputiseasy,leavingonlytheharmonics–whichcanthen be measured, either individually or collectively, as Total HarmonicDistortion(THD).Amore complexmethod is to apply two sinewaves to the device.Again,weshouldonlyseethesetwofrequenciesattheoutput,butadeviceproducingnon-lineardistortioncausesthetwofrequenciestoamplitudemodulateoneanother,producing sumand difference frequencies known as intermodulation products.Intermodulationdistortionmeasurement ispopularwithRadioFrequency (RF)engineersbecauseitiseasytotunetoeachintermodulationproductandmeasureitsamplitude,butthisisnotquitesoeasilydoneataudiofrequencies.It is most important to realise that measuring harmonic distortion is nomore‘correct’thanmeasuringintermodulationdistortion,orviceversa.Bothformsofmeasurement simply reflect the same non-linearity in the device’s transfercharacteristic.What is importantishowthemeasurementismadeandhowtheresultsareinterpreted.

DistortionMeasurementandInterpretation

In an idealworld, everybodywouldmake their distortionmeasurement in thesameway,with the sameequipment, and interpret their results identically.Allresultswouldthenbecomparable,allowingustostatethatdevice‘A’wasbetterthandevice‘B’.Inpractice,therearemanydifferentmeasurementtechniques.Forexample,theintermodulation distortion measurement requires two (or more) frequencies.Whichfrequenciesshouldbechosen,andwhatshouldtheirrelativeamplitudesbe? There are at least three standards for this measurement. Similarly, whichfrequency shouldweuse formeasuring harmonic distortion?Shouldwemakethemeasurementatasingle frequency,orshouldwesweepfrequency through

the entire audible range? Which results should we include, and which onesshould we exclude? Standards attempt to answer these questions and allowresultstobecompared.Engineerslovestandards–that’swhywehavesomanyofthem.Ifwehavedesignedapieceofequipment,wealreadyknowwhere its failingsare likely tobe,soweplanour test toexpose thosefailings.Thisallowsus toquantifythefailings,makeachangetothedesignandmeasuretoseeifwehavemadeanimprovement.The previous paragraph strikes to the heart of themeasurement problem, andraisesvariouspoints:•Weneedtobeawareofthelimitationsofthetestequipment.Thereislittlepoint in attempting to measure the distortion of an amplifier suspected toproduce <0.01% Total Harmonic Distortion+Noise (THD+N) if the testoscillatoritselfproduces0.01%THD+N.•We must know the relevance of our measurements. Measuring wow andflutter on an analogue turntable is useful because thismeasurement exposesknownmechanicalfailings.Conversely,earlyCDplayerspecificationsquotedpointlesswowandfluttermeasurements(essentiallyzeroforadigitalsource),but failed tomeasure jitter (an insidiousproblem in theconversionbetweenanalogueanddigitaldomains).• A designer, seeking to improve their design, makes the test critical.Conversely, the marketing department requests engineering tests that thedeviceisknowntopasscomfortably–suchasharmonicdistortionat10 dBbelow full output for a digital source – because these tests give such goodfigures.•Hopefully,nobodyunderstandsagivendesignaswellasthedesigner–whoisbestplacedtodecidewhichtestsshouldbemade.•Measurementsareofmostusetothedesigner.

For thesereasons,measurementsquotedbymanufacturersorreviewersarenotnecessarily particularly useful – and this is part of the reason for subjectivereviews.(Anotherreasonisthatgoodtestequipmentisexpensive.)However, if we intend to design and build valve amplifiers, then carefullychosenmeasurements employingcheap testgear andcareful interpretationcanbeveryusefulindeed.

ChoosingtheMeasurement

Transistoramplifierstypicallyhaveplentyofglobalnegativefeedbacktoreducedistortion. Because applying feedback can easily turn an amplifier into anoscillator,theamplifierisdeliberatelymadetohaveanamplituderesponsethatfalls with frequency before the feedback is applied. Since negative feedbackreducesboth linearandnon-lineardistortions,when it isapplied thefrequencyresponsereverts toflatnessandnon-lineardistortion isalsoreduced.However,becausetheamplifier’sresponsewasfallingwithfrequencybeforethefeedbackwas applied, less negative feedback is available at high frequencies to correctnon-lineardistortion.Thismeansthathigh-feedbackamplifiersmusthaveTHDthat riseswith frequency, so a single-frequencymeasurement is inappropriate,andasweptmeasurementisbetter.Ifwe test a circuit thatdoesnothaveglobalnegative feedback, thena single-frequency measurement may be appropriate – if we know what causes thedistortion.A valve distorts because of the curvature in its Ia versus Vgk transfercharacteristic, and does so at all audio frequencies without fear or favour.Harmonicdistortionistheeasiestmeasurement,andweareatlibertytochooseanytestfrequencythatwefeelisconvenient.Wemightchoose50 Hzor60 HzbecausewehaveaDVMspecifiedtobeaccurateto0.1 dBatthatfrequency.Ifwe do, we will find that we cannot evenmeasure the fundamental amplitudeaccurately because stray humpicked up fromnearby powerwiring beatswithourwantedsignaltogiveagentlyfluctuatingmeasurement.Weneedtochangeourtestfrequencysothatitisclearofmainshumanditsharmonics.Perhaps we could use 10 kHz. This is nicely clear of mains hum, but hasproblemsofitsown.Somenon-linearitiesproducemainlyhigherharmonics,butiftheamplifier’samplitudeagainstfrequencyresponsewasalreadyfalling,thiswould attenuate the very harmonics we were trying to measure, and give afalselygoodresult.Weneedalowerfrequency.In terms of octaves, 1 kHz is in the middle of the audio band, so it is leastaffectedbyerrorscausedbyreducedbandwidthandissufficientlyfarawayfromACmains frequency for humnot to upset the result.Marketingpeople love1kHzbecauseitmeasuressoverywell.

RefiningHarmonicDistortionMeasurement

Classicalharmonicdistortionmeasurementsweremadeat1 kHzbyremovingthe 1 kHz fundamental andmeasuring the amplitude of the remaining signal.Althoughtheywereappropriateforthevalveamplifiersofthetime,thesetestswererightlycriticisedwhenappliedtotransistoramplifiersbecausetheytookno

accountofthedistributionofharmonicsandtheirsubjectiveannoyance.

WeightingofHarmonics

Various proposals have been made for weighting the levels of individualharmonics to allow harmonic powers to be summed to give a single-figuremeasureofsubjectivedistortion.Shorter[1]suggestedin1950thatlevelsshouldbeweightedbyafactorofn2/4(wherenisthenumberoftheharmonic):

Fromnto2nisoneoctave,sothegradientindB/octaveis:

Thus,ratherthanmeasuringamplitudesofindividualharmonicsandcalculatingTHD, a rising response of 12 dB/octave could be applied to a conventionaldistortion meter. In order that the measurement should be comparable with aconventionalmetermeasuring pure second harmonic distortion from a 1 kHzsource, theweighting filterwould need a −12 dBgain offset to ensure 0 dBgain at 2 kHz.Note that the combination of theweighting filter and its gainoffsetmeansthatweighteddistortionmeasurementsareonlyvalidforthesinglespecifiedfundamentalfrequency.However, there are problems with the n2/4 weighting technique. Using the 1kHzmeasurementexample,20 kHzis10timeshigherthan2 kHz,sothefilterwouldaddaminimumof40 dBofgaintoharmonicsthatareinaudible.Sincethewholepointof theexercisewas that themeasuredresultshouldagreewiththesubjectivenuisance,a20 kHzlow-passfilterisalsorequired.Although theShorter recommendation successfully rankedmeasureddistortionagainstthesubjectivenuisance,thetestsufferedfromthelimitationsofitstime.The levels of deliberate distortion were quite high (0.41–3.7% RMSunweighted), and the loudspeaker was a ‘wide-range coaxial horn’ ofunspecifieddistortion.PeterSkirrowofLindosElectronicsarguedthatdistortionshouldbemeasuredat

1 kHzusingaweightingfilterconformingtoCCIR468-2becausetheresponseofthisfilterwasdeterminedbythesubjectivenuisanceofdifferentfrequencies.Broadly speaking,CCIR468-2 riseswith frequency at 6 dB/octave, has 0 dBgainat1 kHzandpeaksby12 dBat6.3 kHz,afterwhichitfallsswiftly(seeFigure3.2).

Figure3.2FrequencyresponseofCCIR468-2weightingfilter.

SummationandRectifiers

Thewaveformthatremainsafterthefundamentalhasbeenremovedisknownasthe distortion residual and is composed of a number of harmonically relatedfrequencies.Howshouldwemeasure the amplitudeof thiswaveform?This isnotnearlyaseasyaquestionasitfirstappears.PerhapswecouldmeasureVpk–pk(seeFigure3.3).

Figure3.3Theeffectofphaseonwaveformshape.

Bothwaveformsare squarewaveswith correct amplitudeharmonicsup to theseventh harmonic, and none thereafter, but one has had the phase of thefundamentalshiftedby90°,whichsignificantlychangesVpk–pk.Mathematically,thecorrectwaytosumindividualharmonicsistoturnthevoltagesintopowersbysquaring(P=V2/R),takethemeanofthepowers,andthenconvertthisbackinto a voltage by taking the square root, otherwise known as an RMSmeasurement.Thus,classicaldistortionmeasurementsmeasuretheamplitudeofthedistortionresidualusingameterincorporatingatrueRMSrectifier,andtheirmeasurementsmayreflectthisfactbyquotingTHDin%RMS.

AlternativeRectifiers

CCIR468-2specifiesthattherectifiershouldbepeakdetecting,becausenoiseisimpulsive,andwewanttocapturetheamplitudeofthesenoisespikes.Crossoverdistortion produces narrow spikes thatwould contribute very little to anRMSsummation, but are subjectively extremely annoying, so the peak-detectingrectifierofCCIR468-2wouldseemidealfordetectingthesespikes.CCIR468-2 is not quite ideal because it needs the previouslymentioned gainoffset, so theCCIR/ARM recommendation offsets the gain of theCCIR468-2weightingfilterby6 dBtogive0 dBgainat2 kHz,allowingittobeusedfor1kHzdistortionweighting.Unfortunately,italsochangestherectifierfrompeakdetecting to average reading (ARM,AverageReadingMeter),marking it lesslikelytodetectthespikesproducedbycrossoverdistortion,soyoumightprefertouseCCIR468-2andaddthegainoffsetmanually.

NoiseandTHD+N

AlthoughusingaCCIR468-2filtertoweightdistortionischeapandeffective,itsrising responsewith frequencymaycreateanotherproblem.Properlydesignedcircuitrycreatesverylittledistortion.Toputitanotherway,thedistortioncouldbeofcomparableamplitudetothenoisethatallelectronicsgenerates.WhenwemakeourTHDmeasurement,usingourmeter,howdoweknowthatwearenotactuallymeasuringtheamplitudeofthenoise?Thebestsolutionistoviewthedistortionresidualona20 MHzoscilloscope(oronewith the 20 MHz filter engaged). If thewaveform appears clean,we aremeasuringmostlydistortion;ifarepetitivewaveformisdifficulttodiscern,weareprobablymeasuringnoise.Thus,allpracticalmeasurementsmadebyameterare actually THD+N, and we have to be certain that the noise is sufficiently

smalltobeignored.Digitaloscilloscopesareexcellentformakingthisdecisionobjectively.Theoscilloscopecanbe set tomeasure theRMSamplitudeof thedistortion residual, and this measurement can be compared with the samemeasurement but with averaging engaged. Averaging multiple waveformscancels the noise (which is random), but maintains the repetitive distortionresidual.Ifthereisnegligible(<10%)differencebetweenthetwomeasurements,we are measuring distortion. But if the averaged value drops to 71% of theunaveraged value, we are measuring equal amounts of noise and distortionresidual,anditistimetostoprecordingdistortionfigures.By definition, white noise has constant amplitude with frequency, whereasdistortion harmonics occur at very specific frequencies. Our meter is abroadband device, which means that it is equally sensitive to all frequenciesacross the audio bandwidth. Thus, although the noise power in a particularfrequency band could be quite low, and possibly significantly less than theamplitudeofanadjacentdistortionharmonic,whensummed, thenoisepowerscouldeasilyswampthedistortionpowers.Thiswouldn’tbeaproblemifitwerenotforthefactthattheear/braincombinationcanpickdistortionharmonicsoutofthebroadbandnoisebecauseitworkslikeaspectrumanalyser.

SpectrumAnalysers

A spectrum analyser plots amplitude against frequency, allowing us todistinguish easily between noise and distortion harmonics. If we measureindividualamplitudesofdistortionharmonics,andthenmathematicallyapplyasubjectiveweightingsuchasShorter’srecommendationorCCIR468-2tothosenumbers,weavoidnoiseproblems.Analogueaudiospectrumanalysersweretraditionallyexpensive,butthedigitalalternative simply relies on rawcomputingpower, andnow that this is cheap,many digital oscilloscopes have facilities that convert them into spectrumanalysers. Alternatively, a PC with a recording quality (24-bit 192 kS/s)soundcard can perform the entire function of distortion measurement andanalysisat audio frequencies.All that is required is someanalogue interfacinghardware (such as Pete Millett’s ‘Soundcard Interface/AC RMS Voltmeter’design)andsomeaudioanalysissoftware(suchasAudioTester).Suchasolutiondoesnothavequitetheflexibilityandeaseofuseofadedicatedaudiotestset,but it’s a fractionof thepriceand theperformance is excellent.Manymodernaudio test sets are simply outstandingly good soundcards having optimumanaloguescalinganddedicatedaudioanalysissoftware.However, the process of analogue to digital conversion and its subsequent

analysisisnottransparent,sowedoneedtounderstanditslimitations.

DigitalConceptsAnanaloguesignaliscontinuouslyvariablebothinvoltage(orcurrent,distance,etc.)and in time.Conversely,adigital signalcanonlychange itsparameter indiscrete steps (quanta) and at fixed intervals. Takingmeasurements to plot agraph isacrudeformofanalogue todigitalconversion,becausewefreeze thevariation,make a numericalmeasurement, and thenmove on tomake anothermeasurement.Thepowerofthetechniqueisthatreducingthemeasurementstoaseries of numbers allows us to analyse those numbers using a supremelypowerfultool–mathematics–tofindpatterns.Analoguetodigitalconversionisatwo-partprocess.Wefreezetheparameteratfixed intervals, andwe take numericalmeasurements of the parameter. Theseprocessescanbedoneineitherorder.Wecouldtakecontinuousmeasurements,but record only those measurements that occur at particular intervals.Alternatively,wecanfirstfreezetheparameteratfixedintervals,andthenmakethenumericalmeasurement.Itdoesnotmatterwhichwayroundthesetwoquitedistinctprocessesareapplied.

Sampling

Theprocessof freezing theparameter at regular intervals in time is knownassampling. Ifwetake192,000samples inasecond, thenthesamplerate is192kS/s; alternatively we can quote the sampling frequency as 192 kHz. Thesamplingfrequency issignificantbecause theNyquistcriterionstates thatalias(fictitious) frequencieswill appear ifweattempt to samplea signal containingfrequenciesat,orabove,halfthesamplingfrequency.MildabuseoftheNyquistcriterionproduceslow-frequencyaliasesthatwerenotin the originalwaveform.You can demonstrate aliasing to yourself by layingtwopiecesoffinenettingorperforatedmetaloneon topof theotherand thensliding and rotating one against the other. Large circles appear and disappear,whichareknownasMoirépatterns(afteratypeoflace).ThereasonthatMoiréoccurs is that one piece of netting is sampling the other, but the samplingfrequency is the same as the sampled frequency. As the netting slides, therelativephasechanges,whichchangesthefrequencyofthealiases.Toavoidaliasing,theanaloguetodigitalconvertormustbeprecededbyalow-pass filterknown,predictably,asananti-aliasing filter.Asanexample,anon-recording quality computer soundcard operating at a sample rate of 44.1 kHzshouldbeprecededbyananti-aliasingfilterhavingacut-off frequencyof≈20

kHz.Thus, ifweusedsuchasoundcardfordistortionmeasurements, itwouldbeblind to frequencies above20 kHz andprobably attenuate frequencies justbelow20 kHz.Conversely,digitisingoscilloscopescannotbeprecededbyanti-aliasingfilters(becausetheirsampleratechangesoverawiderange).Wemusteitherchooseasufficientlyhighsamplerate thatweareconfident thataliasingwill not occur (such as a 192 kHz recording quality soundcard), or add anexternalanti-aliasingfilter.

Scaling

When we plot numbers on graph paper, we must choose a scale thatconveniently fits ournumbers to the lineson thepaper.As an example, if thegraphpaperhas10 large squares, eachcomposedof10small squares, andwehadacurrentmeasurementrangingfrom0 mAto8 mA,thenwewouldsetascaling of one large square=1 mA. This may seem obvious, but what if wechoseascaleofonelargesquare=0.1 mA,oreven10 mA?Inthefirstinstance,ourdatawouldoverloadthegraphpaper,andinthesecond,itwouldhardlybeseen.Thepurposeofscalingistomatchtherangeoftheparametertotherangeofourmeasurementsystem.Similarly,whenweconvert ananalogueparameter toanumber,we first scaletheparameter tobemeasured,andthenwecanmeasure it. Incidentally, this iswhy 4¾ digitDVMs specify theirbasic accuracy on the 0–5 V range. Theirmeasurementsystemactuallymeasuresfrom0 Vto5 V,andtherangeswitchselectsattenuatorsoramplifiers toscaleexternalvoltagesorcurrents tofit thissystem. Practical problems mean that the scaling cannot be perfect, henceincreased errors on all ranges bar 0–5 V. (3½ digit DVMs typicallymeasurefrom0 mVto200 mV,sotheyspecifytheirbasicaccuracyonthe0–200 mVrange.)

Quantisation

Ifwehavecorrectlyscaledtheparametertobemeasured,theprecisionbywhichwemakethenumericalmeasurementisdeterminedbythenumberofquantaorsteps available.Theprocess of comparing the continuouslyvariable parameteragainsttheseriesoffixedstepsandfindingthestepthatisclosestisknownasquantisation. The result of quantisation is a number, although it is commonlyknownasadigitalwordthatisacodefortheinputvoltage,sothisissometimesknownasPulseCodeModulationorPCM.Wenowhaveasuccessionofdigitalwordsappearingatregularintervalsthatwewriteintodigitalmemoryknownasawaveformrecord.

NumberSystems

Computerscountinthebinary(0,1)system,ratherthanthedenary(0–9)systemusedbyhumans.Thisseemsratherlimitedbecauseitmeansthatwecancounttonine,butnohigher,andthecomputercanonlycounttoone.Thesolutioninbothcasesistoscalethecountingsystem.Eachtimewereach9,andwanttoadd1,werecordthenewnumberasascaled1,butthisisaninconvenientterm,sowecall it ‘ten’. There is no reason why we should not scale tens, so you willprobablyremember‘hundreds,tensandunits’fromwhenyouwerefirsttaughtaddition.ThescalingisshownmoreformallyinTable3.1.

Table3.1PowersintheDenaryNumberSystem

Theterms‘hundreds,tenths’,etc.aresimplypowersofthebase,inthiscase10.Thebinarysystemworksinexactlythesameway,butbecauseituses2asitsbase,ratherthan10,itstableisslightlydifferent.

Thousands Hundreds Tens Units Tenths Hundredths Thousandths1,000 100 10 1 1/10 1/100 1/1,000

103 102 101 100 10−1 10−2 10−3

Thus,eventhoughthebinarysystemonlycountsfrom0to1,ifweuseawordwithenoughbits,wecanhaveanynumberwelike(seeTable3.2).

Table3.2PowersintheBinaryNumberSystem32 16 8 4 2 1 1/2 1/4 1/8 1/16 1/32

25 24 23 22 21 20 2−1 2−2 2−3 2−4 2−5

Precision

Computersusebinarynumbers,soifwemakeournumericalmeasurementmoreprecise byusing smaller quantising levels, theremust bemore of them, and abinary word comprising more bits is required. CD used a 16-bit word, andbecause thereare twopossiblestatesforeachbit, the totalnumberofdifferentlevelsthatcanbedescribedbya16 bitwordis216=65,536.Similarly,a24 bitsystemcandescribe224=16,777,216differentlevels,butrequiresone-and-a-halftimesasmuchmemorytostoreeachword(24/16=1½).As a rule of thumb (ignoring dither), the Dynamic Range (DR) of a digitalsystemis:

wheren=numberofbits.Thus,a16 bitsystemhasatheoreticaldynamicrangeof6×16=96 dBanda24bit system 144 dB (never achieved because Analogue to Digital Convertors(ADCs)simplyaren’tthatgood).

Wecoulddecidetobemoreprecisebymakingmorenumericalmeasurements.Samplingtwiceasoftendoublesthememoryrequired.To sum up, a more precise description generates more data, requiring morememory,andthiswillbecomesignificantlater.

TheFastFourierTransform(FFT)The reason for convertingour analogue signal to a digital signalwas to allowmathematical techniques to be applied to the resulting numbers and allowpatternstobeseen.(Humansaregoodatrecognisingpatterns,soanytechniquethat reveals patterns helps understanding.) An oscilloscope allows us to spotpatterns that repeat in time, suchas a spike thatoccurs each timea sinewavechangespolarity,butaspectrumanalyserallowsustospotpatternsinfrequency,perhapsasmallspikethatindicatesfifthharmonicdistortion.TheFFTisamathematicaltoolthatconvertsdatainitiallypresentedasagraphofaparameterplottedagainsttimeintothatparameterplottedagainstfrequency.TheFFTisimmenselypowerful,butithasitslimitations.

ThePeriodicityAssumption

Inconverting from time to the frequencydomain, themathematicsof theFFTmakes the assumption that the waveform to be analysed repeats itselfperiodically.Thisassumptionmayseemtrivial,butithasmajorrepercussions.Ifwecaptureasinglecycleofthewaveform,anddrawitaroundacirculardrum(likeanold-fashionedseismograph)suchthattheendofthecyclejustmeetsthebeginning,thenbyrotatingthedrumwecanreplaythewaveformadfinitumandreproduce our original signal.Unfortunately, any uncertainty as to the precisetimingoftheendofthecyclecausesastepinlevelwhenweattempttolooptherecordedcyclebacktoitselfonreplay.However,ifwecapturemorecyclesonourdrum,theglitchoccursproportionatelylessfrequentlyandcauseslessofanerror.Thus, capturing 1,000 cycles reduces the error by a factor of 1,000, butmultipliesthelengthofthewaveformrecordbythesameamount.

Windowing

Anotherwayofreducingthestepistoforceperiodicitybyapplyingawindowtothewaveform record. In this context, awindow is a variableweighting factorthatmultipliesthevaluesofthesamplesattheendsofthewaveformrecordbyzero,butappliesagreaterweighting(≤1)tosamplestowardsthemiddle.Sinceanynumbermultipliedbyzero iszero, thisforces theendsamples tozeroandallowsthewaveformrecordtorepeatwithoutglitches(seeFigure3.4).

Figure3.4Windowingforcesperiodicity.

Ifwindowingdistortsthewaveformrecord,itmustdistorttheresultsoftheFFT.Windowing either spills energy from high-amplitude bins into adjacent bins,which produces visible skirts around frequencies having high amplitude, orchanges bin amplitudes. (Because the process of sampling broke time intodiscreteslices,theresultsofanFFTmustproducefrequenciesindiscreteslices,andtheseareknownasbins.)Allwindowsare,therefore,acompromisebetweenfrequencyandamplituderesolution.Awindowthatdoesnotmodifysamplevaluesisknownasarectangularwindow(becauseitmultipliesbyaconstantvalueof1overtheentirewaveformrecord).Because the rectangular window does not modify sample values, it does notcausespreadingbetweenbins,andoffersthebestfrequencyresolution,butanyperiodicity violation causes amplitude errors. FFT software generally offersuser-selectablewindowing,suchasBlackman–Harris,whichshapestheendsofthe waveform record to avoid periodicity violation and minimise consequentamplitude errors at the expense of spreading between frequency bins.Alternatively, Hamming or Hanning windows improve frequency resolution(reducedbinspreading)attheexpenseofincreasedamplitudeerrors.Best results are obtainedby synchronising the oscillator to theFFT system sothatonlycompletecycleswithoutperiodicityerrorsarecaptured in the record,allowing a rectangular window to be used. If true synchronous FFT is notpossible, then a practical compromise is to trigger the analyser from thefundamentalfrequencyandfinelyadjustoscillatorfrequencyforminimalskirtsonthehighestamplitudebin.If multiple waveform records are captured, they can be averaged together toreduceerrors.Thisisaverypowerfultechnique,althoughitslowsmeasurementspeed.

HowtheAuthor’sDistortionMeasurementsWereMade

AnMJS401D analogue audio test set and a Tektronix TDS3032 oscilloscopewithFFToptionwereusedincombination.

Distortion measurements were made at 1 kHz, and a 400 Hz 36 dB/octavehigh-passfilterwasengagedtorejecthum.ThemeterusedanRMSrectifiertosum harmonic amplitudes correctly, and its bandwidth was restricted to theaudiblerangebya22 kHz36 dB/octavelow-passfilter.Thedistortionresidualwasthenpassedtothespectrumanalyser.The 9 bit oscilloscope/spectrum analyser used a sample rate of 50 kS/s tomaximisethenumberofcyclescaptured,andthe22 kHzfilterintheMJS401Dformed theanti-aliasing filter.Theoscilloscopewas triggered from the1 kHzfundamental,andrectangularwindowingwasused,withtheMJS401Doscillatorfrequency fine-tuned for minimum skirts to give quasi-synchronous FFT. Toreduce the contribution of random noise, the FFTs were averaged over 16records (12 dB noise reduction), each 10 kbits long, resulting in >50 dB ofreliablespectrumanalyserdynamicrange.Becausethedynamicrangeoftheaudiotestsetisaddedtothatofthespectrumanalyser,themainlimitationbecomesthedistortionresidualofthetestset,andfiguresbelow−90 dBshouldbeviewedwithcaution.Now that the distortion measurement method is understood, we can use it asnecessarytotestandcomparelow-distortionvalvecircuits.

DesigningforLowDistortionTherearemanywaysofreducingdistortion,ortoputitlesscharitably,it’seasytogeneratedistortioninadvertently.Tosimplifyinvestigation,wewillconsiderthedistortiongeneratedbyasinglestagebeforeprogressingtomultiplestages.Wewillconsider:•Signalamplitude•Gridcurrent•Distortionreductionbyparameterrestriction•Distortionreductionbycancellation•DC-biasproblems•Individualvalvechoice•Couplingfromonestagetothenext.

Wewill investigate each aspect in turn and test our hypotheseswith practicalmeasurements.

SignalAmplitudeIntheory,thedistortiongeneratedbytriodesispredominantlysecondharmonic

(H2). A common-cathode amplifier using 417A/5842 was set up to test thetheory(seeFigure3.5).

Figure3.5Commoncathodetestamplifiercircuit.

Twenty-two 417A/5842swere tested at an output level of +18 dBu (6.16 VRMS);theirresultswereaveragedandarepresentedinTable3.3.

Table3.3AverageLevelofDistortionHarmonicsProducedby417-ACommon-CathodeAmplifierat+18 dBuHarmonic Level(dB)

H1(fundamental) 0H2 −41H3 −100H4 −95

The distortion generated by the 417A/5842 clearly is dominated by H2. The417A/5842type turnedout tobeaparticularlygoodexample,butevenfor theworst valvesH2 ismore than 20 dB higher than any other harmonic. This isuseful because it means that we can use the following formula to estimatedistortionwhendrawingandcomparingloadlinesonreliablegraphs:

Theshapeofatriode’stransfercharacteristicisasimplecurve(Ia∝Vgk3/2),sotraversingasmallerdistanceof thecurvebecomesacloserapproximation toastraightline,andthereshouldbelessdistortion.Thishypothesiswastestedbya7N7/D3aμ-followercircuit(seeFigure3.6).

Figure3.6μ-Followerlinearitytestcircuit.

Inorder that the testcircuit shouldnotbe falselygoodwhenapproachinggridcurrent,itwasdrivenfromasourceresistanceof64 kΩ,thusreplicatingtypicalconditionsofuse.Theupperlimitofmeasurementwassetbytheonsetofgridcurrentatanoutputof+34 dBu(THD+N=−43 dB).Thelowerlimitofreliablemeasurementwassetby theabilityof theanalogueanalyser to lockcleanly tothe distortion waveform, which began to degrade at an output of +14 dBu(THD+N=−63.5 dB).Betweentheselimits,theoutputlevelwaschangedin1-dB steps, and a graphofTHD+Nwasplotted against output level (seeFigure3.7).

Figure3.7Graphofdistortionversuslevelforμ-followertestcircuit.

The graph clearly shows that THD+N is directly proportional to output level.Thus,adistortionmeasurementof1%at15 VRMSimpliesdistortionof0.1%at1.5 VRMS.Thisobservationisextremelyusefulifitisnecessarytoestimatethedistortionofatriodehandlingsmall-signalvoltages–suchaswouldnormallybeencounteredearlyinanRIAAstage.ThesuppositionthattriodedistortionispredominantlyH2andisproportionaltolevel is true forall triodeswhenusedwithpractical resistiveanode loads.Theeffectofanactive load(RL⇒∞)is tominimiseH2,butbarelychangeshigherharmonics.OnceH2 has beenminimised, the effects of the higher harmonicsbecome more significant, with the result that some triodes do not then havedistortionthatisproportionaltolevel.Ifyouuseanactiveload,youmayneedtocheckwhetherdistortionremainsproportionaltolevelforthatparticulartypeofvalve.

CascodesandDistortion

Thecascodeisanidealsmall-signalRFcircuit.Itworksbyplacingtwodevicesinseriesacrossthehightension(HT)sothattheupperdeviceprovidesmostofthegainandloadsthelowerdevicewiththeupperdevice’sloaddividedbyitsvoltagegain.Thismeans that the lowerdeviceseesavery lowresistance load(nearverticalloadline),loweringitsgain(andinasemiconductorcircuit)forcingitsvoltagegaintounity.FromanRFpointofview,thereductionofgaininthelower device is extremely advantageous because it reducesMiller capacitance

fromtheoutputofthedevicetoitsinput.Fromanaudiopointofview,thelowimpedance loadgreatly increasesH2.Worse, the series connectionmeans thateachdevicehasagreatlyreducedHTvoltage,whichtendstoincreasedistortion.Foraphonostage, lownoise is theprimaryconsideration,so the lowerdevicerequireshighgmbecause it reducesnoise,butacarefulbalanceofDCcurrentbetweentheupperandlowerdevicesisrequiredtooptimisethedynamicrangebetween noise and distortion. However, because distortion is proportional toamplitude,minimisingsignalamplitudeminimisesdistortion,andthedominantH2 can be removed by cancellation if a pair of cascodes is configured as adifferentialpair.

GridCurrentDistortion changes withVa and Ia will be investigated later because they arecausedbychangesinthesmall-signalparametersμ,raandgmthatarenormallyassumedtobeconstant.Thus,unlesswealsoneedtomaximisevoltageswing,ourchoiceofoperatingpointsimplyneeds tobewaryofgridcurrentandcut-off. The problems of cut-off are obvious, but grid current causes far moreproblems.

DistortionduetoGridCurrentatContactPotential

AsVgkapproaches0 V,gridcurrentbeginstoflow,andtheinputresistanceofthevalvefallsdramatically.Ifthesourcedrivingthevalvehadrout=0,thiswouldnotbeaproblem,butitishighlylikelythatithassignificantoutputresistance,andthepotentialdividerthatismomentarilyformedatthepositivepeaksofthewaveformwheregridcurrentflowsclipstheinputsignal.Symmetricalclippingproduces a square wave composed of odd harmonics, but grid current clipsasymmetrically,soevenharmonicscanalsobeexpected.The distortion caused by grid current is obnoxious because it is composed ofhigh-orderharmonics.Thefollowingtraceswereobtainedbydrivingthelowervalveofaμ-followerintogridcurrentfromasourceresistanceof47 kΩ.Theinput signal was increased until distortion of the output waveform was justvisible on a carefully focussed analogue oscilloscope. The THD+N wasmeasuredtobe2%,andthedistortionresidualhadaverydistinctivewaveform(seeFigure3.8).

Figure3.8Upper:Thedistinctivedistortionwaveformcausedbygridcurrent.Lower:Softclippingcausedbygridcurrent.

FFTanalysisofthedistortionresidualrevealedasprayofhigh-level,high-order,oddandevenharmonics(seeFigure3.9).

Figure3.9Distortionspectrumproducedbygridcurrentactingon1-kHzsinewave.Verticalscale:10 dB/div.Horizontalscale:2.5kHz/div.(DC−25 kHz.)

AlthoughgridcurrentoccursatVgk=0 Vinanidealvalve,practicalvalvesentergrid current a little earlier due to the thermocouple effect of heated junctionsbetweendissimilarmetalswithinthevalve,andtheaverageenergyofelectronsintheelectroncloudabovethecathodesurface.Typically,gridcurrentbeginsatVgk≈−1 V, and this is known as the contact potential. Measuring distortionwhilstdrivingfromahighimpedancesourceisanexcellentwayofdetermining

contactpotentialforagivenvalve.

DistortionduetoGridCurrentandVolumeControls

Itisperfectlypossibletochangethedesignofthevolumecontrolprecedinganamplifier stageandmeasure achange indistortion.Themostcommon typeofvolume control is a resistor from which a variable tapping is taken, either awiper moving along the resistive track, or a switch wiper selecting a tappingfromachainoffixedresistors(seeFigure3.10a).

Figure3.10Fundamentalbasisofmostvolumecontrols.

Alternatively, we can use a fixed series resistor followed by a variable shuntresistor(seeFigure3.10b).Unfortunately,thecircuitofFigure3.10bhasmuchhigheroutputresistancethanthat of Figure 3.10a. Measuring distortion whilst driving from a high sourceresistance is a very sensitive test of gas current because the (non-linear) gascurrentdevelopsavoltageacross thesource resistance,which is inserieswiththesignal.Asthesourceresistancerises,sodoesthedistortion.A6545PcathodefollowerbiassedbyanEF184constantcurrentsinkwastestedat+20 dBu(7.75 VRMS).Whendrivenfroma5 Ωsource,thedistortionwas0.02%. A 100 kΩ potential divider volume control has a maximum outputresistance of 25 kΩ, so distortion was also measured with a 25 kΩ sourceresistance,andfoundtobeunchanged.However,whenthesourceresistancewasincreased to1 MΩ, thedistortion rose to0.2%.Admittedly, it isunlikely thatthe source resistancewouldbeashighas1 MΩ,but100 kΩwouldbequitepossiblefromthevolumecontrolinFigure3.10b.

OperatingwithGridCurrent(ClassA2)

MostClassAamplifiersoperatewithoutgridcurrentbecausethisallowsahigh

grid resistance that is easily driven. Once Vgk becomes positive, rather thanrepellingelectronsfromthecathode,thecontrolgridbecomesaweakanodeandattractselectrons,mostofwhicharethencapturedbythetrueanodethatisatamuchhighervoltage,butsomeflowoutofthegridasgridcurrent.Gridcurrenthasimportantconsequences:• The electron stream from the cathode is divided between grid and anodecurrent,implyingpartitionnoise.However,asthemostlikelyuseofClassA2isintheoutputstage,wheresignalvoltagesarehigh,thisnoiseisunlikelytobeaproblem.•Thereisapotentialdifferencebetweenthegridandthecathode(Vgk)andcurrent flowing through the grid ( Ig), so it must be dissipating power inexactly the samewayasananode. If thegridwasnotdesigned todissipatepower, it will quickly heat, distorting its shape and possibly destroying thevalve.•Becausetheinputresistanceofthegridwhenoperatingasananodeisverylow, imposingasignalvoltageon thegridrequiresconsiderablepower(P=V2/R),whichmustbeprovidedbythedriverstage.•However,becausethegridisdrivenpositive,itispossibletodrivetheanodeofa triode farcloser to0 V than ifVgkwasnegative.Theefficiencyof theoutputstageisthussignificantlyincreased.

Driver stages for Class A1 are voltage amplifiers that only need to supplysufficient current to charge and discharge theMiller capacitance of the outputstage,butadriverstageforClassA2mustprovidepower.Therearetwowaysinwhichthispowercanbedelivered.Thedriverstagecanbedesignedtobeasmallpowerstage.Onepossiblechoiceisthecommon-cathodedualtriode6N7thatcanbeoperatedeitherinpush–pullor single-ended with the two triodes paralleled to double Pa. A transformerreflectsitsloadimpedancebyn2,soastep-downtransformerwithavoltageratioof2:1increasestheloadimpedanceseenbythedrivervalvebyafactoroffour.BecauseatransformerintheanodecircuitofavalvetheoreticallyallowsVa toswing to 2 V HT, requiring double the anode swing is not a problem.Additionally, the low RDC of the secondary reduces the chances of thermalrunaway in the output stage. Sadly, good driver transformers are even moredifficult to design than output transformers because they operate at higherimpedances.

Alternatively, the Class A2 stage can be driven DC-coupled from a cathodefollower.A power valve is still required, but it no longer needs to be able toswingmanyvolts.Powerframe-gridvalvesthathavehighmutualconductance,but low Va(max), such as the 6545P and E55L, are ideal as power cathodefollowers. Unfortunately, frame-grid valves tend to have modern, efficientheaters(thinheater/cathodeinsulation),whichmeansthattheirVhk(max)isquitelow,possiblycausingaproblem if theClassA2stage requiressignificantgridvoltageswing.TobiastheClassA2stagecorrectly,thecathodeofthecathodefollowercanonlybeslightlypositive,butweneedareasonably largevalueofRL toensure linearityof thecathodefollower,soanegativesupply is required(seeFigure3.11).

Figure3.11UsingaDCcoupledpowercathodefollowertodriveClassA2.

Alowoutputresistanceisofferedbybothoftheprevioussolutions,butitisnotzero.Becauserout≠0,itformsapotentialdividerwiththeinputresistanceoftheClassA2stage,causingattenuation.IfVgkswingsnegative,theinputimpedanceof theClassA2stagebecomes infinite,and there isno longeranyattenuation,

causing distortion. No distortion advantage can be gained using a constantcurrent sink load for the cathode follower because it faces the low-resistanceload of the Class A2 grid, but it allows a lower-voltage negative supply,reducingcost.WhereasaClassA1stageshouldneverbedrivenintogridcurrentforfearofdistortion, theClassA2stagemustneverbeallowedtostrayoutofgridcurrent,ordistortionwillresult.Thus,ClassA2powerstagestypicallyusehigh-μ(μ>100)transmittervalvesoriginallyintendedforClassBusebecausethese valves are designed to pass low anode currents atVg=0 V even at theirintendedanodeoperatingvoltage.

DistortionReductionbyParameterRestrictionTriodes produce primarily H2 distortion because as ra changes with Ia, theattenuation of the potential divider formed by ra and RL changes, with moreattenuationonone-halfcycleofthewaveformthanontheother.However,therearewaysofreducingthisdistortion:•Use a large value ofRL. IfRL>> ra, then the changing attenuation of thepotential divider is insignificant because the attenuation itself becomesnegligible.•HoldIaconstantsothatracannotvary.Thisimpliesanactiveloadsuchasaconstantcurrentsourceisthebasisoftheμ-follower.

ThesetwomethodsareactuallyverysimilarbecausebothseektomakeRL>>ra.(For an ideal constant current source, rslope=∞.) In general, for a given HTvoltageandIa,replacingtheloadresistorRLwithaconstantcurrentsourcecanbeexpectedtoreduceH2byafactorof≈7.Once the previous methods of distortion reduction have been used, theamplifyingvalveseesanalmosthorizontalACloadline,andwhenRL>50ra,thefarlessereffectofvariationofμwithVabecomesobservable.ThevariationofμwithVacanbereducedbyavoidingoperationatlowIa(wheretheanodecurvesbeginbunching)andbychoosingavalvewhosecurvesbunchlessasIatendsto0(seeFigure3.12).

Figure3.12Gridconstruction:Morefineturns(dashed)versusfewercoarseturns(solid).(AfterHenderson(GEC)[2]).

Bunching of anode curves is caused by the inevitable non-uniformity of theelectric field between the grid wires at the grid/cathode region, so the graphcompares twoGEC [2] directly heated triodes having similar μ, but the solidcurvesareduetoagridwoundwithafewturnsofcoarsewire,andthedashedcurvesareduetoagridwoundwithmoreturnsoffinewire.Unfortunately,asthe grid wire becomes finer, it is less able to support itself, but a frame-gridallowsarbitrarythicknessofwire,whichiswhytheE88CC,andparticularlythe6545P(bothframe-grid),exhibitverylittlebunching.Alternatively, it may be possible to holdVa constant. Clearly, this cannot bedone if the stage has gain, but a cathode follower can be arranged to haveconstantIaandVasimultaneously[3](seeFigure3.13).

Figure3.13ThecathodefollowerallowsconstantIaandVatobeforced.

The middle valve is the cathode follower. The lower valve is the traditionalpentode constant current sink that forces Ia in the cathode follower to beconstant.Theuppervalveisalsoacathodefollowerandshouldhavehighμandgm,sothe6545P(μ=52)isideal.Theuppervalveseesahighimpedanceload,soitsgainis:

The upper cathode follower’s grid is AC coupled to the output of themiddlecathodefollower,andbecauseitsgainisalmostunity,itscathodeisatthesameACvoltageasitsgrid.Thus,evenwhenthemiddlecathodefollowerswingsitscathode, the upper cathode follower forces its anode to swing by an almostidentical amount, and constant Va has been enforced simultaneously withconstantIa.Unfortunately,theimprovementisaccompaniedbysignificantcosts:

• The required HT voltage has been raised by Va of the upper cathodefollower.•Weneedathirdelevatedheatersupply(fortheuppercathodefollower).• Cathode followers are already prone to instability, and bootstrapping theanodeofonewiththeoutputofanotherinvitesfurtherproblems.

Youmighthaveadifferentopinion,buttheauthorfeelsthatacarefullydesignedcathode follower sitting on a constant current sink already challenges his testequipment.

DistortionReductionbyCancellationIn theory, if two common-cathode triode amplifiers are operated in a cascode,because each stage inverts, the distortion of the second triode is invertedwithrespect to that produced by the first triode, and cancellation should occur.However, a moment’s thought shows that this is unlikely to occur to anysignificant degree. Distortion is proportional to level, and because the secondtriode has gain, it produces a significantly higher level, and thereforeproportionately higher distortion, than the first triode. A small amount ofcancellationmayoccur,but the improvement is∝1/A2,so if thesecondtriodewasatype76(μ=13)andAv=10,wemightreducedistortionfrom1%to0.9%,whichislessthanthesample-to-samplevariationofdistortionineithervalve.Perhapswecouldchoosethesecondvalvetobemuchmorelinearthanthefirstso that both produce equal amounts of distortion. Low-μ valves are themostlinear, soan845 (μ=5.3)shouldachieveAv=4,and thereforeweneedavalvethat produces four times thedistortionof the845.This canprobablybedone,andadjustingthebiasofthefirstvalvewouldallowcompletecancellationtobeachieved.However, thiscancellationwouldbecriticallydependenton thegainofthe845,whichisdeterminedbyRL,yetRLisaloudspeakerwhoseimpedancechangeswithfrequency.Inpractice,6 dBreductioninH2isfeasible.Surprisingly,itispossibletoachievedistortioncancellationbetweenacommoncathodestagefollowedbyacathodefollowerstage,providedthat thecommoncathode stage has its distortionminimised by a constant current load and thecathode follower has its distortion deliberately increased by an AC load (seeFigure3.14).

Figure3.14Distortioncancellationbetweenacommoncathodeamplifierandacathodefollower.

Thecommon-cathodestageproducesperhaps0.1%THD+N,and thedominantharmonic isH2,with all the others better than 20 dB down. In theory, ifwecouldcancelH2,wewouldbeleftwithonlythehigherharmonics,andbecausetheyare20 dBfurtherdown,ourTHD+Nwouldhavedroppedby20 dBfrom0.1%to0.01%.Inpractice,thesituationisalittlemorecomplicated(seeFigure3.15).

Figure3.15Distortionspectraresultingfromnonulling,perfectandimperfectnulling.

Wecanseethatfullnulling(11.2 kΩACload)reducesH2by27 dBfrom−59dB to−86 dB (0.005%),which is certainly impressive, but at the expenseofskewingthedistortionspectrumsothatH3is8 dBhigherthanH2.Notethata7.5%changeinACloadresistancefrom11.2 kΩto12.05 kΩradicallychangesthedistortionspectrum.Distortioncancellationcanonlybeachievedreliablyifthe two valves are identical, carry exactly the same signal and have the sameloadconditions.

DifferentialPairDistortionCancellation

Thedifferentialpairwithconstantcurrentsinktailprovidesoptimumconditionsfordistortioncancellationbecausethesignalcurrentisforcedtoswingbetweenthetwovalveswithnoloss.Providedthattheloadimpedancesarematched,thevoltageswingsateachanodemustbeequalandopposite,theoreticallyallowingperfectH2cancellation.Theanodeloadresistorscaneasilybematchedto0.2%by a DVM, and if each anode drives a cathode follower, then the shuntcapacitanceissosmallthatanyimbalanceisinsignificantataudiofrequencies.(Even at 20 kHz, Xc=1.6 MΩ for the 5 pF input capacitance of a typicalcathode follower, so this is significantly larger than the typical 47 kΩ anodeloadresistors.)A Mullard 6SN7GT with well-matched sections was compared in differentconfigurationswithIa=7.5 mAandVa=230 V.Eachtestcircuitwasmeasuredatanoutputlevelof+14 dBu,butforthedifferentialpair thesignalbetween theanodeswasmeasured(+20 dBu),correspondingto+14 dBuateachanode(seeFigure3.16andTable3.4).

Figure3.16Testcircuitsfordistortioncomparison.

Table3.4ComparisonofDistortionHarmonicsforDifferentTopologiesHarmonic Commoncathode(dB) Differentialpair(dB) μ-Follower(dB)

H2 −51 −77 −68H3 −93 −89 –H4 (−106) – –

AscanbeseenfromTable3.4,thedifferentialpaircancelsevenharmonics,butsumsoddones.Although0.0035%H3isunlikely tobeaproblem, it indicatesthatdifferentialpairsareideallybuiltwithvalvesthatproducesmallamountsofodd harmonic distortion. Conversely, the μ-follower was not as effective atreducing H2, but all other harmonics were below the limits of reliablemeasurement.

Push–PullDistortionCancellation

A push–pull transformer-coupled Class A output stage meets most of therequirementsfordistortioncancellation.Inpractice,unlessthetwovalvesareanaccurately gain-matched pair, or provision has been made for DC and ACbalance,cancellationcannotbeperfect.Nevertheless,14 dBH2cancellationisroutinely achieved because the tight coupling between the two halves of thetransformerassistsACbalance.

TheWesternElectricHarmonicEqualiser

TheharmonicequaliserisarecentrediscoverychampionedbyJohnAtwoodandLynn Olsen. The surprisingly clearly written patent [4] states that distortionreduction action is due to cancellation between H3 produced directly by thevalve and that produced by intermodulation betweenH2 and the fundamental,H1. Remember that intermodulation distortion produces sum and differencefrequencies, so H1+H2=H3 as stated by the patent, and H1−H2=−H1, whichmeansthatthedifferencefrequencyisatthesamefrequencyasthefundamental,buthasinvertedpolarity,therebyslightlyattenuatingit.In push–pull form, the equaliser consists of a resistor connected from the twocathodes to ground with its value chosen purely from AC considerations –biassingisaseparateissue(seeFigure3.17).

Figure3.17TheWEharmonicequaliser.

Theeasiestwaytodeterminetherequiredvalueoftheresistoristotemporarilysubstitute a constant current sink set to the requiredDC current and bypass itwith a capacitor in series with a variable resistor (the equaliser) (see Figure3.18).

Figure3.18AcrudeJFETCCSpluscapacitor-coupledvariableresistorallowseasydeterminationoftheharmonicequaliserresistor

independentlyofDCconditions.

Sadly, the author’s experiments indicate that although the equaliser affects allvalves,itisn’talwaysapositiveeffect.Asabeneficialexample,addinga91 Ωequaliserresistortoapairofpush–pull6S4Asoperatingwitha9k5a–aloadfrom320 V reducedH3by28 dB so that the spectrumbecamedominatedbyH2,withH3andallothers>20 dBbelowthat(seeFigure3.19).

Figure3.19Theeffectoftheharmonicequaliser.Notethesubstantialreductionofoddharmonicamplitudes.

Side-EffectsoftheHarmonicEqualiser

Although in a harmonic equaliser resistor simple addition can significantlyimprove an output stage’s distortion spectrum, it does so by cancellation, andthatalwaysmeansthatitwillbesensitivetoloadresistance.Oncethevalueoftheharmonicequaliserresistorhasbeenset,loadresistancemustnotchange(seeFigure3.20).

Figure3.20Theeffectofloadresistanceonthirdharmoniccancellation.

Ascanbeseen,theloadresistanceideallyneedstobewithin±5%ofnominaltoachievethefullbenefitoftheharmonicequaliser.Unfortunately,theimpedanceofamovingcoilloudspeakerriseswithfrequencydue tovoice coil inductanceandhas a low frequencyelectrical resonance thatlooks like an inductor and a capacitor in parallel due to the mechanicalresonanceformedbythemassoftheconeandcomplianceofthesuspension.Inorder for anoutput stage’sharmonic equaliser toworkcorrectly, the amplifiermust be connected directly to a single resistive loudspeaker and the harmonicequaliser resistor must be set to match that specific loudspeaker. Fortunately,most moving-coil loudspeakers can be rendered adequately resistive aboveresonancebytheadditionofanappropriateZobelnetworkacrosstheirterminals(seeFigure3.21).

Figure3.21Theauthor’s‘Arpeggio’loudspeakerisanalmostresistiveload>250 Hz.

Unfortunately, applying the harmonic equaliser tends to increase the outputresistance of the output stage. The significance of this increased outputresistanceis that theloudspeakersystemmustbedesignedtobedrivenbythisspecificnon-zerooutputresistance.In short, an amplifier having an output stage using the harmonic equalisertechnique cannot be used as a universal amplifier. Whether it is part of acomplex loudspeaker system employing an active crossover or a loudspeakerwithasinglefull-rangedriver,itisacomplementarysystemwheretheamplifiermust be designed for a specific loudspeaker, and the loudspeaker’s acousticloadingmustbedesignedwiththespecificamplifierinmind.Itisprobablythecombinationoftheserequirementsthathaspreventedwidespreadadoptionoftheharmonicequaliser,yettherequirementscanbemet,aswewillseeinChapter6.Althoughanexplicitharmonicequalisermightnothavebeenintended,cathodefeedback sometimes results in distortion reduction exceeding the feedbackfactor, implying cancellation and consequent load sensitivity. For bothamplifiers,cathodefeedbackintheQuadIIpoweramplifierandintheauthor’s‘ScrapboxChallenge’producedbetter results than expected from the feedbackfactoralone,implyingcancellation.

DCBiasProblemsHavingchosenthetopologyofastagewithgreatcare,wechooseanoperating

point that cunningly maximises output swing, minimises distortion, usesstandard component values, and allwithin the current capability of the powersupply.Wenowneedtobiasthestage,whichcanbedoneinanumberofways:•Cathoderesistorbias•Gridbias•Cathodebiaswitharechargeablebattery•Cathodebiaswithadiode•Cathodebiaswithaconstantcurrentsink.

CathodeResistorBias

Biascanbeachievedbyinsertingaresistorinthecathodepath(seeFigure3.22).

Figure3.22Cathodebiasusingaresistor.

If valve current rises, resistor current also rises, making the cathode morepositivewithrespecttothegrid,thustendingtoturnthevalveoffandofferingsome overcurrent protection. This method of bias has the least sensitivity tovariations between valves,making it by far themost popular bias choice.WeknowIaand therequiredVgk, sowesimplyapplyOhm’s lawtodetermine therequiredcathoderesistor.However,insertingaresistanceinthecathodecircuitofasinglevalvecommon-cathodeamplifiercreatesnegativefeedbackthatreducesgain,whichmightnotbe acceptable. The traditional solution bypasses the resistor with a capacitor(whichisashortcircuitataudiofrequencies),thecathodeisconnectedtogroundatAC,andnegativefeedbackisprevented.Itisgenerallyarguedthattheaudiobandwidthextendsfrom20 Hzto20 kHz,andthataudioelectronicsshouldbeasnearlyperfectaspossiblewithinthisbandwidth.Becauserk tendstobelow

(typically<500 Ω),thecathodebypasscapacitorneedstobequiteahighvalue,forcingittobeanelectrolytictype.Unfortunately,suchacapacitoristypically+25%,−15%tolerancesothishaphazardtimeconstantshouldnotbeallowedtoaffectanyformalfilteringaction,anditsvalueisusuallysettoproducef−3 dB=1Hz,whichisthesameassayingτ≈160 ms.When biassing a stage, we make the assumption that the signal voltage issufficientlysmallthatitdoesnotaffecttheDCconditions.However,asclippingisapproached, thesignalvoltageat theanodeofa triodecouldbehundredsofvolts peak to peak, and the distortion (which contains a DC component)temporarilylowerstheaverageVa.AsecondaryeffectofthisdistortionisthatithasaDCcomponentthatchangesthemeananodecurrent.As an example, a common-cathode triode amplifier was tested. When thegeneratorwasmuted,Va=117.1 V,butwhenthestagewasdriventoalevelthatproduced 5% THD+N, the mean anode voltage fell to 114.2 V, indicating achange in mean anode current. Since this anode current flows through thecathode-bias resistor (which is in parallel with the cathode capacitor), anychangeinmeananodecurrentisintegratedbythecathodeCRnetwork(τ≈160ms).Whentheoverloadpasses,thecapacitortakes5τ≈1 storecoverto99%ofthe previous bias point. During this time, ra (which is dependent on Ia) willchange,slightlychangingrout.Ifthecircuitfeedsapassiveequalisationnetwork,rout is inevitably part of the design, so the change in rout causes a temporaryfrequency responseerror.Althoughaminor frequency responseerrorcouldbeconsideredirrelevantwhentheamplifierisproducing5%THD+N,afrequencyresponseerrorthatdecaystozerooveraperiodof1 safteroverloadmightnotbesoacceptable.Thebiasshifteffectcanbeobservedbymonitoring theDCvoltageacross thecathodebypasscapacitorwithandwithoutalargesinewaveattheanode.Thismethod has the advantage that an ordinary DVM can be used, whereasmeasuringattheanoderequiresaninstrumentthatcanmeasureDCaccuratelyinthepresenceofsignificantAC.Ideally,thereshouldneverbeashiftintheoperatingpointofavalve,whateverthesignal level.Provided that thevalve isneverdriven toproduce>1%THD,cathodebiasisperfectlysatisfactory,butifclippingislikely,analternativebiasstrategyshouldbeconsidered.

GridBias(Rk=0)

IfRk=0,theDCcomponentofdistortioncannotcausebiasshift.

GridbiasfromanauxiliarylowcurrentnegativesupplyiscommonintheoutputstagesofClassABpoweramplifiers,whereasbatterybiasisoccasionallyfoundinpre-amplifiers(seeFigure3.23).

Figure3.23Gridbiasusinganauxiliarypowersupply,oralithiumbattery.

Note thatbatterybiascanbeappliedeither inseriesor inparallel. Inpractice,parallelisusuallypreferredbecausetheoutputimpedanceofthepreviousstageand the battery’s series resistor formapotential divider that attenuates batterynoise,whereasthereisnoattenuationofbatterynoiseinseriesmode.Grid voltage is fixed, and valve current is determined purely by valvecharacteristics,sothereisnoprotectionagainstovercurrent,orcompensationforchangesinvalvecharacteristicswithage.Overcurrent protection is important in transformer coupled stages because thewindingresistanceofthetransformerisnegligibleandanoutputvalveisalmostcertainlybeingoperatedatmaximumanodedissipation.Currentfromthesupplyis,therefore,almostunlimited,andafaultislikelytodamageanexpensivevalvequickly,andworse,riskstheevenmoreexpensiveoutputtransformer.Conversely,inpre-amplifiersordriverstagesusingresistiveoractiveloads,thevalveistypicallyoperatedatlessthanhalfmaximumanodedissipation,andtheanode load limits fault current. It is quite conceivable that a fault resulting inmaximumcurrentcouldleavethevalveoperatingwellwithinitslimits,andnodamageatallwouldoccur.

RechargeableBatteryCathodeBias(rk=0)

Rechargeablecellshaveextremelylowinternalresistance,soiftheyareinsertedinthecathodepath,theydonotallowafeedbackvoltagetoappear(seeFigure3.24).

Figure3.24Cathodebiasusingarechargeablebatteryoperatedattricklecurrent.

Althoughthediagramshowsonlyonecell,anumberof(identical)cellscouldbeconnectedinseriestosettherequiredvoltage,althoughthiscouldbecomeratherbulky.Provided thatIk≤C/10(C is thecellcapacity inA h), theself-heatingcausedbycontinuouschargingwillnotdamagethecell.However,sincethecellisinavalveamplifier,itisprobablyratherwarmerthanthebatterymanufacturerexpected,solimitingthecurrenttoC/20mightbewise.AnAA-sizenickelmetalhydride(NiMH)celldevelops≈1.38 Vwhenchargedcontinuouslyat15 mA.

DiodeCathodeBias(rk≈0)

Rather than using a resistor, we can use a diode for cathode bias (see Figure3.25).

Figure3.25Cathodebiaswithadiode.

Theadvantageisthatadiode’sslope(AC)resistanceissomuchlowerthanthetraditionalcathoderesistorthatwenolongerneedtobypassitwithacapacitor.Although diode slope resistance is low, sometimes it may be necessary tocalculateitseffectonra.Table3.5comparesforwarddropsandsloperesistances(rslope)forvariousdiodes.

Table3.5ComparisonofForwardDropsandSlopeResistancesofVariousDiodes

Table3.5ComparisonofForwardDropsandSlopeResistancesofVariousDiodes

Thecolumn‘PureR’isthevaluerequiredtoachievethediodeforwardvoltageusingaresistor.Thus,thecolumn‘R/r’istheratiobywhichthediodeimprovesuponapureresistance–andthelargerthenumber,thebetter.

Diodetype Forwarddropat10 mA(V) Typicalrslopeat10 mA(Ω) PureRat10 mA(Ω) R/rSilicon(1N4148) 0.75 6.0 75 13Germanium(OA91) 1.0 59 100 1.7InfraredLED(950 nm) 1.2 5.4 120 22CheapinefficientredLED 1.7 4.3 170 40HLMP6000redLED 1.63 3.8 163 43Cheapyellow/greenLED 2.0 10 200 20EZ81 2.3 195 230 1.18TruegreenLED(525 nm) 3.6 30 360 12BlueLED(426 nm) 3.7 26 370 14EZ80 5.5 485 550 1.13

The thermionicandgermaniumdiodesbarely improveonapure resistance,sotheycanbediscountedimmediately.ThewinneristheredLED,butitneedstobe one of the older less efficient designs that youmight find cheap in a junkshop,ratherthanamodernhighbrightnesstype.Alternatively,themoremodern(andmorereadilyavailable)AgilentHLMP6000LEDisslightlybetterandthisredLEDissogoodthatifhighervoltagesareneededitisbettertouseaseriesstringofredLEDsthanasingle,inferiorcolourLED.Asanexample,supposeweneeded3.4 V.ReferringtoTable3.5,wesee thatwecouldapproximateitwithatruegreenLED(3.6 Vand30 Ω)orapairofHLMP6000s(3.26 Vand7.6 Ω)–thesloperesistanceofthetworedLEDsisaquarterthatofthesinglegreenLED.AsmentionedinChapter1,theauthor’smeasurementsshowthatoverarangeof0.3–10 mA,theforwarddropofatypicalHLMP6000maybepredictedfrom:

Differentiating,thesloperesistanceis:

Thisequationissignificantnotsomuchbecauseitallowsustoestimateavaluefor rslope, but because it shows that rslope is inversely proportional to IDC,suggestingthatLEDbiasisbestsuitedinstagespassing5 mA.Nevertheless,itispossibletouseLEDbiasinlowcurrentstagesifadditionalcurrentispassedthrough the LED, perhaps from a resistor connected to the HT, or from aconstant current source to a lower voltage source. In this way, an ECC83requiring 1.6 V but only passing 0.5 mA could be biassed by inserting anHLMP6000 in its cathode circuit and driving additional current through theLED. For a typical HLMP6000 red LED, the current needed to develop therequired1.6 Vforwardvoltagecanbefoundusing:

Wealreadyhave0.5 mAfromtheECC83,soweneedanextra4.16 mAfromsomewhereelse.Ifwehada285 VHT,thena68 kΩresistorwoulddo,butitwoulddissipate1.2 W, soa4 Wcomponentwouldbeneeded.Nevertheless,when the choice is between a 3.2 kΩ cathode-bias resistor (needing a bypasscapacitor)andanLEDwithasloperesistanceof5.7 Ωthatdoesn’tneedtobebypassed,thenthat68kΩ4 Wresistorsuddenlystartsmakingalotmoresense(seeFigure3.26).

Figure3.26CathodebiaswithLEDusingsupplementarycurrent.

Reverse bias generally producesmore noise in a diode than forward bias, butenables higher reference voltages. Low voltage Zener diodes truly use Zeneraction,whereashighervoltagediodesactuallyuse theavalancheeffect.At6.2V,botheffectsarepresent, theiropposing temperaturecoefficientscancelandrslope is at aminimum, so 6.2 V Zeners are themost stable. If a stable highvoltagereferenceisrequired,itisusuallybettertohaveastringof6.2 VZenersthanasinglehighvoltageZener.FromaDCpointofview,diodebiasisidealforthelowervalveofaμ-followerorSRPPbecauseIaisstabilisedbythebiasarrangementsoftheuppervalve.Becauserslope≠0,achangeinsignalcurrentcausesachangeinthevoltageacross

thediode.ThesignalcurrentalsoproducesthevoltageacrossRL,so:

Cross-multiplying:

Thesignificanceofthisequationisthatwehavejustseenthatrslopeisinverselyproportionaltoappliedcurrent,andbecauserslopevarieswithsignalcurrent,thesignalvoltagedevelopedacrossitmustbedistorted.Unfortunately,thisdistortedsignalvoltage is inserieswith the inputsignalbecause thevalveamplifies thedifferenceinvoltagebetweenthegridandthecathode(seeFigure3.27).

Figure3.27Non-lineardiodeinternalresistanceaddsdistortioninserieswiththesource.

However,theequationandthediodecurveshowusthatthedistortionaddedbythediodecanbereducedby:•AvoidingdiodebiasforIdiode<5 mA(becauserslopeisparticularlyvariableatlowcurrents).•Minimisingrslopebydiodechoice(redLED).

•MaximisingRL.

•Reducingtheoutputsignalvoltage .

Theseconditionsimplythatdiodebiasisbestsuitedto:•RIAA input stages: Ia is high and signal levels are low. Additionally, thestage can recover instantly from clipping due to high voltages at highfrequenciescausedbydust,etc.,ontherecord.•μ-Followerstages:TheactiveloadmaximisesRL,andIaislikelytobehigh(minimisingthevariationinrslope).

ConstantCurrentSinkBias

Aconstantcurrentsinkallowscathodecurrenttobeforcedtothedesignvaluedespitevalveparameters.However,becauseaconstantcurrent sink isanopencircuittoAC,itwouldcause100%negativefeedbackinasingle-endedstage,soitmustbebypassedwithacapacitor(seeFigure3.28).

Figure3.28Cathodebiasusingabypassed317constantcurrentsink.

Oncebypassedbythecapacitor,theACperformanceoftheconstantcurrentsinkbecomes irrelevant, so a three-terminal regulator such as the 317 becomesperfectlyacceptable,andthisstrategyisquitepopularinoutput-valvecathodes.This is a very rare occasion when DC accuracy is more important than ACperformance because accuratematching of DC currents in a push–pull outputstageenablesustoeliminatethemagnetisingcurrentthatwouldcauseatoroidaloutputtransformer’scoretosaturateandgeneratebassdistortion.Notealsothatbecause the cathode current has been forced by the 317 CCS (and thereforecannot run away), the grid-leak resistor can become rather larger than themaximum specified by the valve datasheet, enabling a smaller coupling

capacitorfromtheprecedingstage.DifferentialpairsandcathodefollowersrequireexemplaryACperformance,andDC accuracy is generally a secondary consideration,whichwaswhywe tooksuchcarewheninvestigatingtheirdesignattheendofChapter2.

IndividualValveChoiceAlthough a set of anode characteristics having noticeably different spacingsbetween the curves indicates distortion, evenly spaced characteristics do notguaranteelowdistortion.Ultimately,wemusteitherusevalvesdesignedforlowdistortion,ortestvalvesfordistortion.

WhichValvesWereExplicitlyDesignedtobeLowDistortion?

Minimising distortion costs money, so when low-distortion valves weredesigned,theyweretargetedspecificallyattheaudiomarket,whichincludedthebroadcast,recordingandfilmindustriesand,ofcourse,theconsumer.In the1930s,gainwasextremelyexpensive.The ideaofdeliberately throwinggainaway(negativefeedback)wastreatedasheresy,somuchsothatalthoughBlack’s jottednoteswerewitnessedon18August1927,hisUSpatent[5]wasnotissueduntil21December1937.Asaconsequence,lowdistortionwasreliantonvalvedesignandconstruction,sovalveslikethe76weredesignedtobelowdistortion. As feedback became more widely accepted, it became cheaper toreducedistortionbysacrificinggain,sothefinalgenerationofvalveshadhighergain,butlowdistortionbecamelessimportant.Low-distortionvalveswerealsorequiredbythetelecommunicationscompanies,butnotbecausetheywereconcernedwiththefidelityofbasebandaudio.Ifweneed toprovide1,000analogue telephonecircuitsbetween twocities10milesapart,we could lay 1,000 twisted pairs, but a cable containing this amount ofwire is expensive and cumbersome to lay. The solution adopted by thetelecommunicationscompanieswas tomodulateeach telephonecircuitontoanRF carrier with its own frequency – just like different radio stations. Onethousand modulated carriers could then be passed down a single (usuallycoaxial) cablewhichwas cheap and easily laid.All cables introduce loss, andbetween cities the loss becomes significant, so each cable needed repeateramplifiers at regular distances. One of the many advantages of multiplexing1,000telephonecircuitsontoonecablewasthatonlyonerepeateramplifierwasneededeveryfewmilesinsteadof1,000,reducingcost.However,anydistortionin that amplifier would cause one telephone conversation to crosstalk ontoanother. Valves designed for use in broadband telephone repeater amplifiers

werethereforerequiredtoproducelowdistortion.Manyofthefinalgenerationofvalvesusedaframe-grid,andsome,suchasthe417A/5842,wereexplicitlydesignedforlowdistortion.OthervalvessuchastheECC88/E88CC simply benefited from improved production engineering andproduce usefully low distortion. Some valves such as the E182CC and 6350were designed for use in early digital computers, where the most importantconsiderationwas long life evenwith full heater power andno anode current,whichtemptsthegrowthofcathodeinterfaceresistance.Finally, somevalvesweredesignedandmanufacturedwithacomplete lackofregardfordistortion.Theproblemoffield,orvertical,scanninginatelevisionusingaCathodeRayTube(CRT)wasverysimilartothatofanaudioamplifierdrivingaloudspeaker.Bothuseatransformertocoupletothedrivingvalve,andthefrequencyrangeissimilar.However,CRTscancoilsmustbedrivenbyacontrolledcurrent,ratherthan applied voltage as is conventional for loudspeakers. Unfortunately, thefinite (and changing) primary inductance Lp of the small iron-cored outputtransformerdrewa current in addition to the scan coil current, and thismeantthat the current waveform drawn from the field scan valve was distortedcomparedwith the ideal current required by the scan coils. Thereweremanywaysofachievingacompensatingdistortion,butonewastousethecurvatureofthe Ia/ Va characteristic of a triode. Since transformer Lp was not tightlycontrolled, the requireddistortionhad to be controllable, so a variable resistorwas often inserted in the cathode circuit of the valve to allow adjustment ofverticaldisplaylinearity.Thecruxofthepreviousargumentisthattherewasnorequirementwhatsoeverfor the valve manufacturers to produce field scan valves with outstanding oreven consistent linearity, since this had to be individually adjusted for eachtelevision’s CRT. Early field scan valves such as the dual triode 6BX7 showwide variations in distortion (4:1 between best andworst), so they have to beselected for audio use, and the probability of finding a pair of low-distortionvalvesinoneenvelopeislow,soselectingapairoflow-distortion6AH4singletriodeswouldbeamuchcheaperalternative.LatergenerationvalvessuchastheECC82(alsointendedforuseasafieldscanoscillator)benefitedfromimprovedproduction techniques and distortion is extremely consistent from sample tosample;itisconsistentlypoor.

CarbonisingofEnvelopes

Deketh [6] pointedout that not all electrons accelerated from the cathode/grid

interface strike the anode – somemiss and collidewith the envelope, causingsecondaryemission.Secondaryemissionisimportantbecauseitmeansthattheenvelopeacquiresanegativechargethatcandistorttheflightofelectronsfromcathode to anode. Deketh considered distortion at high amplitudes in powervalves and showed that carbonising the inside surface of the envelope wasbeneficial because it reduced secondary emission. At the time, nobody wasworriedaboutaudiodistortionat<1%,andDekethmightnothavehadaccesstoan audio spectrum analyser, so he did not publish distortion results at lowerlevels. Nevertheless, this author’s measurements at +28 dBu (≈19.5 V RMS)showsignificantlyreduced(≈−6 dB)distortionforsamplesofthe6SN7havingacarbonisedenvelopecomparedtoclearenvelopes.

DeflectingElectrons

Amplifyingvalvescontroltheflightofelectronsbyimposingelectricfields,butelectronscanbedeflectedbymagneticfields.TheEarth’smagneticfieldisquiteweak,soitisunlikelythatorientingavalveinanyparticulardirectionwillaffectdistortion, but most sheet electrodes are made of nickel, which can easily bemagnetised.Ifthevalvewasconstructedfromconcentriccylindricalelectrodes,magnetic deflection would not matter unless it caused electrons to miss theanode, but box constructions do not have radial symmetry, so horizontalmagneticdeflectioncouldinfluenceanodecurrent.Beam tetrodes with aligned grids are the most susceptible to magnetic fieldsbecause vertical magnetic deflection could cause the sheets of electrons tointerceptg2ratherthanpassingcleanlybetweentheverticallyalignedwindings.Thus, amagnetic field canchange the Ia/ Ig 2 ratio, and itwouldbe foolish tosuggest that this could not affect distortion. Some years ago, using a coilintendedfordegaussingtelevisiondisplaytubes, theauthor jokinglydegaussedtheKT88(alignedgridbeamtetrodes)ofapoweramplifier,andeveryoneheardaslightdifference.Weshouldbeawarethatdegaussingrequiresthemagneticmaterialtobetakento saturation in both directions and then gently taken through ever decreasinghysteresis loops until the residualmagnetism is zero.Thus,magnetisation anddemagnetisationareachievedbybruteforce–theauthor’sdegaussingcoilis10″(250 mm)indiameter,consumes750 VAandisratedonlyforintermittentuse.Applyinganaudiosignaltoanamplifiercannotpossiblyachievethiseffect,nomatterhowexoticthesignalmaybe.

TestingtoFindLow-DistortionValves

Low-noise input stages demand high gm, and signal levels are so low thatdistortion isnot an issue.Tominimisenoise,well-designedcircuitryamplifieslow-levelsignalsonceonly,andthereaftercarriesline-levelsignals.Whendesigningapowerstage,themostimportantconsiderationisPa(max),andtheconsequentDCrequirementsforcedistortiontobequitelowdownonthelistofpriorities.Further,powerstagesareusedonceonlytodrivetheload.Becauseof theprevious twoarguments, lowdistortionvalves are essential forline-levelprocessing(becausethereislikelytobesomuchofit),buttheyneednothaveoutstandinggmorPa(max).Highμvalvesmightbeundesirableif theirdesignassumedtheuseofnegativefeedbacktoreducedistortion.Sadly,mostofthe low-μ valvesweredesigned for television field scan, so theirdistortion isdistinctly questionable unless individually selected. The remaining valves aremedium-μandhavePa(max)<5 W.The 6SN7 is widely accepted as a low-distortion valve, but howwell does itjustifyitsreputation?Bearinginmindthatvalveswereassembledbyhandandsubject to wide production tolerances, is there a ‘best’ medium- μ valve ormanufacturer?Thissectionseekstoanswerthesequestionsbyreportingonthetestingofaselectionofmedium-μvalvesunderidenticalconditions.

TheTestCircuit

Ifwerequirealow-distortiongainstage,thiscanbeachievedbyasingle-endedstagewithanactiveload,oradifferentialpairwithresistiveloadsandconstantcurrent sink tail. In short, circuit design can reduce distortion, but only to thepoint where the valve’s irreducible distortion takes effect. If we are to selectvalves forminimumdistortion,weshould focuson their irreducibledistortion,sincehigherlevelsofdistortioncanalwaysbereducedbysuitablecircuitdesign.Although this complicates matters by requiring us to measure distortion in astagedeliberatelydesigned for lowdistortion, it has thebenefit of enforcing alevelplayingfield.If we later use a topology that does not minimise distortion, and valve ‘A’sounds better than valve ‘B’, it is because valve ‘A’ suits the topology betterthanvalve‘B’,notbecausevalve‘A’is‘better’thanvalve‘B’.As previouslymentioned, distortion in a triode amplifier is dominated by thevariationofrawithIa.ProvidedthatRL>>ra,thevariationofraisinsignificant,so distortion can be reduced bymaximisingRL. In addition, the valve shouldpasssufficientanodecurrenttoplaceitsoperatingpointwellclearofthetypical

bunchingofanodecurvesexperiencedat lowcurrents.Accordingly, thevalveswere tested in a μ-follower circuit passing ≈8 mA anode current. In thisconfiguration,thetestvalveseesRL≈800 kΩ,whichalthoughfarfrominfinite,canbeputintoperspectivebyrealisingthatifatrue800 kΩresistorweretobesubstituted,a6.4 kVHTsupplywouldberequired.Heaterfilamentswerefedfroma stabilisedDCsupply adjusted for the correctvoltage at theheaterpins(seeFigure3.29).

Figure3.29Medium-μvalvetestcircuit.

AudioTestLevelandFrequency

Since distortion was expected to be low, the valves had to be tested at asufficientlyhighoutputleveltomakethedistortioneasilymeasurable,yetwellbelowclipping.+28 dBu(≈19.5 VRMS)wasfoundtobeagoodcompromise,soeachvalvehad its input level adjusted toproduceprecisely+28 dBuat its

output.Distortion inall the reportedvalves isdirectlyproportional to level, sodistortionatlowerlevelscanbeextrapolatedfromthetestdata.Although initially testedat120 Hz,1 kHzand10 kHz,distortionof the testcircuitwasfoundtobecompletelyindependentoffrequency,sothevalvesweretested at 1 kHzonly.Formost of the valves, harmonics beyondH6were tooclose to the oscillator distortion residual for reliable measurement, someasurementwasonlyattemptedonharmonicsuptoandincludingH6.

TestResults

Allofthevalvestestedwere‘NewOldStock’(NOS),sothenewestvalveswereat least30yearsold,and theoldestwas58.Since thevalveshavebeenoutofproductionfordecades,forsometypesonlyafewsampleswereavailabletotheauthor.Raw data from themeasurementswere analysed in a spreadsheet, and brokenintodifferentgroupsasandwhensignificantdifferencesbecameapparent.Table 3.6 summarises the results of the 6SN7GT/12SN7GT and its directequivalents.Thenumberof samples refers to thenumberof individual triodestested,notenvelopes.

Table3.6ComparisonofDistortionHarmonicsWithinthe6SN7Family

1σ=Onestandarddeviation.

Type Samples H2 1σ H3 1σ H4 1σ6SN7GT/12SN7GT 44 −50 3.6 −85 8.4 −96 5.97N7 82 −52 3.3 −85 8.6 −97 6.714N7 62 −52 3.3 −85 8.6 −97 6.7Carbonised6SN7GT 6 −54 1.8 −94 5.6 –CarbonisedCV1988 12 −57 2.6 −85 7.2 −93 4.212SX7GT 12 −50 1.9 −83 3.2 −94 6.0GEC/MarconiB36 6 −51 2.0 −90 8.1 −88 2.06J5GT(various) 6 −50 4.1 −82 12.7 −97 3.1Pinnacle6J5GT 138 −52 2.6 −90 6.7 −96 3.9RCA6J5 15 −47 4.8 −84 8.3 −89 7.7GECL63 5 −50 1.6 −86 4.4 −89 4.47A4 3 −48 0.2 −73 1.6 −93 1.2

Table 3.7 normalises distortion to the 6SN7GT/12SN7GT to enable clearercomparison.

Table3.7NormalisedComparisonofDistortionHarmonicsWithinthe6SN7FamilyType Samples

H2 H3 H4dB Ratio dB Ratio dB Ratio

6SN7GT/12SN7GT 44 0 1 0 1 0 17N7 82 −2 0.79 0 1 −1 0.8914N7 62 −2 0.79 0 1 −1 0.89Carbonised6SN7GT 6 −4 0.63 −9 0.35 −14 0.2CarbonisedCV1988 12 −7 0.45 0 1 +3 1.4

CarbonisedCV1988 12 −7 0.45 0 1 +3 1.412SX7GT 12 0 1 +2 1.26 +2 1.26GEC/MarconiB36 6 0 1 −5 0.56 +8 2.56J5GT(various) 6 0 1 +3 1.4 −1 0.89Pinnacle6J5GT 138 −2 0.79 −5 0.56 0 1RCA6J5 15 +3 1.41 +1 1.12 +7 2.2GECL63 5 0 1 −1 0.89 −3 0.717A4 3 +2 1.26 +12 4 +3 1.4

Interpretation

The manufacturers claimed that all the preceding valves were electricallyequivalent. Nevertheless, there are significant differences between the valves,andusefulconclusionscanbedrawnfromTable3.7.• Valves with carbonised glass envelopes produce less distortion. Dekethreportedthatcarbonisedenvelopesreduceddistortionatmaximumpower,butthisseriesoftestssuggeststhattheimprovementisproportionaltolevel,andthatcarbonisedenvelopessignificantlyreducedistortionatloweramplitudes.•TheRCA6J5 (metal envelope)has significantlyhigherdistortion than the6J5GT, probably due to increased numbers of gas ions resulting fromoutgassingofthemetalenvelopecausingincreasedgridcurrent.•Despitehavingaclearenvelope,the(Russian-made)Pinnacle6J5GToffersvery low distortion – significantly better than any other manufacturer of6J5GT.• The Loktal™ basewas specifically designed to reduce stray capacitancesand inductances by eliminating the glass pinch required by the Octal base,hencethe6SN7GT/12SN7GThasaclaimedCag≈4 pF,whereasthe7N7hasaclaimedCag=3 pF[7].

• Some valves were selected from the standard production line by theirmanufacturers.This test showsnosignificantdifference indistortion for the12SX7 (simply a 12SN7GT selected for transconductance [8] atVa=28 V)comparedtothestandard6SN7GT/12SN7GT.• The third harmonic distortion of the Loktal™ 7A4 single triode is verydisappointing,butasonlythreesampleswereavailablefortesting,theresultsare probably not statistically significant even though the standard deviationwasonly1.6 dB.• The *SN7GT family is available with four different heater filamentconstructions[9],soTable3.8comparesthedifferenttypes.

Table3.8HeaterVoltagesandCurrentsWithinthe*SN7FamilyVoltage(V) Current(mA) Heatingpower(W)

6SN7GT 6.3 600 3.788SN7GT 8.4 450 3.7812SN7GT 12.6 300 3.7825SN7GT 25 150 3.75

AscanbeseenfromTable3.8,theheaterpowerisalmostidenticalforalltypes.Physically,the6SN7GThasitsheaterswiredinternallyinparallel,whereasthe12SN7GT sometimes has them wired in series, but electrode construction isidentical,sodistortionought tobesimilar,soTable3.9comparesdistortionofthe6SN7GTwiththatofthe12SN7GT.

Table3.9ComparisonofDistortionHarmonicsBetween6SN7and12SN7

Thetwovalvesareverysimilar–thedifferencesarewellwithinthemarginsofuncertainty.

Samples H2 1σ H3 1σ H4 1σ6SN7GT 28 −50 3.5 −83 8.9 −96 5.712SN7GT 16 −51 3.8 −87 7.3 −97 6.5

Similarly,wecancomparethe7N7withthe14N7(Table3.10).

Table3.10HeaterVoltagesandCurrentWithintheLoctalFamilyVoltage(V) Current(mA) Heatingpower(W)

7N7 6.3 600 3.7814N7 12.6 300 3.78

Again, we would expect the distortion between the two types to be similar(Table3.11).

Table3.11ComparisonofDistortionHarmonicsBetween7N7and14N7Samples H2 1σ H3 1σ H4 1σ

7N7 82 −52 3.3 −85 8.6 −97 6.714N7 62 −52 2.4 −88 7.8 −95 6.4

Summarising, the differences between valves having different heater voltagesarewellwithinthemarginsofuncertainty.Thisisgoodnewsbecauseitmeansthatwe don’t have to use the expensive 6.3 V heater valves, but can use thecheaper and more plentiful 12.6 V heater valves and enjoy the reduction inelectromagnetichumcausedbytheirreducedheatercurrent,althoughthehigherheatervoltagecausescommensuratelymoreelectrostatichum.Thesignificanceoftradingelectromagnetichumforelectrostatichumisthatalthoughbothtypescan be shielded, earthed aluminium cooking foil is an effective electrostaticshield, whereas effective electromagnetic shielding requires a far greaterthicknessof ironorexpensivemu-metal.Naturally,bothproblemsdisappear ifweuseregulatedDCheaters.

AConvention

Theauthorhasadoptedaconventionthatwillbeappliedthroughoutthisbook.Having established that the 6J5GT, 6SN7GT, 12SN7GT, 7N7 and 14N7 areelectrically virtually identical, and that the 8SN7GT and 25SN7GT can beexpected to be similar, economy of nomenclature is necessary. From now on,this familywillbecalled theSN7/N7family (todistinguishbetween thebasesandcapacitances).Pleasenotethat the6N7isacompletelydifferentbeast,andbearsnorelationtoa7N7.

AlternativeMedium-μValves

Table3.12showspossiblealternativestotheSN7/N7family.

Table3.12ElectricalAlternativestotheSN7/N7Family

Foreachvalve,μwasreadfromthemanufacturer’sanodecurvesatthe8mAoperatingpoint.

Type μ Samples H2 1σ H3 1σ H4 1σ H5 1σ H6 1σ7AF7 16 4 −38 0.3 −62 1.5 −74 0.6 −89 4.2 −91 5.7ECC82/12AU7/B329 18 28 −37 −56 1.4 −73 3.9 −86 6.6 −96 3.1E182CC/7199 18 30 −45 1.7 −70 1.5 −92 3.7E288CC 20 14 −49 1.3 −69 0.9 −89 5.4 −95 7.2 −96 4.937 9 9 −45 0.6 −69 4.9 −87 5.7 −88 10.1 −86 14.25687(various) 16 22 −49 1.1 −72 1.7 −91 3.9Philips5687WB 16 14 −42 2.5 −68 2.8 −92 2.46350 20 26 −44 1.4 −65 2.4 −84 2.4 −98 6.2

Table 3.13 allows quick comparison of these alternatives by normalising theirdistortiontothe6SN7GT/12SN7GT.

Table3.13Distortion(normalisedto6SN7GT/12SN7GT)ofElectricalAlternativestotheSN7/N7FamilyType Samples

H2 H3 H4dB Ratio dB Ratio dB Ratio

6SN7GT/12SN7GT 44 0 1 0 1 0 17AF7 4 +12 4 +23 14 +23 14ECC82/12AU7/B329 28 +13 4.5 +29 28 +23 14E182CC/7199 30 +5 1.78 +15 5.6 +4 1.58E288CC 14 +1 1.12 +16 6.3 +7 2.237 9 +5 1.78 +16 6.3 +9 2.825687(various) 22 +1 1.12 +13 4.5 +5 1.78Philips5687WB 14 +8 2.5 +17 7.1 +4 1.586350 26 +6 2 +20 10 +12 4

The results in Table 3.13 speak for themselves. All of the alternatives areinferiortothe6SN7GT/12SN7GTandproducesignificantlymoreH3.The Loctal 7AF7 dual triode and B9A ECC82 dual triode are particularlyghastly. Perhaps significantly, these valves have an electrode structure thatsignificantly reducedCag compared to theSN7/N7family (2.3 pFand1.6 pFversus4.0 pF).These tests suggest that themeasures necessary to reduceCag

withintheelectrodestructuremightadverselyaffectdistortion.There was a significant difference between the Philips 5687WB and othermanufacturers’ samples, so this type was isolated. Although H2 and H3 aresignificantlyhigherthancompetingmanufacturers,H2wouldmostlybenulledifusedinadifferentialpair.

Weighted-DistortionResults

Towardsthebeginningofthischapter,distortionweightingwassuggestedasauseful technique, so Table 3.14 mathematically weights the measurementsaccording toCCIR468-2withagainoffsetof−6 dB inorder tomake theH2resultcomparablewithanunweightedmeasurement.Becausethisparticulartestwas limited to harmonics up to H6 (6.3 kHz is the corner frequency forCCIR468-2) and thedistortionwasdominatedbyH2harmonic, thedifferencebetweenCCIR468-2less6 dBandtheShorterrecommendationwasonly≈0.1dB – well below measurement uncertainties, and validating Peter Skirrow’sCCIR468-2single-measurementargument.

Table3.14WeightedDistortionComparisonofAlltheValvesTestedType Numberofsamples Weighteddistortion(dB)

CarbonisedCV1988 12 −58Carbonised6SN7GT 6 −55Pinnacle6J5GT 138

−527N7/14N7 144GEC/MarconiB36 6 −516SN7GT/12SN7GT 44

−5012SX7GT 126J5GT(notPinnacle) 6L63 5

−49E288CC 145687(notPhilips) 227A4 3

−48RCA6J5 15E182CC/7199 30 −456350 26 −44Philips5687WB 14 −427AF7 4 −38ECC82,12AU7,B329 28 −36

OverallConclusions

Atotalof529valveswastested,andtheresultsshowthatthereputationoftheSN7/N7 family is well justified. Distortion for the dual triodes varied fromsample to sample,with a few significant trendsvisiblebetweenmanufacturers(probably because manufacturers were well known for buying in another

manufacturer’svalvesandbrandingthemastheirownintimesofshortsupply).Ifindividualmeasurementandselectionforlowdistortionarenotpossible,thencarbonised envelope valves from theSN7/N7 family are likely to produce thelowest distortion. If these are not available, then a 7N7, 14N7 or a Pinnacle6J5GTislikelytobeagoodchoice.ValveswithelectrodestructuresshrunktofitB9Abasesaresignificantlypoorer.

CouplingfromOneStagetotheNextThemostcommonwayofcouplingonestage to thenext isviaacapacitor.Aperfect capacitor does not generate distortion. Unfortunately, even a perfectcapacitorcangreatlyexacerbatethedistortiongeneratedbyvalvesortransistors.

Blocking

Blockingisanextremelyunpleasantmechanismwherebyanamplifiermutesforashorttimeafteramomentaryoverload.Insimpleterms,blockingiscausedbythecapacitorthatcouplestoastagethatisoverloaded(seeFigure3.30).

Figure3.30Capacitorcouplingandblocking.

Capacitorcouplingbetweentwostagesformsahigh-passfilter.Inordernottoaffecttheaudio,wedeliberatelydesignforalowf−3 dBfrequencyusing:

Thus,settingf−3 dB=1 Hzmeansthatτ=160 ms,butthetruesignificanceofτinthiscontextwilltakealittletimetoemerge.BecauseofKirchhoff’svoltagelaw,thefollowingmustbetrueatalltimes:

Example: , and the followinggrid is tied togroundvia agrid-leakresistor,so ,causingVC=100 V.

IfweapplyanimpulsetoV1sothattheanodeswings20 Vpositively,thegridofV2attemptstoriseto+20 V,butwhenitreaches+10 V,Vgk=0,andthegridconductssoheavilytothecathodethatitsvoltageisclampedto+10 V.Atthisinstant,thepreviousKirchoffequationmuststillbetrue,so:

Thecapacitorwasable tochange itsvoltagealmost instantaneouslybecause itcharged through the low impedance path of the overloaded grid. When theimpulsepasses,wecanfindthegridvoltageofthesecondvalvebyrearrangingtheequation:

Thegrid isat−10 V,but thecathodeisheldat+10 Vbythecathodebypasscapacitor, soVgk=−20 V, and thegridhas reverted to ahigh impedancepath.More importantly, the valve is now switchedoff and remains so until the gridrecoversto0 V.Theonlypathforthecapacitortochangeitschargeisthroughthegrid-leakresistor,butaswesawearlier,thiscombinationhasatimeconstantof160 ms.Worse,5τisrequiredforthecapacitortochangeitschargetowithin99% of its final charge, so the grid does not reach 0 V until 0.8 s after themomentaryoverload.Recovery from overload is complicated by the fact that once the valve isswitchedoff,thereisnocathodecurrent,sothecathodebypasscapacitorbeginstodischargethroughthecathode-biasresistor.Althoughthiscausesthevalvetobeginconductingearlierthanwouldotherwisehavebeenexpected,italsohastorecoverfromthechangeimposedbyblocking.Thus,amomentaryoverloadhashaditseffectsextendedtoalmostasecond.It might be thought that the severe overload posited to cause blocking isunlikely, but applying global feedback around a power amplifier containing acapacitor-coupled output stage almost guarantees blocking. Suppose that atransient causes clippingof theoutput stage.Feedbackattempts to correct thisdistortion of the waveform by increasing substantially the drive to the outputstage,andtherequirementsforblockinghavebeensatisfied.Blocking occurred because a coupling capacitor was allowed to change itschargesignificantlyduringanoverload.Ifthecapacitorcouldbeeliminated,ormoved so that it coupled to a stage that couldnot beoverloaded, theproblemwould not arise. This techniquewill be explored in the non-blocking ‘CrystalPalace’amplifierdescribedinChapter6.Alternatively, the time constant of the coupling capacitor could be reduced,

reducing the duration of blocking. The price paid for this solution is lowfrequency attenuation in a zero global feedback amplifier or increased lowfrequencydistortioninafeedbackamplifier.However,ifsuchanamplifierwerepart of a loudspeaker system having an active crossover (valve treble,semiconductorbass),degradedlowfrequencyperformancewouldbeirrelevant.StuartYaniger’s‘RedLightDistrict’amplifieravailableatthediyAudiowebsiteisagoodexampleofthisdesignphilosophy.

TransformerCoupling

Transformersareexpensive,but theyareessential forconnecting loudspeakerstovalveamplifiersunlesswearepreparedtotolerateappallinglylowefficiency.Inter-stagetransformersoffersomeuniqueadvantages:•Fromthepointofviewoftheprimary,ifthetransformerisusedastheanodeload,thevalvecanachieveamuchlargersignalswingbecausetheanodecantheoreticallyswingtodoubletheHTvoltageifnecessary.Alternatively,fromaloadlinepointofview,theHTvoltagehasdoubled,yetthesignalswinghasremained constant, typically halving the distortion compared to a resistiveanodeload.• If the transformer steps downby a ratio of 2:1, the stage canproduce thesame swing as a resistively loaded stage, but with a quarter of the outputresistance.•Apush–pullstageallowscancellationofevenharmonicdistortion.•Fromthepointofviewofthesecondary,acentre-tappedwindingprovidesidealphase-splitting.• Larger power valves need low grid-leak resistances because of their gridcurrent,sotheverylowRDCofthesecondaryisideal.

Againsttheseadvantageswehavetoweightheinescapablefactthatinter-stagetransformerssuffermostfromtransformerimperfectionsbecausetheyoperateathighimpedances,andsingle-endedstagesforcethetransformertopassthe(DC)anodecurrent,requiringagappedcore,whichreducesbandwidth.

LowFrequencyStepNetworks

One possibility sometimes seen in power amplifiers is to bypass the couplingcapacitorwitha resistor to formastepnetwork.Lowfrequencystepnetworksarebest insertedjustbeforeadifferentialpairandmayevenease their tailDC

arrangements(seeFigure3.31).

Figure3.31Astepnetworktoreducelowfrequencyphaseshift.

Notethatbecause110 Vhasbeenappliedtothesecondvalve’sgrids,asimpleresistorsufficesforcathodebias,althoughperformancewouldbeimprovedifitweretobereplacedbyaCCS.Astepnetwork is intermediatebetweenDCandACcoupling. In theexample,thestepnetworkisa6 dBDCpotentialdividerbypassedabove15 Hzbythe22 nFcapacitors.Thesignificanceisthatcarefuldesigncanproducelesslow-frequency phase shift with a smaller capacitor than pure AC coupling andbecause reduced low frequency phase shift improves stability, more globalfeedbackcanbeapplied,reducingdistortion.Further,blockingbecomeslessofaproblembecausetheoffendingcapacitorhasadischargeresistordirectlyacrossit.Unless another low frequency timeconstant isdominant, stepnetwork timeconstants generally have to be determined by experiment because they aredependentonthe(non-constant)primaryinductanceoftheoutputtransformer.

LevelShiftingandDCCoupling

IntheabsenceofPNPvalves,DCcoupledvalveamplifiersrelyfundamentally

onthepotentialdivider(seeFigure3.32).

Figure3.32ThethreepotentialdividerarrangementsthatallowDCcoupling.

InFigure3.32a,wehaveasimpleresistivepotentialdividertothenegativeHT.Wewanttoachieve−10 Vattheoutputofthepotentialdivider.Ratherthanusethepotentialdividerequation, it is easier to set acurrent through thepotentialdivider and apply Ohm’s law to find the required resistances. Our potentialdividerwill steal current from theanodeof theprecedingvalve, sowe shouldminimise this current. If we set the potential divider current to 100 μA, theupperresistormustbe:

Similarly,thelowerresistormustbe:

The nearest value of 910 kΩ is fine. Unfortunately, not only have we levelshiftedoursignalbytherequiredamount,wehavealsoattenuatedit.ThinkinginACterms:

Pure resistive level shifters inevitablyattenuate thewantedAC,and this is theprice thatmust be paid for simpleDC coupling.A capacitor across the upperresistorwouldavoidtheACattenuationbutcreateastepnetworkwhichmightnotbedesirable.TomaintainDCcouplingwithoutACattenuation,we could replace theupperresistorwithabattery,tomakeaThéveninlevelshifter(seeFigure3.32b).BecausethebatteryisaperfectThéveninsource, it isashortcircuit toAC,so

this level shifter does not attenuate AC. Because 110 V batteries areinconveniently large,wewouldreplace thebatterywithaZenerdiodeorneonreferencevalve.Sadly,bothdevicesmustpassasignificantDCstandingcurrent(typically 5 mA), whichmakes them awkward to use.Worse, they both addnoise.Ourfinalpossibilityistoreplacethelowerresistorwithaconstantcurrentsink,tomakeaNortonlevelshifter(seeFigure3.32c).There is no reason why we should not make a constant current sink out ofbipolar transistors or a pentode. Provided that the sink has rout>> Rupper, theNortonlevelshifterdoesnotattenuateAC.However,thenoiseproblemremains.Pentodesandtransistorsaretransconductanceamplifiers,whichmeansthattheyconverttheirinputvoltageintoanoutputcurrent.AcurrentsinkamplifiesitsDCreference voltage, and we propose to convert its output current back into avoltageusing a highvalue resistor. In effect,wehave constructed a high-gainamplifierthatamplifiesthenoisevoltageoftheDCreference.Although Thévenin and Norton level shifters are theoretically usable, theirpractical problem is noise, and almost all the design effort must focus onreducing this noise to acceptable levels. (Constant current sink tails indifferentialpairsdonotaddsignificantnoisebecausethelowimpedanceloadrkseverely reduces their gain, and their noise is applied commonmode, so it ismostlyrejected.)Sadly, eachof these techniques connects the signal to thenegativeHT,whichmayaddhumandnoisetothewantedsignal.

ADCCoupledClassAElectromagneticHeadphoneAmplifier

Aswithallamplifiersfacingadifficultload,thiscircuitwasdesignedworkingbackwardsfromtheoutputtotheinput.Beawarethatthecircuitispresentedasa vehicle for investigating the problems of DC coupling – not as a detailedexemplarofheadphoneamplifierdesign.Acathodefollowerisneededtoprovidealowoutputresistance.High-μ,high-gmvalvesarebestsuitedascathodefollowersbecausethehighgmensureslowrout,andhighμallowsplentyoffeedbacktoreducedistortion,sothe6545Pisideal. The cathode is connected to the negative HT via a standard pentodeconstantcurrentsinkusinganEL822.We know that we want to apply DC feedback to stabilise the output of theamplifier at 0 V, and we need our completed amplifier to have a high inputresistance so that it does not load volume controls. The ideal input stage is

therefore a differential pair, and because we already have a negative HT, itseems churlish not to use another pentode constant current sink (see Figure3.33).

Figure3.33ADC-coupedamplifierusingapotentialdividertothenegativeHT.

Electromagnetic headphones are low impedance devices. Because portableequipmentmustoperatefroma3 Vbattery(possiblyonly1.5 V),headphonesdesigned for portable use are typically 32 Ω, but better quality designs tendtowards200 Ω.Eitherway,theyrequireconsiderablecurrent,andareextremelyonerous loadsforvalves.AsweincreaseIa,Pa rises,sowemustreducePabyloweringVaasfaraswedarewithoutrunningintogridcurrent.SettingVa=135Vkeepsusjustclearofgridcurrent.AlthoughitisclaimedthatPa(max)=7.8 W,alltheother6C45_specificationsaresomewhatoptimistic,andtheenvelopeislittle larger than an ECC88, so it does not seem wise to operate at the fullclaimedpower.IfwesetIa=34 mA,thenPa=4.6 W.Wenowneedtoconsidertheinputdifferentialpair.Becauseweonlyhave135VofHT,weneedavalvehavinggood linearityat lowvoltages.TheECC86wouldbeideal,buttheECC88wasavailable,andalittleslitheringofloadlinessuggestedthat27kΩloadresistorswouldworkwellwithananodevoltageof68V,resultinginatailcurrentof5 mAatVgk=2 V.

We are finally in a position to be able to investigate the more significantproblemsofDCcouplingusingapurepotentialdivider.EachECC88 anode is at 68 V. The grid of the 6545P cathode follower is at≈−1.5 V(remember thatweneed thecathode tobeat0 V),sowemustdrop69.5 V.Ifweweretoset100 μAofpotentialdividerchaincurrent,wewouldneedanupperresistorof695 kΩ,whichisanawkwardvalue.Ifwechoosethenearestpreferredvalueof680 kΩ,ourpotentialdivider currentbecomes69.5V/680 kΩ=102.2 μA.Thelowerresistormustdropfrom−1.5 Vto−135 V=133.5 V,so102.2 μArequires a 1.3 MΩ resistor,which is a preferred value.However,we need toconsideranotherfactor.At the calculated anode voltage, the potential divider chain steals ≈100 μAcurrent from the anode current of 2.5 mA. 2.5 mA is a low current for thisvalve,sosamplevariationsbetweenvalvesaregreatlymagnified,andthesmallstolencurrentisnegligiblebycomparison.Thetheft/valveerrorpullstheoutputDC in the final circuit away from 0 V, so why not make the divider chainadjustabletocompensateforvalvevariation?Usinga1.2 MΩfixedresistorinseries with a 250 kΩ resistor allows ±10% variation. You could apportion alarger value of variable resistance, but this would make the output DCadjustmentmorefiddly.EveniftheoutputDCiscarefullyadjustedto0 V,itwilldrift.Weneedameansof forcing the output DC to 0 V, and the best way of doing this is to applynegativefeedback.Weconnectourfeedbacknetworkinparallelwiththeoutputof the amplifier, but because the output of the feedback potential divider isconnected to the other grid of the differential pair, and the differential pairamplifies thedifferencebetween its inputs, it is inserieswith the inputsignal.Thefeedback is, therefore,parallel-derived,series-applied,so it reducesoutputresistanceandincreasesinputresistance.Reducedoutputresistanceissignificantbecause all contemporary electromagnetic transducers rely on rsource=0 toproducetheirdesigner’sintendedtransientresponse.Ifwearetoapplyfeedback,wemustknowhowmuchgainisavailable.27 kΩisquitealowanodeloadresistanceforanECC88,andaloadlinepredictsagainof 26.75.The input stage operates as a differential pair, but because only oneoutputisused,wemustimmediatelyhalvethegainto13.375.Weincuralossof0.657inthelevelshifter,whichreducesthegainto8.78.Consideringthe6545P,atIa=34 mA,rk≈25 Ω,soa32 Ωloadincursafurtherlossof0.56,leavingatotal gain of ≈5. Thus, even 100% global feedback could produce only (1+βA0)=5,or14 dB,ofimprovement.

The circuit was tested with 100% negative feedback because this is themostcriticalconditionforstability,yetdeliveredanexemplarysquarewaveresponseat10 kHzintoa200Ωload(seeFigure3.34).

Figure3.34Near-perfect10 kHzsquarewaveresponse.

Thecircuitwastestedintovariousloadresistances.Unsurprisingly, Table 3.15 shows that little valves don’t like 32 Ω loads andthatthiscircuitcanonlydeliver8 mWat0.5%THD+Nintoa32 Ωload.Theperformance improves markedly into a 200 Ω load, whereupon the circuitdelivers double the power at <0.1% THD+N and, more importantly, thespectrumofthedistortionharmonicsbecameacceptable:H2=−60 dB,H3=−82dB,H4=−100 dB.Curiously,theauthorstilldoesnotownanyelectromagneticheadphones of plausible quality, so he was unable to test this amplifiersubjectively.

Table3.15HeadphoneAmplifierDistortionAgainstLoadResistanceOutputindBuforspecifiedTHD+N

0.5% 0.2% 0.1%100 kΩ – – +20200 Ω +16.7 +12.8 +7.832 Ω −3.7 – –

Eagle-eyed readers having a 6C45_ datasheet will notice that this circuit farexceedsthemaximumspecifiedgrid-leakresistanceof150 kΩ.Rememberthatthepurposeofthegrid-leakresistoristoholdthegridatitscorrectvoltageinthefaceofgridcurrent.Iftheresistoristoolarge,gridcurrentraisesthevoltageonthegrid, reducingVgk, increasing Ia, causingmoregridcurrent,until thevalve

dies.Inthiscircuit,Iaforthe6545Pissetpurelybytheconstantcurrentsink,soconsiderationsof thermalrunawaycausedbyexcessivegrid-leakresistanceareirrelevant.Ifyouneedtosetupacircuitofthistype,itiseasiesttobreakitintotwopartsbefore applying feedback. Build the output stage first, short-circuit the uppergrid toground,andadjust theCCScurrentprogrammingresistor tosetcorrectcathode follower current. Build the differential pair and associated CCS, andadjust theCCScurrent programming resistor to set required anode conditions.Connect the two stages, and fine-tune the level shifter for 0 V at the output.Finally,closethenegativefeedbackloop.

UsingaNortonLevelShifter

Asmentionedpreviously, theNorton level shifter is ahigh-gain amplifier thatamplifiesthenoiseofitsreferencevoltage.Thenoiseproblemcanbetackledinvariousways:• Reduce the noise produced by the reference. Forward-biassed diodesproduce less noise, so redLEDsmay be useful. If a reverse biassed highervoltagediodemustbeused,use5.6 VbecausethisisatrueZenerandquieterthanhighervoltages(whichareavalanche).•Noiseisn’taprobleminitself;itbecomesaproblemwhenthesignalvoltageis sufficiently low that the signal-to-noise ratio is compromised. Solution:Don’tuseNortonlevelshiftersinpre-amplifiers.• If the noise can be arranged to become common mode, then it can berejectedbyadifferentialpair.Thisisthemostpowerfulindividualtechnique.

Don’ttrytoobtainallthenoiseadvantageyouneedfromonesingletechnique–itisalwaysbettertouseacombinationofsmalladvantagesthatsumtoalargeadvantage.Someyears ago, the authorpickedup40N-channel andP-channelMOSFETsfromajunkshop,andafterpassingthemthroughhislatelamentedcurvetracer,he found two reasonably complementary pairs. The hybrid idea promptlyresurfaced,coupledwithawishtousesomeofthemoreobscurevalvesinstock.Theauthorhadpreviouslybeenunabletofindauseforthewonderfullyhighgm(55 mA/V)oftheE55L,butrealisedthatitmightmakeagoodcathodefollowerfordrivingthehigh-gatecapacitanceofMOSFETs.AlittledoodlingresultedinacircuitrequiringaNortonlevelshifter(seeFigure3.35).

Figure3.35DCcouplingusingaNortonlevelshifter.

TheN-channelMOSFETneeds+5 Vonitsgatetopasstherequiredcurrentof1.7 A, whilst the P-channel MOSFET requires −6 V, so the Vbe multiplierbetweenthegatesallowsthesevoltagestobeappliedandoutputstagecurrenttobe set. TheE55L cathode follower has a power cascode constant current sinkmadefromanMJE340andaBC549asitsactiveload.The7N7differentialpairhasacascodeconstantcurrentsink tail thatshares thereferencevoltageof thesinkfortheE55L.Tobalancetheanodeloads,theunusedoutputofthe7N7hasanRCnetworktogroundtosimulatetheinputimpedanceoftheE55Lcathodefollower.TheECC808inputdifferentialpair isreasonablyconventionalexceptthat it has constant current source anode loads to improve its linearity whenoperatingfromapositiveHTofonly+150 V.Because the 7N7 differential pair is directly coupled to the E55L cathodefollower,itsgridsmustbeat,orcloseto,thevoltageofthenegativeHT,yettheanodesoftheECC808areexpectedtobeat+123 V.Thus,theproblemistoDCcouplethetwostageswithaminimumofnoise.Arbitrarilyselecting1 MΩfortheupperresistorofthelevelshiftersuggeststhatthecurrentpassing through itwillbe≈250 μA.Weneed toknowthiscurrentbecauseitisthedesigncurrentfortheconstantcurrentsink.Ifwechoosea6.2V reference voltage, a 24 kΩ is required. If we treat the level shifter as acommon-emitter amplifier, we can find its gain. Ic=250 μA, so gm=35Ic=35×0.25=8.75 mA/V. The gain of the amplifier is Av= gm·

RL=8.75×1,000=8,750. However, the amplifier has considerable feedbackbecauseof theunbypassed24 kΩemitterresistor,sowecanuse thefeedbackequation:

Alternatively, now thatwe know that the gain before feedback is likely to belarge,wecansimplyusetheapproximation:

The significance of this exercise is that a larger reference voltage reduces thegainoftheamplifierbecauseofthehighvalueofRethatitenforces.Althougha1.6 V redLEDwouldbeperhaps9 dBquieter thana5.6 VZener, itwouldenforce14 dBmoregainintheCCS,makingit5 dBnoisierinthisexample.If the level shifters share the (potentially noisy) DC reference, its noise isamplifiedidentically,soitispresentedtothedifferentialpairascommonmodenoise,whichitcanreject.Toensurethat thenoiseremainscommonmode,theemitter resistors and 1 MΩ must be matched, so 0.1% tolerance types arenecessary.At high frequencies, the common-mode rejection of the differentialpairdeteriorates,butifwebypassthe1 MΩresistorswithcapacitorstoformastepnetwork, the levelshifter’snoiseattenuationriseswith frequency, tendingtocompensateforthedifferentialpair’sfallingCMRR.

DistortionandNegativeFeedbackNegativefeedbackreducesdistortion.Allengineersagreeon this,butshoutingbegins immediately afterwards regarding the character and subjective effect ofthe new distortion. Baxandall [10] investigated the problem in 1978 andoriginated the graph that has been reproduced elsewhere with little or noexplanation(seeFigure3.36).

Figure3.36TheubiquitousBaxandallfeedbackanddistortiongraph.

Baxandall’s original graph tested the hypothesis that if negative feedbackwasapplied to a distorting amplifier, then the feedback signal would itself bedistorted,generatingharmonicsofdistortionharmonics,andthattheamplitudesof these new harmonics could be predicted if the amplifier’s transfercharacteristic was simple and known. The chosen amplifier was a resistivelyloaded 2N5458 common source JFET because theory indicated that a JFET’sdistortionshouldbedominatedbyH2,andtoeasethemeasurementproblem,itwas testedatasufficientlyhigh-signalamplitude to force7.6%H2.Ascanbeseen, theagreementbetweenmeasurementand theory isgood,butdeterioratesasharmonicorderincreasesbecausethefundamentalassumptionthattheJFETproduces onlyH2 becomes increasingly invalid at these distortion levels. It isvitaltorealisethatthegraphistheresultoftheneedtosettestconditionsthatwouldproducemeasurabledataandwhilst itvindicates thehypothesis, itdoesnot represent real-world conditions and therefore almost all conclusions andextrapolationsbasedonthisrawgrapharewrong.Despite the previous damning statement, Baxandall’s hypothesis is usefulbecause,aswesawearlier,triodesproducedistortiondominatedbyH2–andallthat isnecessary is tochange theequation’sstartingconditions (levelofopen-loopH2)toamorereasonablevalue(seeFigure3.37).

Figure3.37TheeffectonBaxandall’sgraphofreducingopen-loopdistortionto1%.

Atriodeamplifiermightproduce1%distortionattheexpectedsignalamplitude,dominatedbyH2,andthemodelshowsthatif20 dBofnegativefeedbackweretobeapplied,H2woulddropinamplitudeby20 dB(asweshouldexpect),andfeedback would produce H3 at an amplitude of −95 dB with respect to thefundamental.Thereareaudiosourceswithnoise/distortionfloorsbetterthan−95dB,butthemostcommondigitalsource(CD)is16bitandthisisitsnoisefloor.In short,whatBaxandall’s hypothesis really showedwas that if the distortionspectrumafterfeedbackisnottobequestionable,open-loopdistortionmustbe1%orbetter.Althoughit isdifficult todesignapoweramplifier thatproduces<1%THDatfull power dominated byH2 before applying feedback, designing small-signalstagestothisstandardistrivial.Thus,ifweneededalinestagewithagainof6dB(perhaps tomakeup the6 dBlosscausedby insertingabalancecontrol),wecouldloadatriodefromtheSN7/N7familywithaconstantcurrentsourcetoachieveanopen-loopgainequaltoμ(20),bufferitwithacathodefollower(toavoidthefeedbackresistorloadingthegainstageandincreasingdistortion),thenapply20 dBoffeedback(seeFigure3.38).

Figure3.38ThiscommoncathodetriodewithCCSloadandcathodefollowerbufferhaslowopen-loopdistortion–idealfortheadditionofnegativefeedback.

Referring to themeasurementsmade earlier in this chapter, we would expectopen-loopH2 at +28 dBu (19.5 VRMS) to be better than −50 dB, but at themore reasonable level of 2 V RMS, we could expect −70 dB (0.03%).Using0.03%as thestartingvalue inBaxandall’sequationspredicts thatH2dropsby20 dB to −90 dB, and that the H3 produced by feedback will be entirelynegligible at −156 dB. In practice,we know that the gain triode and cathodefollowerwillproducesmallamountsofH3andhigherharmonics,butthesewilleachbereducedbythefeedback,andwecancalculate theiramplitudes(Table3.16).

Table3.16CalculatedDistortionHarmonicsofCCS-LoadedSN7/N7BeforeandAfter20 dBofNegativeFeedbackH2(dB) H3(dB) H4(dB)

Beforefeedback −70 −105 −110After20-dBnegativefeedback −90 −125 −130

Summarising, negative feedback only degrades the distortion spectrum ifdistortionbeforefeedbackis>1%,otherwiseitpushesallharmonicsfurtherinto

thenoisefloor.Note,however,thattherewasapricetobepaidforthelowdistortion;thegridcircuit now has a 100 kΩ series resistor that generates noise and thereforedegradesthesignal-to-noiseratioofthecompoundstage.

CarbonResistorsandDistortionCarbonhasmuchhigherresistivitythanmanganin(resistancewire),soashorterpath gives the same resistance. Since resistors are commonly constructed as ahelix, higher resistivitymeans fewer turns and reduced inductance, sowe usecarbonresistorsforvalveandFETgrid/gatestoppers.However,notonlyarecarbon resistorsnoisy,but theyalsoproducedistortion.Bailey(betterknownfor‘transmissionline’loudspeakersandlong-hairedwool)warned in an article on designing an audio generator with less than 0.02%distortion[11]that‘Itisimportantthatonlywire-woundresistorsareusedinthefilter,ascarbontypesarenon-linearandcanproducedistortionsofupto0.5%.This non-linearity is often overlooked, but where low levels of distortion arebeingdealtwith,theresultsmaybeveryserious.’Aquicktestofa100kΩcarbonresistorinapotentialdividerrevealedresistordistortionat−81-dBH2and−71-dBH4.WhilstnotasbadasBailey’sexample,the fact that a single resistor can produce measurable distortion is distinctlyalarming.Nevertheless, carbon is still a valid choice for grid/gate stoppers because thedistortion is causedby the resistor’s non-linear voltage to current relationship,and if there is nogrid/gate current through the resistor, there canbe no seriesvoltagedevelopedacrossitandtherecanbenodistortion.

NoiseIn this section, I will define noise to be strictly uncorrelated random eventspossiblyduetothegranularityofacurrentthatisthesumofindividualelectronsover time. More simply, we will include thermal noise and its relatives, butexcludeman-madeinterference.Tomaximisedynamicrange,wemustminimisenoise.Inaudio,therearethreemainsourcesofnoise:•Resistances•Amplifyingdevices•DCreferences.

NoisefromResistances

WesawinChapter1thatallresistancesproduceanoisevoltage:

where

k=Boltzmann’sconstant≈1.381×10−23 J/KT=absolutetemperatureoftheconductor≈°C+273.16B=bandwidthofthefollowingmeasuringdeviceR=resistanceoftheconductor.

This leads directly to the well-known requirement that low-noise amplifiersshouldminimisethevalueoftheirresistancestominimisenoise.

NoisefromResistiveVolumeControls

Atsomepointintheamplifyingchain,weneedameansofcontrollingvolume,withvariableattenuationfrom0 dBperhapsupto60 dB.Allresistivevolumecontrolscanbereducedtoapotentialdivider,soatthesametimethatthecontrolisattenuatingthesignal,itisalsogeneratingnoise.Ifweassumethatthesourceresistancefeedingthevolumecontrolisnegligible,asfarasnoiseisconcerned,the two resistors of the potential divider are in parallel, so we can find thatparallel resistance and calculate its noise voltage (over a 20 kHz bandwidth).Becausethevolumecontrolattenuates, thenoisegeneratedat theoutputof thevolume controlmust be comparedwith that attenuated signal. Ifwe assume apeakinputlevelof2 VRMS,wecandeterminethesignaltonoiseratioofa100kΩvolumecontrolatvariousattenuations(seeFigure3.39).

Figure3.39Volumecontrolsignaltonoisechangeswithsetting.

WewillinvestigatedetaileddesignofvolumecontrolsinChapter7,butsufficeto say that a TypeC attenuator has a fixed value series resistorwith variableshunt,whereastheTypesAandBcanvarybothseriesandshuntarms.Notethatforthespecifiedvaluesofinputvoltageandresistance,asattenuationincreases,all three types tend towards a signal to noise ratio of 111 dBminus half thevalue of attenuation (in dB).More importantly, if we reduce the input signalfrom2 VRMSto1 VRMS(−6 dB),weimmediatelyreducethesignaltonoiseratiobythesameamount.Nowimaginethatwehaveanamplifierwithaninputsensitivityof400 mVRMSandweconnectittoadigitalsource(2 VRMS)viaavolumecontrol.Atmaximumvolume(beforetheamplifieroverloads),wemusthave 14 dB of attenuation, sowe have limited ourmaximum signal to noiseratioto97 dBpurelybecauseofnoiseinthevolumecontrol.Ifwerequirethesamesignaltonoiseratiosat400 mVRMSthatwehadat2 VRMS,wemustreduceourvolumecontrolresistancefrom100 kΩto5 kΩ,andthisiswhysemiconductorelectronicstypicallyhasthisvalueofvolumecontrol.Alternatively,wecouldstate thatsincevalveelectronicsgenerallyneedsa100kΩvolumecontrol,itmustbeatapointof2 VRMSsensitivity.(Asanexampleofnoisydesign,theLeakStereo20poweramplifierandPointOneStereopre-amplifier combination placed a 100kΩvolume control at a point of 125 mVRMS sensitivity, resulting inamaximumsignal tonoise ratiopurelydue to thevolumecontrolof87 dB.)

NoisefromAmplifyingDevices

Thereare twodistinctnoisesourceswithina triodeand, likea transistor, theirrelativeamplitudedeterminestheoptimumsourceresistance.Internalshotnoiseduetothegranularityofanodecurrentcanbeconsideredtobeavoltagesourceatthegrid(usuallyexpressedasthevalueofresistancethatwouldproducethatnoisevoltage).Rememberingthatthenoiseproducedbyaresistoris:

Andthattheequivalentnoiseresistanceofatriodeisapproximately:

Substitutingweget:

Thus,voltagenoisereferredtothegridisproportionaltotheinversesquarerootofgmand this is the reasonwhyquietRIAAstages formovingcoilcartridgesrequirehigh-gmvalvessuchasE810F,D3aandEC8010.Thegranularityof(unwanted)controlgridcurrentformsacurrentsource,andavalve’soptimumsourceresistanceistherefore:

whereVn(g)=noisevoltageatthegrid

in(g)=noisecurrentfromthegrid.

Althoughthisequationpredictstheoptimumsourceresistanceforagiveninputstage, itdoesn’tguaranteeminimumnoise–afterall,wecouldquadruplebothvoltageandcurrentnoiseandobtainthesameoptimumsourceresistancewithanoisier amplifier. However,what the equation does tell us is that high sourceresistances require low grid current noise. We can see this intuitively byobservingthatanygridnoisecurrentmustpassthroughthesourceresistanceanddevelopavoltageacross it, so the smaller thecurrent, the smaller thevoltage.Notethatalthoughreactancescannotproducenoise,Ohm’slawguaranteesthatdriving a noise current through the inductance of a moving magnet cartridgeconvertsgridcurrentnoiseintoanoisevoltage.Nevertheless,inanoisesourcecontext, evenmovingmagnet cartridges are not high impedance and the gridcurrentnoiseofacompetentlymanufacturedvalveoughttobeinsignificanteven

withahighinductancemoving-magnetcartridge.However, capacitive transducers are unquestionably high impedance sources,and for audio thatmeans condensermicrophones. The typical large (20 mm)capsulemicrophonepopularforleadvocalshasasourcecapacitanceof≈30 pFand, for sucha source, it isnotgridvoltagenoise thatmustbeminimisedbutgridcurrentnoise.

GridCurrentNoiseandthePoissonDistribution

Beforeinvestigatinghowtominimisegridcurrentnoise,wemustmakeaverybrief foray into statistics. Valve control grid current is so low that we areconcernedwiththeexactnumberofelectronsthatleaveorenterthegridcircuit.Ifweweretoconsider1 μsslicesoftime,andeach1 μsslicecontainedexactlythe same number of electrons, then there would be no audible noise currentbecauseitisthevariation(ACcomponent)thatwehear,nottheDCcomponent.The valve manufacturers will always have designed to minimise grid currentnoise, and therefore theprobabilityof agivenphysicalprocess resulting in anelectronthatcontributestogridcurrentislow,butthermalagitationensuresthatthere is a large number of tests, so their statistical result has a Poissondistribution. The significance is that a Poisson distribution is completelydescribedbyitsmeanvalue,and:

whereσ=standarddeviation(fromthemean)μ=mean.

Thisequationis theOhm’slawofstatisticsandthatsquarerootrelationshipisubiquitousinnoisecalculations.Foraudiopurposes,themeanistheDCcomponentofacurrent(orvoltage)andthe standard deviation is the AC (noise) component. Thus, if we want tominimise grid current noise (standard deviation), we must minimise the(unwanted)gridcurrent.Note that this argumentdoesnot apply to thevalve’sinternalshotnoisebecauseweneedtheanodecurrentinordertomodulateit,soit is the ratio between the standard deviation and the mean that must beminimised.

ElectrometersandGridCurrent

WhereasaDVMmightmeasurecurrentsdowntofractionsofamicroampere,an

electrometer is an instrument designed specifically to measure very smallcurrents,typicallyrangingbetween1 fA(10−15 A)and1 nA(10−9 A).Wheninvestigatingelectrometerinputvalves,Dagpunar[12]showedthatgridcurrentcouldbesplitintobroadcategories,firstlydeterminedbywhetherelectronswerearriving(positivegridcurrent)orleaving(negativegridcurrent).Giventhateachpositiveionarrivingat thegridsurfacerequiresoneormoreelectronstoleavethegridtodischargeit,arrivingpositiveionscontributetonegativegridcurrent.Positivegridcurrentisdueto:

I1Electronsleavingthecathodebutinterceptedbythegrid.Negativegridcurrentisdueto:

I2Photoelectricandthermionicelectronemissionleavingthegrid.Positiveionsarrivingfromtheheatedcathode(atomsofcathode-emissivematerial).Thesesources produce a fixed number of electrons/ions within the valve’sgrid/cathode region, so Vgk simply determines how many are collected,leadingtoasaturationvalueirrespectiveofVgk.

I3Positivegas ionscausedby thedirect impactofacceleratedelectronsduringtheir flight to the anode. Positive gas ions caused by the Bremmstrahlung(braking radiation) and X-rays produced by the anode due to arrivingelectronsbeingabruptlydecelerated.Positiveionsofanodematerialdislodgedoremittedfromtheanodeheatedbyelectronbombardment.

I4Secondaryelectronsemittedfromthegridduetotheimpactofpositiveions.

I5Surfaceleakageoverglassorinsulationinsideandoutsidethevalve.Thisisassumedtobearesistivecomponent,directlyproportionaltoVgk.Brimar[13]noted that themost commoncauseofnoisevariationbetweenvalvesof thesame typewas grid current noise caused by surface leakage currents acrossmicaspacersandstrayfibresorlintbetweenelectrodes.Inasimilarvein,the

externalsurfacesofelectrometervalvesmustnotbetouchedwithbarefingersastracesofsweatwillcausesurfaceleakagecurrents.

When represented graphically these idealised categories sum to produce thefamiliar grid current curvewith its crossover point typically atVg≈−1 V (seeFigure3.40).

Figure3.40Idealisedsourcesofgridcurrentandtheireffectongridcurrentnoise.(AfterDagpunar[12].)

Each individual physical noise processwas earlier assumed to have a Poissondistribution,implyingthatthestandarddeviation(noise)wasequaltothesquareroot of the mean. But we have seen that grid current is due to a number ofsources,sototalgridnoisecurrentmustbethepowersummationof individualnoisesources,andthisiswhygridcurrentnoisedoesnotfalltozeroatIg=0,buthas a very broadminimum at the inflection of Ig (Vgk=−4 V in thismodel).Notethatanychangeinindividualnoisesources(andparticularlyleakage)willcompletelychangethenoisecurrentcurve.Photoelectricemissionfromthegridiseasilyminimisedbyoperatingthevalveindarkness,but it iscurrently fashionable tomountabrightLEDin thevalvebasethatshinesdirectlyintothevalve’sinternalstructure.Whilstthisisclearlythe worst possible photoelectric scenario, any application that is sufficientlyinsensitivetohumtoallowthevalvetobeondisplayisalsoinsensitive to theincreasedgridcurrentnoiseduetoLEDillumination.However,rememberthatLEDsareeasilycapableof trackinga100 Hz/120 Hzhumwaveformand its

harmonics, so it would be unfortunate to prove that an illuminated valvewassensitivetoopticalhum–ifyoumusthavealightshow,usecleanDCfor theLED.Prior to the production of valves designed specifically for electrometers,Gillespie [14] investigated the possibility of using the Mullard EF37 in anelectrometer,andfoundthattherewerethreepracticalwaysofreducingthegridcurrent of a given valve (ranked in order of decreasing effectiveness andcategorisedaccordingtoDagpunar):

I3Reducinganodevoltage reduces theenergy involved inacollisionbetweenanaccelerated electron and a gas molecule. Gillespie stated that gas/ion currentvarieswith the squareof acceleratingvoltage, so electrometervalves typicallyoperate with an accelerating voltage of only 10 V (whether provided by theanodeorscreengrid).

I3Biassing the grid further negative reduces anode current and therefore thenumber of collisions between electrons and gas molecules, thereby reducinggas/ioncurrent.

I2Reducing heater dissipation reduces grid electron emission and cathode ionemission. (Dedicated electrometer valves avoid indirectly heated cathodesbecause the unavoidable temperature drop across the heater/cathode insulationrequirestheheaterneedstobehotter,increasingphotoelectricemission.)Gillespiefoundthatbecausegridelectronemissionandcathodeionemissionaresecond-ordereffects,reducingheaterdissipationwasonlyworthwhileifallothersourcesofgridcurrenthadbeenminimisedandthevalveshadbeenselectedforlow grid current. Only one valve in six passed Gillespie’s low grid currentselectionprocess,sowhenMullardadoptedit,suchEF37swerereleasedastypeME1400.Despite the previous caveats, the reduced heater dissipation technique haserroneouslyenteredaudiofolkloreasageneralsolutionforlownoise,yetonlyacondensermicrophoneheadamplifierusingavalvepreviouslyselectedforlowgrid current would be likely to achieve a noise reduction from judiciousreduction of heater dissipation. Unfortunately, reducing heater dissipationdrasticallyreducesgm,increasinggridvoltagenoise,soitseemsunlikelythatan

improvementofmorethan1–2 dBcouldbegained.We can summarise grid current noise by stating that for a competentlymanufacturedvalve:•Gridcurrentnoise isonlysignificantwithhighsource impedancesandforaudio,whichmeanscondensermicrophones.•Gridcurrent(anditsnoise)ishighlysampledependentbecauseitisusuallydominated by surface leakage currents, but a quiet valve is likely to have averybroadminimumwellawayfromthecrossovervoltage.

Thecrucialsignificanceofthisinvestigationintogridcurrentnoiseandmakingthedistinctionbetweenavalve’sinternalshotnoiseanditsgridcurrentnoiseisthatwhereasthemagnitudeoftheinternalshotnoisecanbepredictedreasonablyaccuratelybyfundamentalphysics,themagnitudeofgridcurrentnoiseiswhollydependentonthevicissitudesofproductionengineering.It must be remembered that valves were/are assembled by hand, requiringconsiderable manual dexterity and attention to detail. Experience shows thatmanufacturingprocessesdependentonskilledmanuallabourrequirenotonlyamotivated workforce adroitly directed by a good engineer/manager, but also,more importantly, a great deal of practise to determine the exact productiontechniquenecessary tomeet therequiredstandard,andevenin thegoldenage,valves needed to be selected when low grid current was required. The valvemarketisfarsmallernowthaninitsheyday,soeconomiesofscalecannolongerbe applied, making the production engineering problem far greater. In short,making valves is high technology dependent on mass production, and it isunrealistictoexpectsmallrunsofcontemporaryvalvestoachievethelowgridcurrentnoiseorconsistencyofselectedgoldenagevalves.

NoiseinDCreferencesWeoccasionallyneedaDCreferencevoltage.Themostobviousexampleisthereference in a regulated power supply, butwemight also need a reference toenforce operating conditions in an amplifier. We will investigate the DCreference in a regulated supply because it produces some initially counter-intuitive(butveryuseful)results.Thetypicalseriesregulatorisnothingmorethananon-invertingpoweramplifieramplifyingtheDCreference.Asanexample,ifwehada317ICregulatorwithareferencevoltageof1.25 Vandneededanoutputvoltageof15 V,wewouldchooseexternalresistorvaluesthatcausedtheamplifiertohaveagainof12.Butthismeanswehavealsoamplified thenoisevoltageof theDC referencebya

factorof12,andthisiswhythe317datasheetspecifiestheoutputnoisevoltageasapercentageofoutputvoltage.If we need a high voltage, it seems sensible to start with a high-voltage DCreference and amplify it only a little rather than start with a low voltage andsuffer higher noise amplification. The key factor is the noise produced by thereference. Sadly, not all the gasDC reference datasheets specified their noisevoltage, and information on how that measurement was made was sparse.Clearly,itwastimefortheauthortomakesomemeasurements.

HowtheAuthor’sDCReferenceNoiseMeasurementsWereMade

The references were all operated at a current of 5 mA set by a cascodeDN2540N5 JFET constant current source powered from a filteredDC supply.Noise was measured by an MJS401D audio test set coupled by an inputtransformer to improve rejection of mains hum and a capacitor coupled toprotectthatinputtransformer(seeFigure3.41).

Figure3.41MeasuringmicrovoltsofnoiseonaDCsupplywithoutdamagingtestequipment.

The test setwas set toRMS rectifier in order tomake the results comparablewith datasheets. Unless specified otherwise, bandwidth was limited by theMJS401D’smaximally flat36 dB/octave22 kHz low-passand18 dB/octave22 Hz high-pass filters. This bandwidth is wider than the 10 Hz to 10 kHzbandwidthcommonlyusedbydevicemanufacturers,butrememberingthatnoiseisproportionaltothesquarerootofmeasurementbandwidth:

which amounts to −3.4 dB, and enables comparison ofmeasurements. As anexample,theauthormeasured138 μVRMSofnoiseovera22 kHzbandwidthfrom a batch of 85A2s, which corresponds to 93 μV RMS over a 10 kHzbandwidth, but the Mullard 85A2 datasheet claimed ‘of the order of 60 μVRMS’,whichis4 dBquieter.(Mullarddidn’texplicitlystate‘RMS’,butstatingthatthenoisewasequivalenttoa22 MΩresistorimpliesRMS.)Therearefourpossibilitiesforthis4 dBdiscrepancy:•Thedeviceshavedeterioratedoverthedecadesandbecomenoisier.•Thedevicesneededtobeoperatedfor3 mintoachievetheirlowestnoise.•TheMullardmeasurementusedadifferentrectifier(perhapsaveragereadingbutcalibratedRMSonsinewave)plussmoothing.•Mullarddetermined85A2noisebycomparison.Anoisemetercouldhavebeen switched between the 85A2 and a selection of resistors, andwhen thetworeadingswereequal,thenoisedeemedtobethatofa22 MΩresistor.

The first possibility seems unlikely, and although the second is true for DCstability,nonoisechangewasobservableover2 h.Thethirdpossibilitycouldaccount for 1 dB (switching from RMS to average reading gave a 1 dBreductionontheauthor’sMJS401D).However,thefactthatthenoiseisstatedtobeequivalenttothatofanE6standardvalueresistorsuggeststhatthiswasthemethod used, and it could be that the noise measurement on the resistorproducedhighernoisethanshouldbeexpectedfromthesquarerootof4kTBR.One distinct possibility is that any grid current noise from the noise meter’sinput amplifierwoulddevelop a significantly higher noise voltage across a 22MΩresistor thanacrossthetypical300 Ωsloperesistanceofagasreference,leadingtoafalselysmallvalueofresistorbeingneededforequalnoise,andthusaperceivedlowergasreferencenoise.ThereisalwaysadangerwhenmeasuringsmallsignalsthatthemeasurementisactuallyofinterferencesuchasmainshumorADCsamplingnoisefromDVMs.As a check, a Tektronix 2213 analogue oscilloscope and a TDS3032 digitaloscilloscopewereconnectedtothemonitoringoutputoftheaudiotestset.Iftheaudiotestsetwasmeasuringpurenoise, thensettingthedigitaloscilloscopetoaverage over 512 samples should average the noise nearly to zero and nocoherent waveform should remain.Mains humwas the most likely source ofinterference, so the digital oscilloscopewas triggered fromAC line to ensurethataveragingrevealedmainshumifpresent.Similarly,thereisadangerthatthetestset’sownnoisecouldbeconfusedwith

externalnoise.Withnoinput,MJS401Dself-noisemeasuredwith22 Hzto22kHzfilterandRMSrectifierwas−116 dBu.

GasReferenceNoiseMeasurements

Sadly, the author doesn’t have very many gas references, so the statisticalvalidity of the following measurements is somewhat questionable, althoughsamplevariationwasverylowat<1 dBforalldevices.Table3.17showsthatthereisverylittledifferenceinthevoltage-referrednoisebetweendevices,althougha108 Vreferenceappearstobeaquieterchoicethantheubiquitous85 V85A2.

Table3.17ComparisonofNoiseforVariousGasReferenceValves

Voltage-referrednoiseisthemeasurednoisevoltagedividedbythereferencevoltageandisthusanabsoluteindicatorofthenoisethedevicewouldcontributewhenusedinatypicalregulator.Voltage-referrednoiseindBisreferencedtothe85A2.

Numberofsamples

Averagenoise(dBu)

Referencevoltage

Voltage-referrednoise(μV/V)

Voltage-referrednoise(dB)

75C1 3 −74.5 75 1.46 −0.985A2 9 −75.0 85 1.62 085A1 1 −74.0 85 1.82 +1QS1215 1 −75.5 90 1.45 −1QS95/10 2 −72.7 95 1.67 +1.3VR105/30 4 −74.5 105 1.39 −1.3CV286 4 −74.3 108 1.38 −1.40B2 6 −74.3 108 1.38 −1.4QS150/15 10 −69.2 150 1.78 +0.80A2 5 −69.8 150 1.67 +0.3

VariationofGasReferenceNoisewithOperatingCurrent

Wehavepreviously seen thatnoise isdue to thegranularityof current, soweshouldexpect thenoiseof a reference tobeproportional to the inverse squarerootofoperatingcurrent.AMullard0B2wastestedovera4–26 mArange(seeFigure3.42).

Figure3.420B2gasreference:22 Hzto22 kHznoiseagainstoperatingcurrent.

Theuncertaintyofthenoisemeasurementswasestimatedtobe±0.5 dB,sothisuncertainty has been added to each measurement as an error bar. An inversesquarerootrelationshippassescomfortablythroughtheerrorbars,andalthoughaflattercoefficient(I−0.475)givesabetterfit,inversesquarerootisquitegoodenoughwhenchoosingoperatingcurrent.To sum up, the 108 V references seem the quietest, and noise is inverselyproportional to the square root of operating current. Having investigated gasreferences, the author realised that (for completeness) some semiconductorreferencemeasurementsoughttobemade.

SemiconductorReferenceNoiseMeasurementsandStatistical

Summation

Sincetheseriesofgasreferencetestshadbeenreferredtothe85 V85A2,itnotonlyseemedsensibletocomparesemiconductorsatasimilarvoltage,butitwasexpected that the noise of such a high voltage reference would be easier tomeasure. Thus, 16 BZX55 Zeners having a nominal voltage of 5.6 V wereconnected in series toproducean84 VcompositeZener.Using the same testset-upasbefore,thiscompositeZenerproducednoiseat−101 dBu,whichis29dBquieterthanthe85A2.A29 dBnoise improvement is soenormous that it immediatelyquestions themeasurementtechnique,sothe85A2swereimmediatelycheckedandtheirnoiseconfirmed.5.6 VisaquietvoltagestillwithintrueZeneraction,butasZaphod

Beeblebrox[15]complained,‘leavesusaverylargeimprobabilitygapstilltobefilled’. The improbability gap is that the noise of each individual Zener isuncorrelatedwiththeothers,sonoisepowersmustbesummedandthenoiseofthecompositeZenerisnot16timesthenoiseofeachindividualZener,butonlyfourtimes.Thistechniqueisthedualofreducingcurrentnoisebyconnectingndevicesinparalleltoreducetheirnoiseby√n.If the √ n hypothesis is true, connecting an even larger number of Zeners inseriesshouldproduceapredictablenoiseadvantage,andthiswastested.Thirty-five5.6 VZenerswereconnectedinseriestoformacomposite195 VZener.Ifthe√nhypothesis is true, thenoiseadvantageproducedby thisnewreferencecomparedtotheoldshouldbe:

Hadthe√nhypothesisbeenuntrueandthenoisesourcescorrelated,wewouldexpectincreasingthereferencevoltagefrom84 Vto195 Vtoincreasenoiseby7.3 dB(195/84),butthehypothesised3.4 dBstatisticalnoiseadvantageshouldreducethisto3.9 dB.WithbothcompositeZenersmeasuredat10 mA,the84VcompositeZenerproducednoiseat−103 dBu,whereasthe195 VcompositeZenerproducednoise4 dBhigherat−99 dBu,confirmingthe√nhypothesis.

VariationofZenerReferenceNoisewithOperatingCurrent

Wesawearlierthatthe0B2gasreferenceproducednoiseinverselyproportionaltothesquarerootofitsoperatingcurrent,andthesamestatisticsshouldapplytothecompositeZener.Aftercarefuloptimisationof the testset-up,uncertaintiesatthesemeasurementlevelswerereducedtoanestimated0.7 dB(unavoidably0.2 dBhigherthanobtainedinthegasreferencetests)(seeFigure3.43).

Figure3.43BZX55Zener:22 Hzto22 kHznoiseagainstoperatingcurrent.

Ascanbeseen,aninversesquarerootcurveonceagainpassesthroughtheerrorbars, confirming thehypothesis.But this result ismore significant thanbeforebecausea5.6 VBZX55(500 mW)hasacurrentratingof89 mA,sowecouldsafelypassamuchhighercurrentthanwecouldthroughagasreference.25 mAwouldnotbeanunreasonablecurrent,reducingthe84 VcompositeZenernoiseto−107 dBu,or3.5 μVRMSmeasuredovera22 Hzto22 kHzbandwidth.

NoiseoftheCompositeZenerComparedtoa317

The317ICregulatorhasbeenmentioned inpassing,andLinearTechnology’s317 datasheet [16] states that a 317 produces noise (10-Hz to 10 kHzbandwidth,RMSrectifier)equalto0.001%ofoutputvoltage,soifweneededa195 V supply we would expect it to produce 1.95 mV RMS of noise. Bycomparison, the195 VcompositeZenerpassing10 mAproduced8.7 μVofnoiseovera22 Hzto22 kHzbandwidth.Adjustingforbandwidth,thismakesthe195 VcompositeZener50 dBquieterthanthe317.Admittedly,theusualspeed-upcapacitoraddedto the317reduces itsnoisegainathighfrequencies,butitmusthavefullgainatDC,andtoavoiddestroyingtransientresponse,thespeed-upcapacitoronlybecomeseffective>100 Hz, implying≈100 Hznoisebandwidthandthereforea20 dBimprovementcomparedtothe10 kHznoisebandwidth,reducingthenoiseadvantageofthecompositeZenerto30 dB.AsanasideduringthesemiconductorDCreferencetests,theauthortriedan84VcompositedevicemadeupofsevenBZX5512 Vavalanchediodes,andat10mAitproducednoiseat−75 dBu(comparablewiththegasDCreferencesbut

28 dBworsethanthe5.6 Vversion).Tobefair, the12 Vdevicessuffereda3.6 dBstatisticaldisadvantagecomparedtothe5.6 V,butitdoesseemthatthe12–15 Vregionisaparticularlynoisyavalanchevoltage.AsingleZPY5656 Vdevice was tried at 6 mA, and this produced noise at −82 dBu, which issignificantly better than the gasDC references, but not nearly as good as thecompositedevicesusing5.6 VZeners.

RedLEDNoise

Finally,theauthormeasuredastringofHLMP6000redLEDs.TheseLEDsarereputed to be very quiet, so 105 were soldered together to form a 167 Vreference.Noisedidnotvarysmoothlywithcurrent(althoughitwasrepeatable),perhaps suggesting a questionable soldered joint. Nevertheless, the resultsnormalisedto84 VsuggestedthattheLEDswerebetterthan6 dBquieterthanthe compositeZener using 5.6 V devices.However,whilst hand-soldering 35wire-ended Zeners in series on a tag strip is perfectly practical (if a littletedious), hand-soldering 105 LEDs isn’t, restricting the use of LEDs to low-voltagereferences,althoughasurfacemount‘pick-and-place’machinefollowedbywavesolderingwouldundoubtedlyhaveno trouble reliablymakingahigh-voltagelow-noise(butratherexpensive)reference.

References[1]Shorter,DL,Theinfluenceofhigh-orderproductsinnon-lineardistortion,

ElectronEng.April(1950)152–153.[2]Henderson,FE,Introductiontovalves.2nded.(1943)WirelessWorld.[3]WrightA.Thetubepre-ampcookbook.2nded.;1997.[4]Reductionofdistortioninvacuumtubecircuits.USpatent_1,970,325;1934.[5]BlackHS.USpatent_2,102,671.[6]Deketh,J,Fundamentalsofradio-valvetechnique.(1949)Philips

Gloeilampenfabrieken;pp.439–444.ReprintedbyAudioAmateurPress,1999.

[7]TechnicalmanualSylvaniaradiotubes.6thed.Emporium(PA):SylvaniaElectricProducts;1946.

[8]Electrontubes,receivingtypes12SN7GTand12SX7GT.MIL-E-1/63B.USAmilitaryspecificationsheet;4March1954.

[9]Mikolajczyk,P;Paszkowski,B,ElectronicuniversalVade-Mecum.2nded.(1994)WydawnictwaNaukowo-Techniczne;p.442.

[10]Baxandall,PJ,Audiopoweramplifierdesign–5.(1978)WirelessWorld;

53–6.[11]Bailey,AR,Low-distortionsine-wavegenerator,ElectronTechnol.

February(1960)64–67.[12]Dagpunar,SS,Electrometervalves,Mullardtechcommun66(August)(

1963)194–199.[13]BrimarapplicationreportVAD/508.46BS7;January1952.[14]Gillespie,AB,Signal,noiseandresolutioninnuclearcounteramplifiers.(

1953)PergamonPress;pp.33–7.[15]AdamsD.TheHitchhiker’sGuidetotheGalaxy.FirstbroadcastonBBC

Radio4;15March1978.[16]Lineardatabook.Section4,p.139.LinearTechnology;1990.

RecommendedFurtherReading•Metzler,B,Audiomeasurementhandbook.(1993)AudioPrecision;Asshould

beexpectedfromamanufacturerofaudiotestequipment,thislittlebookisexcellentonpurelyanaloguetechniques,butitsageprecludesrecentdigitaladvances.

•Lowlevelmeasurements.4thed.Keithley;1992.Atfirstglance,thislittlebookmightnotseemrelevanttoaudio,butthetechniquesneededtomeasuresmallcurrentsaccuratelyareinvaluableforminimisingaudionoise.

•DoveS.Designingaprofessionalmixingconsole.StudioSound;September1980toFebruary1982.Thisdown-to-earthseriesofarticlesisanexcellenttutorialonhowtomaximisedynamicrangewrittenfromtheperspectiveofamanufacturerofbroadcastdesks.

•FletcherTBalancedorunbalanced?StudioSound;December1981.Asabove.•FletcherT,DoveS.Developmentofadigitally-controlledconsole.Studio

Sound1983;October.Thisarticleincludesaparticularlyinterestingcircuitdubbedthe‘Superbal’.

•VanderZiel,A,Noise:sources,characterization,measurement.(1970)Prentice-Hall;NoiseappearstohavebeenVanderZiel’slifework,andthisisoneofhisshorterbooksthatsummariseshispreviouswork.Coversnoiseinbipolartransistors,FETsandvalves.Ifyoubuyonlyoneofhisbooks,choosethisone.

•SelfD.Audiopoweramplifierdesignhandbook.5thed.Newnes.Thesolidstatedesigner’sbibletotheHCLinpoweramplifier–allitsproblemsare

examinedinmicroscopicdetailanddesignsolutionsoffered.•Duncan,B,Highperformanceaudiopoweramplifiers.(1997)Newnes;A

somewhatmoregeneraltreatmentofsolidstatepoweramplifiersprimarilyfromaprofessionalaudio(studio,stage)viewpoint.

Chapter4.ComponentTechnologyInChapter2,webegantodesignsimplecircuits,whichwilllaterbecombinedtoformcompletesystems.Indoingthis,wecalculatedvaluesforcomponents.Wenowneedtoknowhowtospecifyvoltageorthermalratingsofcomponents.Correct specification of individual components is extremely important. Anunderspecified component may fail prematurely and cause further damage,whereasanoverspecifiedcomponentmaywastemoney,whichcouldhavemadeanimprovementelsewhere.Tobeabletospecifycomponentscorrectlyrequiresknowledge of the stresses that will be applied to the component (electrical,thermal andmechanical) andof the imperfectionsof thatbreedof component.(Nocomponentsareperfect,althoughsomearemoreequalthanothers).Much has been said about the ‘sound’ of components, particularly capacitors.Thishascausedsuchpolarisationoftheengineersversusaudiophilesdebatethatrationalspeechhasonlyrarelybeenheard.Thisiscurious,sincetherearewell-known physical imperfections in components, and it seems reasonable tosupposethattheycouldhaveaninfluenceonsoundquality.Ontheotherhand,althoughcomponentsarenotmagical,therearepurveyorsofsnakeoil.This chapter will help you to avoid the more obvious pitfalls, but it is not asubstitute for detailed manufacturers’ data sheets and the application ofintelligence.

Resistors

PreferredValuesSofar,wehavecalculatedresistorvaluesandthenpickedthenearestpreferredvalue.Thesepreferredvaluesarederivedfromanexponentialfunction,sotheyare known as E series (E6, E12, E24 and E96), whose values are given inAppendixA.Eachseriesdenotesthenumberofdifferentvaluesinadecade.Forexample,E6containsthevalues1,1.5,2.2,3.3,4.7and6.8,makingatotalofsixvaluesperdecade.Ifwenowconsiderthatwewillprobablyneedvaluesfrom1 Ωto10 MΩ,thenthisissevendecades,andwewillneed43differentvalues(10 MΩisthestartofanewdecade).ForacompletesetofE24(themostcommonlyusedrange),wewouldneed169differentvalues.The E series is loosely related to the tolerance of the component, so 20%tolerancecomponentsareE6.Thereasonis that theupperlimitoftoleranceofonevalue justmeets the lower limit of toleranceof the next highest value, so

therearenogapsintherange.TheargumentbeginstofalldownwhenwelookatE24,since1.3+5%≠1.5–5%,buttheE96seriesisalignedmoreclosely.

Heat

Resistors convert electrical energy into thermal energy.The amount of energyconvertedpersecondisthepower,andthisdeterminesthetemperaturerise.A signal resistor is unlikely to be a problem, but an anode load resistor coulddissipatesignificantpower.WecaneasilycalculatethepowerdissipatedasV²/R,andselectanappropriatecomponent.This isnotactuallyquiteaseasyas itsounds,andthereisplentyofscopeforgettingitwrong.Resistormanufacturerstypicallyspecifypowerratingsatacomponenttemperatureof70 °C(158 °F).Ifyourequipmentoperatesatatypicaldomestictemperatureof20 °C(68 °F),then the internal temperaturemust be higher than this, since the equipment isconsumingenergyandisnot100%efficient.Anaverageinternaltemperatureof40 °C(104 °F)wouldbequitelikely,whilst temperatureofareasoflocalisedheating(hotspots)couldbeconsiderablyhigher.Ifyouarefortunateenoughtolivesomewherewarmer, thenanexternal temperatureof35 °C(95 °F)mightnotbeunusual,andtheinternaltemperaturewouldriseaccordingly.We can lose heat only from a higher temperature to a lower one, andwe canmakeausefulelectricalanalogy.TemperaturedifferenceΔT(°C)isequivalenttopotentialdifference.Powerdissipationq(W)isequivalenttocurrent.ThermalresistanceRθ(°C/W)isequivalenttoelectricalresistance.

Fromthis,wecanderiveathermal‘Ohm’slaw’:

Thistellsusthatagiventhermalresistancewillcreateagreatertemperatureriseaboveambientasmorepowerisdissipated.ResistorspecificationsgiveavalueforthethermalresistanceRθ,butthisvalueassumesthattheflowofairtocooltheresistorbyconvectionisnotrestricted.Inpractice,weoftenmounttheresistoronaPrintedCircuitBoard(PCB),whichconsiderably restricts the flow if the board is mounted horizontally. Evenmountedvertically,theremaystillbelargecomponents,suchascapacitors,thatblocktheairflow.Combiningtheargumentsofrestrictedairflowandhighambienttemperature,itisnotgenerallyadvisabletooperateresistorsatmorethanone-thirdoftheir70

°Cratingunlessyouareable todoadetailedthermalanalysis.Evenwith thisproviso,aresistoroperatedatone-thirdofitsratingwillbesignificantlywarmerthan its surroundings, so if it changes its temperature, we should expect itselectricalparameterstochangetoo.Andtheydo.Electricalresistancevarieswithtemperatureinaccordancewiththetemperaturecoefficientof the resistor,generallygiven inpartspermillionchangeofvalueperdegreeCelsius.Thismaysoundsmall,buta30 °Criseintemperaturecancauseasignificantchangeinvalue.Therefore,ifwehavegonetotheexpenseofusing 0.1% resistors in a critical part of a circuit, we should not allow anysignificant power to be dissipated in them if we want their value to remainsubstantially the same.Maximumdissipationofone-eighthof full-ratedpowerwouldnotbeunreasonable.Inaddition,weshouldensurethattheresistorisnotheatedbyothercomponents.Resistors are available in twomain types:metal film resistors andwirewoundresistors. Despite their recent minor cult status, carbon film resistors are ananachronism and will not be considered, as their tolerance and noisespecifications are so very poor, although they are useful as grid-stoppers.(Carbon resistors have reduced inductance compared to metal film resistorsbecause the higher resistivity of carbon means that a given resistance can bemadewithfewerturns.)

MetalFilmResistors

Thecontrolof thequalityof thematerialsandprocesses in themanufactureofmetal film resistorsdetermines theirperformance, so it isworthdetailing theirconstruction.The process starts with the individual insulating ceramic rods onto which theresistive film is to be deposited. These rods must have a smooth surface, asexcessivesurfaceroughnessvariesthethicknessoftheresistivelayerandcausesdiscontinuities that produce electrical noise. Although the ceramic material ischemicallyinert,itmayhavepickedupsurfacecontamination,suchasgreaseorpackagingmaterials,sothisisburntoffbypassingtherodsthroughanovenatatemperature>1,000 °C.Whilst the rodsarestillhot, theyare transferred toadruminbatchesofup to50,000 at a time. The drum is in a high vacuum sputtering system, which iseffectively a large valve. An electron gun fires sufficiently high velocityelectrons at the nickel–chromium anode (known as the target) that surfacemoleculesaredislodgedtoformanickel–chromiumvapour.Tumblingtherodsinthedrumcausesthevapourtodepositevenlyuponthem.Thedurationinthe

drum determines the thickness of the film, and this is the first process thatdeterminestheresistanceofthefinalresistor.The thickness of the applied film affects the noise of the final resistor, withthinner films being noisier than thicker films. If the nickel–chromium alloycontainsimpurities,itwillbecomemoregranular,andthisalsocausesnoise.Ifthe adhesion of the film to the ceramic rod is poor, the filmwill lift, causingnoise,instabilityandopencircuitfailure.A simple nickel–chromium film cannot achieve a temperature coefficient of 5ppm unaided, but proprietary techniques can improve this by adjusting thechemistryofthefilmifnecessary.Endcapsarefittednext,toallowconnectiontotheresistivefilm.Theseendcapsareaninterferencefitontotherods,andtheirprecisefittingiscritical.Iftheyaretootight,thenastheyarepushedon,theywilldamagethefilm,butiftheyaretooloose,thentheywillnotmakeagoodcontact.Eitherofthesedefectscausesnoiseinthefinishedresistor.Becausetheendcapisofadissimilarmetaltotheresistivefilm,theinterfacebetweenthetwoisathermocouplewhichgeneratesathermalElectroMotiveForce(EMF),butbecausetheEMFsateachendoftheresistorare inopposition, theirDCcancels.Unfortunately,anyACcomponentofthisEMFdoesnotcancel,sothecapmaterialmustbecarefullyselected.Commonly, ferrous end caps are used, but somemanufacturers, such asMECHolsworthy,usenon-magneticendcapsontheirHolcorange,anditissuggestedthatthismaybeacontributoryfactortotheirgoodsound.Manycomponentsusesteel-cored leads because the poor thermal conductivity (compared to copper)reducesthetemperatureriseinassociatedwiring.Theauthorisscepticalthatthesignal currents in resistors could be adversely affected by the magneticpropertiesof theendcapsorwires,but ismuchmoreprepared tobelieve thatsteelmightmakeapoorercontactthancopperandthatthethermocoupleeffectsateachendcap(whichcancelintheory)mightnotcancelperfectlyinpractice.Whateverthereason,endcapsorleadsofanycomponentcaneasilybecheckedwithasmallmagnet.Sputtering is not a particularly precise process, and the resistance of the filmstypicallyhasaspreadof±10–20%.Nowthattheendcapshavebeenfitted,itispossibletomeasurethisresistanceandgradetherodsintobatches.Thepurposeof this is to ensure consistency of helixing (see shortly) and hence of theperformanceoftheproduct.Although the rodsnowhavea resistiveelement, it isquite lowresistance,andthismustbeincreased.Thisisdonebycuttingahelixthroughthefilmfromoneend cap to the other in order to lengthen the resistive path whilst making itnarrower.Iftherearemoreturnstothehelix,thismakesalonger,narrowerpath,

and the resistance of the final resistor is proportionately higher, so resistormanufacturerscallthisparametergain,andwewillreturntothislater.Traditionally,thehelixwascutbyadiamond-edgedcircularsawwhosedepthofcut was critical. If the cut was too shallow, then the resistive film would beincompletelyremoved, leavingtracesofmaterialbridgingadjacentturnsof thehelix. If thecutwas toodeep, the sawwouldbedamagedon theceramic rod,andsubsequentresistorswouldbecutpoorly.Eitherdefectcausednoiseinthefinishedresistor.ThemoderntechniqueistouseaYAglasertocutthehelix,whichproducesanarrower,moreprecise cut,but even thisprocess isnotwithoutpitfalls. If theenergy directed by the laser is insufficient, the resistive layer is incompletelyburntaway,causingbridging.Iftheenergyreceivedfromthelaseristoogreat,then the resistive film at the edges of the cut becomes disrupted and has anunevenedge.Bothdefectscausenoise.Asthegainoftheresistorrises,thetracknarrows,causingedgeimperfectionstobecome proportionately more significant. This is reflected by manufacturers’published noise performance,which shows that the excess noise generated byfilmresistorsrisesforvalues>100 kΩ.Thiseffectisparticularlynoticeableforresistors of low power rating because their smaller physical size demands ahighergainforagivenvalue.Filmresistorsalsohaveamaximumvoltageratingwhichisindependentoftheirpowerrating,butisdeterminedbythemaximumallowablepotentialacrossthegap between adjacent turns of their helix. As the applied voltage rises, itbecomesmore likely that tracking (intermittent voltage-dependent conduction)willoccuracrossthegapduetoimperfectremovalofthefilminthegap.Takentoitsextreme,asufficientlyhighappliedDCcausesarcingbetweenturnsofthehelix and permanently damages a film resistor. When using film resistors asanode loads, it is not sufficient simply to ensure that the power dissipation issatisfactory, the voltage ratingmust also be checked. Typically, higher powercomponentshavehighervoltageratingsandlowerexcessnoise.Atmuch lower voltages, tracking is partly responsible for the inclusion of anexcessnoise specification for the resistor,which is typicallygiven in termsofμVofnoisepervoltofappliedDC.Forminimumnoisewithfilmresistors,theappliedDCacrossthemshouldbeminimised.Rarelyspecified,a typicalvalueforthisexcessnoiseis0.1 μV/Vforvalues<10 kΩ,buttypicallydoublesforeachdecaderiseinvaluebeyond10 kΩ,soa100 kΩanoderesistormightbeexpectedtoproduce0.2 μV/V.That100 kΩresistorwouldprobablyhave150VDCacrossit,resultingin30 μVofnoiseduetotheDC,butiftherewerealso

1 V of signal, thiswould create 0.2 μV of noise. By thismeans, applying asignalvoltageacrossafilmresistorgeneratesasignalleveldependentnoiseormodulation noise. Since amplifiers contain many resistors, modulation noisecould conceivably rise above the thermal noise floor in a very low noiseamplifier,butbemaskedbyapooreramplifier.Laser cutting of the film resistor produces a precise tolerance resistor, whichthen has tinned copperwire leadswelded to its end caps before being coatedwithaninsulatingprotectiveepoxyfilmontowhichthevalueismarked.It will be seen that almost every process can cause noise if carried outincorrectly,soresistormanufacturersroutinelymeasurenoiseorthirdharmonicdistortion as ameans of quality assurance. Unfortunately for audio designers,theirnoisemeasurementgenerallyusesa1 kHzbandwidth filtercentredon1kHzratherthana20 Hzto20 kHzaudiobandfilter.Nevertheless,thefigureisausefulguidetoproductrangesfromagivenmanufacturer.The resistor need not have end caps and leads fitted. Surfacemount resistorshave their ends plated with a silver–palladium alloy.When soldering surfacemountresistors,itisessentialtouseasilver-loadedsoldertopreventthesilverleachingoutfromtheplatingandreducingsolderability.MetalfilmresistorsarecommonlyavailableinE24valuesfrom10 Ωto1 MΩ,althoughvaluesupto50 GΩarenowavailableofftheshelf,andeven500 GΩisavailable(ataprice).

Power(Wirewound)Resistors

Powerresistorsaregenerallywirewound,with50 Wcomponentsbeingreadilyavailable,butratingsupto1 kWarepossible.Resistancevaluescoverasmanydecadesasmetalfilmresistors,butthemaximumvalueavailableistypically100kΩ.Again, the process begins with a ceramic rod as a former for the resistiveelement,butthistimeresistancewireortapeiswoundontotherodandweldedtotheendcaps,towhichleadsarethenwelded.Smallercomponents(<20 W)arethencoatedwithaceramicglazetopreventmovementofthewindingsandalso to seal the component. Larger componentsmay have screw terminal endcaps and be fitted into an aluminium extrusion to conduct the heat from theresistiveelement toanexternalheatsink.However,high-valueresistors requiremanycloselyspacedturnsoffineresistancewire,sothepossibilityoftrackingbetween adjacent turns defines a voltage rating which can easily override thepowerrating.

AgeingWirewoundResistors

AgeingWirewoundResistors

Scroggie[1]pointedoutthatbecausetheresistancewireiswoundundertensiontoensureaconsistentwind,thissetsupstrainswithinthewirethatrelievewithtime, causing the resistor’s value to change. He further suggested that theprocesscouldbeacceleratedbyheatingtheresistorsinanovento135 °Cfor24h.Theauthortestedthetheorybymeasuringhisentirestockofaluminium-cladwirewound resistors, leaving them in thekitchenovenon itsminimumsettingforaday,allowingthemtocoolslowlyintheoven,andmeasuringthemagain.Evena3½digitDVMwasable toshowsignificantdifferences; resistorsmorethanfouryearsoldshowednochange,butthenewestresistorschangedbyupto0.5%invalue. It thereforeseemssensible toagewirewoundresistors intendedforanodeloadsindifferentialpairsbeforematching.

NoiseandInductanceofWirewoundResistors

Becausethefilmresistors’resistiveelementisathintrack,theydevelopexcessnoise proportional to the DC voltage drop across them (≈0.1 μV/V). Bycontrast, surface imperfections of the resistance wire in a wirewound resistorform a very small proportion of its cross-sectional area, and excess noise isvirtually non-existent, making them ideal as anode loads in low-noise pre-amplifiers.Wirewoundresistorsarewoundasacoil,andeventhoughμr≈1forthealuminacore(makingitcomparablewithanaircore),allcoilshaveinductivereactancewhichmightconceivablybesignificantcomparedwiththeirresistance.Theresistanceofaconductoris:

whereρ=resistivityofconductorl=lengthofconductorA=cross-sectionalareaofconductor.

Butthewireisofcircularcross-section,andtheareaofacircleis:

Substitutingweget:

Tomakeresistorscheap,theresistancewireiswoundontostandard-sizedcores.To ensure efficient heat transfer to the surroundings, and to reduce thepossibility of hotspots, the core is completely coveredwith one layer of wirefromendtoendwithaninfinitesimalgapbetweenturns.ThenumberofturnsofwiretocompletelyfillacoreoflengthCis:

Thelengthofthiswireis:

Substitutingintotheresistanceequation,πcancels,andtheresistanceachievablebyasingle-layerwirewoundresistoris:

Simplifying:

Inductanceisproportionalton2,andsincenisproportionalto1/d:

Asobservedearlier, it is theratioofL toR that is important,not theabsolutevalue,so:

This result is very significant because it shows us that L/ R rises as we usethickerwire,soweshouldonlyexpectlowvaluewirewoundresistorstopossesssignificant inductance.This theorywas testedonacomponentanalyser,whichproducedmodels for a selection ofwirewound resistors. Because the resistorswerealuminiumclad,transformeractiontotheshortedturnmightbeexpectedtoreduce inductance, but later dissection of a WH25 type showed that the coildiameterwas half the internal claddingdiameter, implying loose coupling andinsignificanttransformeraction(seeFigure4.1).

Figure4.1Equivalentcircuitsofpracticalwirewoundresistors.

Ascanbeseenfromthemodels,measurementconfirmsthetheorybyshowingthatonlylowresistancewirewoundresistorshadmeasurableinductance.Besidesderiving models, each resistor was swept from 100 Hz to 100 kHz whilstmeasuring phase deviation from a perfect resistor. Only the 220 Ω resistorshowedameasurabledeviation(0.2°).Alloftheresistormodelsrequiredasmallshuntcapacitor,andoncetheresistorvalueswere typical of anode load resistances, this shunt capacitor settled to avalueof3 ± 1 pF,avaluecommensuratewiththestraysthatonewouldexpecttofindinapracticalcircuit.Summarising, the inductanceofwirewoundresistors isentirelynegligibleevenat 220 Ω, but, as predicted, inductance ismore observable at low resistancesthanhighresistances.Some resistors aredeliberatelywound tominimise inductance.Oneway todothisistotakethecentreofthewiretobewoundandbeginwindinginthemiddleoftheresistoruntiltheendsofthewirereachtheendcaps.ThesignificanceofthisAyrton–Perrywinding is that one coil ofwire is effectivelywound in theopposite direction to the other and their mutual inductance tends to cancel.Fortunately,theauthor’sstockofvitreousenamelledresistorsincludedavarietyof 1 k2 resistors,with somewound to theAyrton–Perrymethodology (easilyidentifiablebecause thismanufacturerusedabrazedconnectiondirectly to theterminatingwiresratherthanpress-fittedendcaps)(Table4.1).

Table4.1Inductanceof1 k2WirewoundResistorsPowerrating(W) Inductance(μH)

2.5 64 186(Ayrton–Perry) 9

Fromthepreviousmodel,weshouldexpectaphysicallylargerresistortohavehigherinductance,andthisistruewhencomparingthe2.5 Wresistorwiththe4W resistor, but the Ayrton–Perry winding of the even larger 6 W type

significantlyreducesinductancefromwhatmightbeexpected.Notethateven18μHisentirelytrivialcomparedto1k2andcausesonly0.5°ofphaseshiftat100kHz.Thewirewoundresistortobeavoidedatallcostsistheold-fashionedwirewoundrheostatoccasionallyfoundlurkingatthebackofacupboardinanoldphysicslaboratory.Withapowerratingof200 Wormore, thesebeastsseemidealaspoweramplifierdummyloads,buttheirtypical≈1″(25 mm)corediameterandlength of ≈4″ (100 mm)mean that their inductance becomes significant at 1kHz, and if their DC resistance is used in a V2/ R power calculation, theassumedoutputpowerofanamplifierwillbewrong.Asanexample,theauthorused one of these deviceswhilemeasuring the output power of his ‘ScrapboxChallenge’ single-ended amplifier for the third edition, and measured 6.8 Wwhen 6 Wwas expected. The reason for the error was that the very slightlyhigher impedance load allowed the amplifier to swing a higher voltage thanexpected,andthiserrorwasmagnifiedbytheV2terminthepowercalculation.

Non-InductiveThickFilmPowerResistors

The hybrid technology that was initially used to make wide bandwidthamplifiers by printing resistors and tracks directly to a ceramic substrate andthenaddingsurfacemounttransistorshasbeenborrowedtomakenon-inductivepowermetalfilmresistors.Atthelowerend(5 W)oftherange,theresistorsarethesizeofapostagestampandarecooledbyconvection,buthigherdissipationtypes are now available either in transistor packages (TO-220) or inmouldedplasticpackageshavingafootprintidenticaltothatofthetraditionalaluminium-cladresistors,butwithnon-magneticterminations.Notonlyistheirinductancedominatedbytheleadssolderedtothem,butstraycapacitancealsotendstobeeven lower than the typical 0.5 pF of smallmetal film resistors and certainlylowerthanthe3 pFtypicalofwirewoundresistors.

GeneralConsiderationsonChoosingResistors

Tolerance• Is the absolute value important? If the resistor is part of a network thatdetermines a filter or equalisation network, then we need a close tolerance(perhapseven0.1%)componenttominimisefrequencyresponseerrors.•Matching:Isthecomponentpartofapair?Anodeloadsindifferentialpairsshould be matched, and so should corresponding components in filter

networksforeachstereochannel.

Heat

Willtheresistorbeheatedbyothercomponents?Willitsvaluechange?Willthismatter?

VoltageRating

• Is thevoltage ratingof the component adequate, evenunder conditionsofmaximumsignal? (Grid-leak resistors for low-μpowervalves, suchas845,mightneedtoconsiderthisfactor.)•Will theDCvoltagedropacrosstheresistordevelopanunacceptablelevelofexcessnoise?Ifso,awirewoundorabulkfoiltypeshouldbeconsidered.

PowerRating

Is thepowerratingof thecomponentadequateunderallconditions?Could the(varying)audiosignalheattheresistorsufficientlytochangeitsvalueandcausean error? If a power component is required,what provision has beenmade tolose the heat that this component will generate? Will it heat other, sensitivecomponents?

CapacitorsCapacitorsstorecharge.Thischarge isstored in theelectric fieldbetween twoplates having a potential difference between them. If there is no potentialdifferencebetweentheplates,thenthereisnostoredcharge,andthecapacitorissaidtobedischarged.Capacitors for electronic circuits aremade of two fundamental components: apair of conducting plates and an insulating material called the dielectric thatseparatesthem.Initssimplestform,acapacitorcouldbeapairofparallelplatesseparatedbyavacuum.

TheParallelPlateCapacitor

Unsurprisingly,thecapacitanceofaparallelplatecapacitorisproportionaltothearea(A)oftheplatesandinverselyproportionaltothedistance(d)betweentheplates.We should expect this, since ifwemove theplates an infinite distanceapart,theycannolonger‘see’oneanother,andaplateonitsownisnotmuchofa capacitor. If the charge is stored between the plates, then it is reasonable to

supposethattheinterpositionofanymaterialbetweentheplateswillaffectthecapacitance. We can formalise these arguments by combining them into aproportionality:

whereC=capacitanceA=areaofplatesk=relativepermittivityofinterposeddielectricd=distancebetweenplates.

Tocalculaterealvalues inelectronicunits,wemustaddsomefudgefactors togeneratetheequation:

This equation looks a lotmore impressive, but ε0 is simply a fudge factor tomaketherealworldfitintooursystemofunitsandisknownas‘thepermittivityoffreespace’;ithasameasuredvalueof≈8.854×10−12 F/m.εr(alsoknownas‘k’) is the relative permittivity of the material we insert as the dielectric,comparedtothevalueforavacuum,andisalways>1.Aquickcalculationusingthisequationshowsthataparallelplatecapacitorinavacuum(althoughairisalmostidentical)withplates1 m2,separatedby10 cm,wouldhaveacapacitanceof88.5 pF. Ifwearegoing tomakepracticalvalveamplifiers,wearegoingtohavetodosomethingaboutthesizeofthiscapacitor.

ReducingtheGapBetweenthePlatesandAddingPlates

Oneobviousmethodofincreasingcapacitanceistoreducethegapbetweentheplates,sotypicalcommercialcapacitorsusegapsof5 μmorless.Anothermethod is to addmore conductive plates in the form of a stackwithalternateplatesconnected together.Thisalmostdoublescapacitanceoverwhatmightatfirstbeexpectedbecausewenowusebothsidesofeachplate(exceptforthetwooutermostplates).Thisformofconstructionisusedforsilveredmicacapacitorsandforstackedfilm/foilcapacitors(seeFigure4.2).

Figure4.2Cross-sectionofgeneralformofparallel-platecapacitor.

Cuttingsquaresofdielectricandplatesandassemblingthemtoformacapacitorare an expensive business, somost capacitors are constructed bywinding twolong strips of plates and dielectric together to form a cylinder, and thenconnectingawiretoeachplate.

TheDielectric

Maintainingapreciseairgapof5 μmbetweenasetofplateswouldbevirtuallyimpossible,soaninsulatingspacerisneeded.Thisinsulatingdielectricwillhaveεr>1,whichfurtherreducesthephysicalsizeofthecapacitorforagivenvalueofcapacitance.Unfortunately, we gain this increase of capacitance at the expense of otherparameters, and so we should investigate these. The dielectric has threeimportant properties: relative permittivity εr, dielectric strength and dielectricloss.Relativepermittivityεrhasbeenmentionedearlierand iseffectively the factorbywhichthecapacitanceofacapacitorisincreasedbytheinsertionofthenewdielectric.Dielectricstrength refers to themaximumfieldstrength,measured involtspermetre, that can be applied to a given insulator before it breaks down andconducts.Itisthislimitthatsetsvoltageratingsforcapacitors.Dielectriclossreferstohowcloselythedielectricapproachesaperfectinsulatoratvoltagesbelowbreakdown.Onewayofspecifyingthislossistomeasuretheleakagecurrent, inμA, that flowswhen themaximumratedvoltage is appliedacross the capacitor – thismethod is typically used for aluminium electrolyticand tantalumcapacitors.Filmcapacitors are typically rather less lossy, and sotheinsulationresistanceorleakageresistanceofthecapacitormaybespecified.Dielectric loss may be different from AC to DC, and so a more usefulmeasurement is to measure tan δ, which is the ratio of the total resistivecomponentofthecapacitortothereactivecomponentataspecifiedfrequencyorfrequencies.Note that tan δ does not distinguish between the parallel leakageresistance of the dielectric or any series resistance, such as lead or plate

resistance.LeadandplateresistancearecollectedtogetherasonetermandareknownastheEffective Series Resistance ( ESR). In components such as high-capacitanceelectrolytic capacitors for power supplies, or cathode bypasses, the ESR ishighlysignificant,sinceitmaybeanappreciablefractionofthetotalimpedanceof the capacitor. In power supplies, significant currents flow in the reservoircapacitors,whichcauseself-heatingof the internalstructure.For this reason,aparameter is quoted that is very closely linked to ESR, and this ismaximumripplecurrent(seeChapter5).Both the leads and the plates have series inductance. For amodern capacitor,series inductancemeasuredasclose to thecapacitorbodyaspossible typicallyranges between 10 nH and 100 nH.We can now draw a simple equivalentcircuitforarealcapacitor(seeFigure4.3).

Figure4.3Basicequivalentcircuitofpracticalcapacitor.

It is immediately apparent thatwe are dealingwith a resonant circuit, and forelectrolytic capacitors, this self-resonant frequency is often specified in themanufacturer’sdatasheets,andwewillreturntothislater.

DifferentTypesofCapacitorsWith the various ways of making the plates or the dielectric, there are manycombinationsofcapacitorconstructionavailable(seeFigure4.4).

Figure4.4Comparisonofdifferenttypesofcapacitor.

This tree of capacitors shows the various possibilities available. The firstbranching is between polarised and non-polarised capacitors. A polarisedcapacitor would be damaged by having DC applied in the reverse direction.Non-polarised capacitors branch into their plate construction, self-supportingplates, foil or a surface coating ofmetal sputtered directly onto the dielectric.Thefinalbranchingsdealwiththedielectric,andalthoughsomedielectricsarerepresented in both categories, others are not, due to their manufacturingimpossibility.Broadly speaking, themore nearly perfect capacitors are at the bottom of thetree,whilsthighcapacitanceperunitvolumecapacitorsareatthetopofthetree.Thiscanbefurthergeneralisedbyobservingthathighqualitycapacitorstendtobephysicallylargefortheirvalueofcapacitance.

AirDielectric,MetalPlate(εr≈1)

These capacitors are invariably constructed as trimmer or variable capacitorswith sets of intermeshing semicircular rigid plates and are primarily used inradio frequency (RF) circuits, although they are occasionally useful in audio.Becauseofthedifficultyofsupportingplatesthatareverycloselyseparated,airdielectric capacitors have lowvalues of capacitance and are not usually largerthan500 pF.Theygenerallyhave≈10:1rangebetweenmaximumvalue(vanesfullymeshed)andminimumvalue (vanes fully separated).Possibleaudiousesinclude:

•Thetypical2×365 pFtuningcapacitorfromanoldradioacrosstheinputsofamoving-magnetRIAAstageallowsanycartridgetobeoptimallyloadedbythepre-amplifier.• RIAA stages with the equalisation in the feedback network may requiresufficientlylow-valuecapacitorsthattheyarewithintherangeofairtypes.•≈50 pFfortrimmingequalisationcapacitorstotheirexactvalue.

Valve short-wave radios often contain many smaller ‘beehive’ trimmercapacitors, and although theymight not be the exactmaximumvalue requiredforyourparticularapplication,thesilver-platedbrassvanesaresolderedtotheirsupports, so they can easily be desoldered to reduce the maximum value asnecessary(seeFigure4.5).

Figure4.5Selectionofvariableair-spacedcapacitors.Notethattheright-handtrimmerhasitsvanesdisengagedsothattheycanbeseen.

PlasticFilm,FoilPlateCapacitors(2<εr<4)

Thisisthemostimportantclassofcapacitorsforuseinvalveamplifiers,aswewill use these for coupling stages and also for precise filters. The betterdielectrics are very nearly perfect, and manufacturers usually describe theirimperfectionsintermsofthevalueoftan δordissipationfactor‘d’:

whereR=sumofresistivelossesexpressedasparallelresistanceXC=capacitivereactance.

Thereappearstobeastrongcorrelationbetweenthesubjectivesoundqualityofcapacitors and their value of ‘ d’, with low‘ d’ capacitors being subjectivelysuperior.Thesignificanceof‘d’inengineeringtermsisnotsimplythatthecapacitorhas

aleakageresistanceacrossit,butthatthecapacitorisactuallyaladdernetworkofcapacitors,separatedbyresistors,thatextendsindefinitely(seeFigure4.6).

Figure4.6Equivalentcircuitofpracticalcapacitortomodeldielectricabsorption.

Ifwewere to charge a capacitorwhilstmonitoring its terminal voltagewith avoltmeterofinfiniteresistanceandthendischargeitbybrieflyshort-circuitingit,wewouldexpectthecapacitorvoltagetoremainat0 V.However,weactuallyseethevoltagerisefrom0 Vtheinstantthattheshortcircuitisremoved.Thisisbecause we discharged the capacitor that is ‘near’ to the terminals, but othercapacitorswereisolatedbyseriesresistorsandwerenotdischarged.Removingthe short circuit allowed the undischarged capacitors to recharge the ‘near’capacitorandthevoltageatthecapacitorterminalsrose.Thiseffectisknownasdielectricabsorption,anditismorepronouncedasthevalueof‘d’rises.Applying a pulse to a capacitor is equivalent to instantaneously charging anddischargingthecapacitor,soanyvoltageleftonthecapacitorat theendof thepulse isdistortion.Music ismadeupofaseriesof transients,orpulses,and itmaybethatdielectricabsorptionisonecauseofcapacitor‘sound’.Film/foilcapacitorsareconstructedby layingfouralternate layersofdielectricandfoilwhicharethenwoundintoacylinder.Guidingthesefourlayerswhilstwindingthecapacitortightlyisnotatrivialtask,andispartlyresponsibleforthehigher price of these capacitors. The foils are wound slightly offset to oneanother(knownasextendedfoilconstruction)sothatoneendofthecylinderhasanexposedspiraloffoilthatisoneplate,whereastheexposedspiralattheotherendistheotherplate.Eachspiralisthensprayedwithzincortin–zincalloytoconnectallpointsofthatspiraltogether,andbecausethisputsallofthefoilinparallel,thisgreatlyreducesseriesinductanceandresistance.Afurtherreductionofseriesinductanceandresistancecanbeobtainedbyreducingtheaspectratio(canlengthdividedbydiameter)becausethissimultaneouslyshortenstheseriespaths and increases their parallel number, but the narrower film strip requiresmore turns for a given capacitance, increasing the time taken to make eachcapacitor.Because of the lowmelting point of polystyrene, traditional small (<100 nF)

polystyrenecapacitorsmadeasingletabcontacthalfwayalongthefoil,althoughlarger capacitors (470 nF)made two tab contacts to reduce series inductance.However, LCR appear to have circumvented the polystyrenemelting problemandmakecontactovertheentireextendedfoil(seeFigure4.7).

Figure4.7Polystyrenecapacitor.

Polystyrenecapacitorsoftenhaveoneterminalof thecapacitordelineatedbyared or yellow band or a dot. This does not mean that they are sensitive topolarity,butthatthemarkedendisconnectedtotheouterfoil.Thisissignificantbecause one end of the capacitormay be connected to a less sensitive part ofcircuitrythantheother.Forinstance,ifasmallpolystyrenecapacitorwasusedas part of an active crossover network and connected as a series couplingcapacitor(high-passfilter),thentheouterfoilshouldbeconnectedtothesourcetoreduceinducedhum.Alternatively,ifoneendwereconnectedtoground,thentheouter foil shouldgo toground to reducestraycapacitance toactivesignals(strays to ground rarely cause problems, but theMiller effect can cause otherstraystobesignificant).Although polytetrafluoroethylene (PTFE) is an excellent dielectric, there is anabruptphasechangeat19 °Cthatcausesa1%changeinvolume.Ifthematerialisunconstrained,thechangeinvolumeisseenasachangeincapacitance.Whenconstrained, theattempt tochangevolumecausesachangeofcapacitorchargebecausePTFEispiezoelectric.Theeffectisnegligibleinmostapplications,butthe temperature-induced change in charge caused by a PTFE feed-throughinsulatorcompressedintoaholeinaconductivechassiswasenoughtoruintheperformance of a prototype electrometer. Fortunately, the heating effect ofnearbyvalvesislikelytopreventthe19 °Cphasechangebeingobservableeveninahighimpedanceaudioapplicationsuchasacondensermicrophone.PTFEis

also triboelectric (scraping it with a conductor transfers charge), so tappingPTFEinsulatedwiresinahigh-gainamplifiercausesadisturbance.Asaminorpoint of interest, PTFE sleevedwire is silver platednot because the improvedconductivity compared to copperwould reduce skin effect at high frequencies(HFs),butforthemuchmoreprosaicreasonthattinningwouldmeltatthehightemperatureneededtoextrudePTFE.

MetallisedPlasticFilmCapacitors

Becauseofthedifficultyofwindingthelayersofdielectricandfoil,mostfilmcapacitorsaremadebysputteringonesideofthefilmwithalayerofaluminiumup to12 μmthick to formtheplate.Thismakes thecapacitoreasier tomake,and a higher capacitance per unit volume is obtained because the plate is somuchthinner,butESRisusuallyhigherthanforafoilcapacitor.SinceESRforaplasticcapacitorisonlysignificantatveryhighfrequencieswhenitbecomescomparable with the reactance of the capacitor, this may not be a problem.However,foilcapacitorsaregenerallydescribedbytheirmanufacturerasbeingmore suitable for high frequency pulse applications because their lower ESRreducesself-heating(I2R).If thereisgranularityduetoimpuritiesinthefilmofametalfilmresistor, thisgenerates excess noise, and film resistors are always noisier than wirewoundresistors. Since the plates in ametallised film capacitor are also produced bysputtering,itisnotunreasonabletosupposethattheywillsufferfromthesamequalitycontrolproblems–with thedifference thatcapacitorsarenot routinelytestedformodulationnoise.Foilcapacitorshavetraditionallybeenpreferredinaudio,possiblyforthisreason.Recentmetallised capacitors are almost indistinguishable from foil capacitors.Theauthorcompareda100 nF2 kVVishayRoedersteinMKP1845metallisedpolypropylenetoa100 nF1 kVLCRfoilpolypropylene,andafterallowingforthedifferentworkingvoltages(andthereforedielectricthicknesses),thetwohadalmostidenticallossesandESR.

MetallisedPaperCapacitors(1.8<εr<6)

Metallised paper was the traditional dielectric for capacitors in classic valveamplifiers, and depending on the paper and its impregnant, the performancerangedfrompoortotolerable.Unfortunately,ifthesealsofthecapacitorarelessthanperfect,humidityentersand thecapacitorbecomeselectrically leaky.Theauthor once bought a Leak Stereo 20 power amplifier having paper-coupling

capacitors,everyoneofwhichhadgoneleaky.Becausepapercapacitorsareinherentlyself-healing,theyarewidelyusedinthepowergeneratingindustry.Intheeventofanovervoltagespike,thepaperbreaksdownat itsweakestpoint and themetallisationat thatpoint isvaporised, thuspreventingashortcircuitandcatastrophicfailure.Ithasbeenknownforacentury[2]thatpapercapacitorshavecapacitancethatfallswithfrequency,soalthoughtheymightbesuitableascouplingcapacitors,they should not be used for equalisation (especially avoid RIAA because thewide separation of time constants exacerbates response errors due to errors incomponentvalues).

SilveredMicaCapacitors(MuscoviteMica,εr=7.0)

Thiswasthetraditionalsmall-valuecapacitorusedforRFcircuitry,orforaudiofilterswhereexcellentstabilityofvaluewasimportant.Micaisacrystallinerockthatcanbeeasilycleavedintofinesheets,whicharethencoatedwithsilver,andastackedconstructiongiveslowinductance.Sincemicaisanaturalmaterial,itissubjecttoalltheaccompanyingvagariesofinconsistency.Therearevarioustypesofmica,butmuscovitemakesthelowestloss capacitors. Although muscovite mica and polystyrene have comparablelosses(0.001<d<0.0002),dielectricabsorptionis80timesworseformuscovitemicathanpolystyrene[3],sopolystyreneisgenerallypreferredforaudio.Mostoftheworld’smicahasbeenmined,makingtheremainderexpensiveandofvariablequality, sosilveredmicacapacitorshavenowbeenalmosteclipsedbypolystyrene,which,inturn,isbeingsupersededbytheveryslightlyinferiorpolypropylene.

CeramicCapacitors

Thesehavenoplaceinthepathofanalogueaudio!Until now, the dielectrics that we have seen have had εr<10, but ‘high- k’ceramic capacitors can achieve εr (or k)≈200,000! Commonly, ceramiccapacitors are made up of barium or strontium titanate, both of which arepiezoelectric materials. This means that they generate a voltage whenmechanicallystressed(thesematerialswerethebasisofceramiccartridgesusedbyinferior‘musiccentres’forplayingvinylrecords).Ceramiccapacitorsexcelashighfrequencybypassesindigitalorheatercircuitrywheretheirpoorstabilityofvalueandlow‘d’areirrelevant.

ElectrolyticCapacitors

ElectrolyticCapacitors

Thesecapacitorsarepolarised.Reversebiassed,theyformquiteagoodqualityshortcircuit,anddamagethedrivingcircuitry,whilstthecapacitorexpirestotheaccompaniment of heat, smoke and noxious fumes. Aluminium electrolyticcapacitorsmay even explode and shower the surrounding circuitrywith soggypaperandaluminiumfoil,causingfurtherdamage.Somepeoplehavereligiousconvictionsagainstusingelectrolyticcapacitors,butwithalltheirfaultstheyarestillusefulcomponents,andourchoiceofdesignisseverely restricted if we refuse to use them. Most of the faults ascribed toelectrolyticcapacitorsrelatetoinappropriateusage.Electrolytic capacitors take high capacitance per unit volume to the limit, andtheydosobyattackingallpartsoftheparallelplatecapacitorequation.Thegapbetween the plates is minimised, surface area is maximised, and εr ≈ 8.5 foraluminium oxide, as opposed to εr≈3 for the plastic films. The principle ofoperation is broadly similar for all types, so only the aluminium typewill bedescribedindetail.

AluminiumElectrolyticCapacitors(εr≈8.5)

The aluminium foil of one plate is anodised to form an insulating layer ofaluminiumoxideonthesurface(≈1.5 nm/Vofappliedpolarisingvoltage),anditisthismicro-thinlayerthatisthedielectricofthecapacitor.Sinceanodisingisanelectrochemicalprocess,and thealuminiumoxide isan insulator, it followsthat there must be a maximum thickness of aluminium oxide that can beproducedbeforetheinsulationofthelayerpreventsdeeperanodising,implyingamaximum possible working voltage of ≈600 VDC.Unfortunately, a practicalproblem intervenes somewhat earlier. Aluminium oxide is a very brittleinsulator,buttheelectrolyticcapacitorisformedasaroll,sothereisadangerofthe rolling process cracking the oxide and causing leakage paths. Because ofthis, thepracticalmaximumworkingvoltageofelectrolyticcapacitors tends tobe≈500 VDC,andold>450 Vcapacitors shouldbe lookeduponwithgravesuspicion.Becauseofthefragilityofthebrittledielectric,weshouldbecarefulnottodentelectrolyticcapacitorsbyoverzealoustighteningofcapacitorclamps.Although by anodising the aluminium foil we have both a plate and thedielectric,westillneedtheotherplate.Wecoulduseanotherpieceofaluminiumfoilpressedtightlytothefirst,butanygapbetweenthetwofoilswouldnegatetheadvantageofthemicro-thindielectric.Thesecondplateisthereforemadeofthinsoggypaperorsimplyagel,whichbecauseitiswetmakesperfectcontactwiththeanodisedsurfaceofthefirstplate,andthisistheelectrolytefromwhich

the component derives its name. The electrolyte is not a particularly goodconductor of electricity, and so a second aluminium foil is laid on top of theelectrolytetoallowalowresistanceplatetobemade.We now have two aluminium foils separated by electrolyte that can be rolledintoacylindertomakeourcapacitor.If,beforeanodisingthealuminiumfoil,wehadetchedthesurfaceofthealuminiumfoil,thiswouldroughenthesurfaceandgreatly increase the surface area on amicroscopic level. Since the electrolyteplateis inperfectcontactwiththissurface,wehavedramaticallyincreasedtheareaoftheplatesofthecapacitor,andthecapacitancerisesaccordingly.Unfortunately, the electrolytic capacitor has its disadvantages. Electrolyteresistanceissignificant,sodeepetchingofthefoilincreasestheresistancefromthebulkofthefoiltotheextremitiesthatformtheplate,andwecanexpectthehighestcapacitanceperunitvolumecomponentstohaveahigherESR.Notonlydothesetortuouspathsintothenooksandcranniesincreaseresistance,buttheyhave also limited current carrying ability before heating significantly andcausingtheelectrolytetoevaporate.CompactcapacitorsthereforenotonlyhavehighESR,butalsohavealowripplecurrentrating,althoughSanyo’sOS-CONrangeofcapacitorsusesanorganicsemiconductorelectrolyte thatsignificantlyreduces ESR. Interestingly, the best use for OS-CONs is not in analogueelectronics but in digital electronics, bypassing supply rails adjacent to noisydigitalchips(seeFigure4.8).

Figure4.8CapacitorimpedancefallswithfrequencytoitsESR.

Spraying molten zinc onto the entire spiral of an extended foil capacitor

connected all parts of each plate together,whichwas equivalent to an infinitenumberofconnections,andminimisedseries inductance.This technique isnotpossiblewithanelectrolyticcapacitor,andweareforcedtoconnecttotheplateatasinglepointusingaweldedfoiltab,butwedohaveachoiceastowheretopositionthattabalongthefoil.Theworstplacetopositionthetabwouldbeatoneendofthefoilbecausethatwouldgivemaximuminductancetotheoppositeendofthefoil.Conversely,placingthetabinthemiddleofthefoilgivesequalinductancetoeachend,whichwouldbeinparallel,andthereforehalved.Given the electrolytic capacitor’s single tab connection, series inductance andresistancecanbereducedby increasing theaspect ratio (can lengthdividedbydiameter) to obtain the required capacitance because this makes the unrolledplatenearertoasquarethananarrowstrip.Foragivencapacitance,thestripandsquaremusthaveequalarea,but inductance isproportional to lengthand fallswithwidth,soasquareistheoptimumshape.Although the manufacturer aims to minimise series inductance and thusinductivereactance(XL=2πfL),foralargecapacitor,XCisalsolow,soevenasmall series inductance becomes significant. Electrolytic capacitors typicallyhaveseries inductancerangingbetween10 nHand100 nHdependingoncansize and shape, with older types tending to have higher inductance. As aconsequence of this series inductance, larger capacitors always have a lowerresonantfrequency,whichmaybeaslowastensofkHz(seeFigure4.9).

Figure4.9This10,000-μFcapacitormayhaveitsresonantfrequencywithintheaudiobandwidth,butit isstillaneffectiveshort

circuittoAC.

Notethatalthoughthiscapacitorhasaresonantfrequencyof15 kHz,itisstillaveryadequateshortcircuit(8 mΩ)at100 kHz.Limitationsoftheauthor’stestequipment(Hameg8118)meanthatthegraphsuggestsanoverlyoptimisticESRof 0.6 mΩ, but the series inductance (derived from resonant frequency andcapacitance)isreliable.Electrolyticcapacitorsarelossy.Whentheyarefirstmanufactured,apolarisingvoltage is applied, and this causes an anodising current to flow through thecapacitor,formingthealuminiumoxidelayerontheplate.Oncethisoxidelayerhas been formed, very little leakage current flows. However, over time, thismicro-thin layer is corroded by the electrolyte and needs to be re-formed.Provided that the capacitor always has DC applied across it, the capacitorbalances itself by always passing theminimumnecessary anodising current tomaintaintheoxidelayerfortheappliedDCvoltage.Theauthorselectedanumberof470 μFelectrolyticcapacitorshavingaswidelydifferent technologies as possible that were known to have been storedunchargedforat least10yearsand tested thembyapplyingaconstantvoltagefromalow-noisesupplyandmeasuringchargingcurrentat1-s intervalswhilstlogging the resultdirectly toa spreadsheet.All thecapacitorsproducedaverysimilarcharacteristiccurve(seeFigure4.10).

Figure4.10Electrolyticcapacitor‘leakage’currentdecayswithtime.

Themeasured current is clearly the sumof a slowly decayingDC term and apureACnoise term,so theauthorexperimented tofindamodel thatwouldfitthedecayingDCterm.TheidealmodelwouldfitthedecayingDCtermsowellthatwhen subtracted from themeasured results, the remainderwould be purenoise(noDCcomponent)(seeFigure4.11).

Figure4.11Oncethedecayingcurrentissubtracted,purenoiseremains.

Giventhattheremainderisacloseapproximationtonoise,therelationshipusedtofitthedecayingDCtermcanbeusedwithconfidence.Moreimportantly,thedecayingDCtermcanbedeemedtobetheanodisingcurrentreferredtoearlier–andthishypothesiswasverifiedbyrepeatingtheexperimentwitha120 μF400V polypropylene capacitor and noting that the DC term decayed in a fewsecondsratherthanmanyminutes(seeFigure4.12).

Figure4.12Apolypropylenecapacitorshowsnodecayingcurrent.

Electrolytic capacitor anodising current can be fitted using an equation of theform:

wheret=timeinminutesa,bandc=experimentallydeterminedconstants.

The author’s measurements suggest that a typical aluminium electrolyticrequires at least 45 min after voltage is applied before the anodising currentdecays to its steady-state value. Capacitor manufacturers neglect the (veryvariable)time-dependenttermandrefertoanodisingcurrentasleakagecurrent,andthenspecifyitsfinalvalue(‘c’intheanodisingcurrentequation)intermsof the CV product of the capacitor. An electrolytic in good condition has aleakagecurrentcomprisedoftheDCanodisingcurrentplusatypicalACnoisecurrentof≈50 nARMS.Given that the model for anodising current was good, a comparison of themodelledresultswasmade(seeFigure4.13).

Figure4.13Comparisonofdifferentelectrolyticcapacitor‘leakage’currents.

The current following the descriptor in the graph is the RMS noise currentcalculatedfromthemeasurements,anditisnotablethatthecapacitorswiththehighest leakage current displayed the highest noise current andvice versa – iflownoiseisrequired,lowleakagecurrentshouldbespecified.Unsurprisingly, the two capacitors that were known to be noisy also had thehighest anodising currents, and the unknown generic capacitor displayedpredictablymediocreperformance.TheSanyoOS-CONhadasurprisinglyhighanodisingcurrent;perhapstheorganicsemiconductorelectrolytethatallowsitsverylowESRisalittlemorecorrosive,anditsslightlyhighernoisecurrentof53 nARMSsuggeststhatitsuseasacathodebypassinalow-noisestagemightbeunwise.TheaddedvoodoooftheBlackGatecapacitor(noisecurrent,50 nARMS)didn’tpreventitsperformancebeingsurpassedbytheElnaRSH.Onceequipmentisswitchedoff,whenpowerisreapplied,ahigherthannormalanodisingcurrentmustflowuntiltheoxidelayerhasbeenre-formed.Thelongertheelapsed timewithoutbiasvoltsapplied, thegreaterdurationandamplitudethis initial anodising currentmust be, and there is a danger that it will causeseriousheatingoftheelectrolyte.Astheelectrolyteisheated,itevaporatesmorereadily,andtheresultinggasmaybuildupsufficientpressuretocausethecantoexplode. Because of this, it is wise to use a Variac to gently apply power toequipmentcontainingelectrolyticcapacitorsthathaslainidleforsometime.Moderncapacitorshavesafetypressuresealstoventthegasviaarubberbunginthe base of the component (large capacitors), or the aluminium can may bedeliberately weakened at the top with a series of indentations that allowcontrolled rupturing for the gas to escape (small capacitors). Either of theseoccurrencessignifiesthedemiseofthecomponent,buttheydopreventdamagetoothercomponents,withthebonusofasimplevisualinspectionoftheirhealth.Theleaky500 μFcapacitornotonlyhadameasurednoisecurrentof560 nARMS,butalsowasvisiblyvented(seeFigure4.14).

Figure4.14Notetheburstingpimplethatwarnsofaleakingelectrolyticcapacitor.

Gentleheatingevaporates theelectrolyte through thesealsof thecapacitor (nosealscanbeperfect), andas thequantityofelectrolyte falls, itmakes lessandlesscontactwiththenooksandcranniesoftheetchedplate,sotheESRrisesandcapacitancefalls.Thus,ESRcansometimesbeausefulguidetothehealthofanelectrolyticcapacitor,anddedicatedESRmetersareavailable(PeakAtlasintheUKandDickSmithkitinAustralia),butmoresignificantly,theyareusefulforgivingavalueofESRthatcanbefedintoPSUD2(seeChapter5),andalthoughtheyarenotquiteasaccurateasagenuinesweptfrequencycomponentbridge,theyarefarcheaper.Electrolyte evaporation causes electrolytic capacitors to be heat sensitive, socapacitorlifedoublesforevery10 °Cdropintemperature.Applied voltage also affects electrolytic capacitor life.Without a bias voltage,theoxidelayercannotbere-formedandisgraduallycorrodedbytheelectrolyte,causingthecapacitortobecomeleaky.Thiswasawell-knownfaultinanaloguesoundmixers using symmetrical + and − supplies with operational amplifierscoupledbyelectrolyticcapacitors,whichthenhadlittleornopolarisingvoltage.Provided that there is a polarising voltage, operating electrolytic capacitorsbelowtheirmaximumratedvoltageincreasestheirlifesignificantly:

Usingthisrelationship,weseethatoperatinganelectrolyticcapacitorat87%ofitsratedvoltagedoublesitslife.Itiswisenottoreadtoomuchintothisformula,since we could easily use it to predict a lifetime measured in centuries byloweringtheoperatingvoltagesufficiently.Agoodengineeringruleofthumbisthat,ifpossible,electrolyticcapacitorsshouldbeoperatedattwo-thirdsoftheir

maximum voltage rating, giving a theoretical eight-fold increase in lifeexpectancy, which is probably at the limit for which the formula is valid.Fortunately, all of the capacitor manufacturers offer detailed datasheets thatenable far more accurate lifetime predictions to be made taking into accountsuchfactorsasambienttemperature,ripplecurrentandappliedvoltage.Many classic valve amplifiers had electrolytic capacitors with more than onecomponent concentrically wound in a single can. The outer capacitor wasmarkedwitharedspot,andinanamplifierusingcascadedRCsmoothing,thiscapacitorshouldbeconnectedtothemostpositivepotential.Thelogicforthisisthatthehighestpotentialhasthegreatestripplevoltage,andasthereisnofieldwithina conductor, this ripple isnot coupled to subsequent stages.Wiring thecapacitorsinthewrongordercausesexcesshum.Historically, electrolytic capacitors had poor tolerance on their capacitance(typically +100% to −50%). Although modern types are typically ±10%, weshouldneveruseanelectrolyticcapacitorinapositionwhereitsvaluecouldnotbesafelydoubledorhalvedwithoutupsettingoperationofthecircuit.ThereisaclassofaluminiumelectrolyticsavailableforuseatACthatisknownas bipolar. These capacitors used to be ubiquitous in loudspeaker crossoversbecause theyweresomuchcheaper thanplastic-filmcapacitorsofcomparablecapacitance.Theirconstructioniseffectivelytwoelectrolyticcapacitorsbacktoback(seeFigure4.15).

Figure4.15Thebipolarelectrolyticcapacitor.

Thereisnoconstantpolarisingvoltage,andeachindividualcapacitorhastobetwicethevalueofthefinalcapacitor.Defectsaretherebymultipliedbyafactorof fourover thenormalunipolar electrolyticcapacitor, so theirperformance ispoor.

TantalumElectrolyticCapacitors(εr≈25)

The increased relative permittivity significantly reduces component volumecomparedtoaluminiumelectrolyticcapacitors(εr≈8.5).Tantalumfoilcapacitorshave two additional advantages directly related to the increased chemicalinertness of the tantalum oxide layer. Firstly, ESR can be reduced by using a

lowerresistanceelectrolytethatwouldhavecorrodedaluminiumfoil.Secondly,because the oxide layer is more inert, leakage current is reduced. However,tantalumisexpensive,whereasaluminiumelectrolyticcapacitorsareimprovingallthetime.Tantalum bead capacitors are only available in low voltages and are oftenspecified by semiconductor manufacturers for bypassing voltage regulators orlogicchips,but thereisaverylargevariationinESRbetweentypes–anESRmeter is essential here. Unfortunately, they are only available in low values(rarely>100 μF)andareoftennotlargeenoughtobeusedascathodebypasses.Tantalum bead capacitors have extremely limited ripple current capacity, sothey’re not a good choice for power supply coupling where switchers areinvolved. When tantalum bead capacitors fail (they have zero tolerance toreverse polarity), they tend to fail dead short circuit, and the consequentialdamagetendstobespectacular.Theyareexpensive.Themain justification for using tantalum capacitors is that (unlike aluminiumelectrolytic capacitors) theyhave almost indefinite shelf life, a useful propertyforrarelyusedinstrumentsthatmustbeultra-reliable,butlessusefulforaudio.

VariationofCapacitancewithFrequency

Someplasticsarepolar;thisdoesnotmeanthatthecapacitorcanbedamagedbyreversingthepolarityofanyappliedDC,butthatatamolecularlevelwithinthedielectric,therearepermanentlychargedelectricdipoles,similartothemagneticdipoles in a magnet. Under the influence of an external electric field, thesedipolesattempttoalignthemselvestothatelectricfield.Bycontrast,non-polardielectrics haveverymuch smaller losses and are very nearly perfect at audiofrequencies.Almostalldielectricswithεr>2.5arepolar(Table4.2).

Table4.2ComparisonofCapacitorDielectricsand‘d’

aAlthoughPTFEispolar,thebalanceddipolesofitspolymerchainmakeitappearnon-polar.

Dielectric Commonname εr Typical1 kHz‘d’(100-nFcapacitor) Polar?

Polytetrafluoroethylene PTFE,Teflon™ 2.1 0.00001 Ya

Polystyrene 2.6 0.00020 NPolypropylene 2.2 0.00010 NPolycarbonate 3.2–3.0 0.00090 YPolyethyleneterephthalate PET,polyester 3.2–3.9 0.004 Y

Because work must be done each time a dipole is flipped, capacitors havingpolar dielectrics suffer frequency-dependent losses that are reflected incapacitancethatvariessignificantlywithfrequency(seeFigure4.16).

Figure4.16Capacitorshavingapolardielectricdonothaveconstantcapacitancewithfrequency.

Ascanbeseen,theuseofpaperorpolyestercapacitorsinvalveamplifierscanonly be justified in areas such as power supply decoupling where theircapacitancedeviationwith frequency is irrelevant.Althoughnot shownon thegraph, electrolytic capacitors are even worse, and their 1 kHz capacitance istypically−10%comparedtotheirDCcapacitance.

ImaginaryCapacitance

Since permittivity has a real and imaginary component, capacitancemust alsohaverealandimaginarycomponents.Ifwemeasuredtheseriesrealcomponentofacapacitor’simpedanceoverarangeoffrequencies,wewouldexpecttoseealowandconstantvalueequaltothecapacitor’sESR,butwhatweactuallyseeisa low frequency loss componentdue to the imaginarycapacitance that falls tothecapacitor’sESRathighfrequencies(seeFigure4.17).

Figure4.17Imaginarycapacitancecausesafrequency-dependentlossatlowfrequencies.

Imaginarycapacitanceisinserieswiththerealcapacitanceandisideallymuchlarger(seeFigure4.18).

Figure4.18Imaginarycapacitanceshouldideallybelargeandconstantwithfrequency.

PTFEisnotshownontheimaginarycapacitancegraphbecauseitissimplytoogoodfortheauthor’sbridgeandeventhedataforpolystyrenearequestionable.Nevertheless,itcanbeseenthatnotonlydothebetterdielectricshaveahigherratio of imaginary to real capacitance, but it is nearly constant over the audiobandwidth. More significantly, it should be noted that the measurement ofimaginarycapacitancecorrectlyshowspolystyrenetobeasuperiordielectricto

polypropylene,whereasthe1 kHzcomparisonof‘d’inTable4.2impliedquitethereverse.

GeneralConsiderationsinChoosingCapacitors

VoltageRating• Will the voltage across the capacitor change polarity, or is it simply avarying DC? If the voltage across the capacitor is AC, then conventionalelectrolyticcapacitorsareeliminated.•WillthecapacitorhaveanacceptablepredictedlifetimewiththeappliedDCvoltageplusthemaximumexpectedsignalvoltage(Vpk,notVaverage)?

• Could the capacitor withstand themaximum possible High Tension (HT)voltage? If not, what arrangements have beenmade to ensure that its ratedvoltageisneverexceeded?

CapacitanceValue

• Is the absolute value important? If it is part of a filter or equalisationnetwork, thenweneedaclose tolerancecomponentwhosecapacitancedoesnotvarywithfrequency,andonlyair,PTFE,polystyrene,polypropylene(nowavailable in±1%)or silveredmicawill do. Polycarbonatewould once havebeen a marginal candidate, but now that it is obsolete no longer need beconsidered.•Matching: Is the capacitor part of a pair, such as coupling capacitors in apush–pull amplifier, or the corresponding component in the other stereochannel?Ifitis,thenthecapacitorsshouldbematchedifpossible.• Each family of capacitor dielectric is only available in a limited range ofvalues,andifweneed330 μF,thenonlyanelectrolyticcanprovidethisvalueatasensiblepriceandsize.

Heat

Will thecapacitorbecomewarm?Will theconsequentchangeinvaluematter?Ingeneral,capacitorsshouldnotbeoperatedatmore than50 °C(because theresistance of all insulators falls with increasing temperature), but even thisambient temperature could reduce the life of an electrolytic capacitorunacceptably.

ESR

ESR

Thereservoircapacitorinacapacitorinputsupplyhastopasssignificantripplecurrentthatcausesself-heating,raisingtheinternaltemperatureaboveambient–thisiswhyelectrolyticcapacitorshavearipplecurrentrating.

Leakageand‘d’

•Isleakageimportant?AcathodebypassorHTsmoothingcapacitormaybeallowedtopassasmallleakagecurrent.Agridcouplingcapacitormaynotbeallowedtobeleakyunderanycircumstances.• Is this component important for final sound quality? Capacitors in theobvioussignalpathareimportant,butthesignalcurrenthastoreturnthroughtheHTsupply,soHTsmoothingandbypasscapacitorsareequallyimportant.Smoothing capacitors for bias circuitrymaybe less important if there is noaudiosignalonthem.

Microphony

Allcapacitorsaremicrophonictogreaterorlesserextent.Thereasonforthisisverysimple.Supposethatwehavestoredafixedchargeonacapacitor:

Thecapacitanceofaparallelplatecapacitoris:

Combiningtheseequations,andsolvingforV:

SinceQ,A,ε0andεrareconstants, ifwevarythespacingbetweentheplates,thevoltageacross thecapacitormust change.Thisprinciple is thebasisof thecapacitormicrophones used in studios and the ubiquitous electretmicrophonefoundinportablerecorders.The principle is reversible, and varying the applied voltage across a capacitoralterstheattractiveforcesbetweentheplates,andiftheplatesarefreetomove,thiscausesvibration.Thisisthebasisoftheelectrostaticloudspeaker.It might be thought that the plates of a plastic film capacitor would besufficiently tightlywound thatnomovementwaspossible,but theauthoroncebuilt a stabilisedHTpower supplywhere theoutputbypasscapacitorwhistled

loudlyat≈2 kHz.Thecircuitwastherebydiagnosedasunstableevenbeforetheoscilloscopewasready!The problem of capacitor microphony can be tackled in three ways, listed indescendingorderofdesirability:•Avoidusingcapacitors.Toalimitedextent,thisisfeasible.•Isolatecapacitorsfromvibration.Capacitorscarryinglow-levelsignalswillbe proportionately more sensitive to microphony than those carrying high-level signals. Pre-amplifiers are therefore most susceptible, and it is wellworth isolating themfromvibration.This is easilydoneat thedesign stage,butismuchharderoncebuilt.• Capacitors are physical objects, so they have mechanical or acousticalresonances. If we excite these resonances, we should expect them to beaudibleinthesamewaythatstrikingatuningforkproducesanaudiblenote.Ifwemechanically damp the capacitor bygluing it to another surface, thentheseresonanceswillbereduced.Providedthatthecapacitorcansurvivetheheat,thesoftglueusedbyhot-meltgluegunsisideal.

Thereisnoreasonwhyweshouldnotuseallthreemethodsincombinationifitseemsthatmicrophonyislikelytobeaproblem.Agoodtestformicrophonyisto tap each component with a plastic pen (to avoid shock risk) with theequipment turned on whilst listening to the loudspeaker. The results maysurpriseyou!

Bypassing

Allmoderncapacitors(whetherplasticorelectrolytic)haveseriesinductanceofbetween 10 nH and 100 nH, so their impedance becomes inductive asfrequency rises.Early capacitors hadmuchhigher series inductance, so itwasworthwhilebypassingalargecapacitorwithasmalloneinordertomaintainlowimpedance at high frequencies, but modern electronics operates at higherfrequencies, forcing capacitor design to improve, rendering the techniquesuperfluous.Wires have inductance, and although this is not really linearwith length, 0.75nH/mm is a good working approximation, so there is no point in spendingmoney on a filter capacitor having only 10-nH series inductance if it is thenconnected to the circuit via a pair of wires 100 mm long (adding ≈150-nHinductance).WemaynotbeabletoconnectthefiltercapacitordirectlybetweentheoutputtransformerHTtapandthecathodereturnsoftheoutputvalve(s),butwecan,andshould,connecta low-ESRbypasscapacitorbetween thosepoints

usingtheshortestwirespossible(tominimiseitsseriesinductance)(seeFigure4.19).

Figure4.19Connectionofabypasscapacitor.

MagneticComponentsMagneticcomponentsincludetransformersandinductors.Transformersmaybesignal transformers, such as output transformer and moving coil step-uptransformers, or theymaybemains transformers. Inductorsmaybe the small-signal inductors used in filters, or they may be the power chokes in an HTsupply.Magneticcomponentsareeasilytheleastperfectpassivecomponents(resistors,capacitorsandinductors/transformers),andforthisreasonmanydesignersshunthem.Thisisunfortunatebecauseitseriouslyrestrictsdesignchoice.

InductorsInductorsstoreenergyintheformofamagneticfield.Anywirepassingcurrentgenerates amagnetic field, so itmustpossess inductance.Wecandeliberatelyincreasethisinductancebywindingthewireintoacoil,whilstplacingthecoilaroundanironcoreincreasesinductancestillfurther.Theseproportionalitiescanbeexpressedby:

whereL=inductance

μ0=permeabilityoffreespace=4π×10−7 H/m

μr=relativepermeabilityofthecoremagneticmaterial

A=magneticpathcross-sectionalareal=magneticpathlengthN=numberofturns.

Relative permeability is themagnetic analogue of relative permittivity thatwemetearlierandhasavalueof1forairand≈5,500foriron.Themagneticpathlength is the length through the core back to the starting point, and the cross-sectionalareaofthemagneticpathissimplythecross-sectionalareaofthecore,soitoughttobeeasytoderiveausefulequationforcalculatinginductance.Unfortunately, μr varies hugely with flux density, the path length is easilyaffectedby air gaps, and some flux escapes the core.Wewill look at eachofthese problems inmore detail in amoment, but suffice to say thatwe cannotoften accurately calculate the inductance of a coil.We are forced tomake aninformed guess, add a few turns, measure the inductance under the actualoperating conditions, and then remove turns until the desired inductance isachieved.AcurvethatappearsinvirtuallyeverydiscussionofmagneticmaterialsistheB/Hcurve.Thisisaplotoftherelationshipbetweenappliedmagnetisingforceandresulting magnetic flux. For our purposes, we need only note that μr isproportional to thegradientof thecurveand that as thegradient changeswithlevel,somustμr(seeFigure4.20).

Figure4.20B/Hcurve:Non-constantslopeimpliesnon-constantμ.

Air-CoredInductors

Wecancompletelyavoidtheproblemofnon-constantμrwithlevelbynotusingamagneticmaterial in the core.Air-cored inductors have constant inductancewith applied signal level, and do not therefore cause distortion, making thempopular in high quality loudspeaker crossover networks. Determining themagneticpatharea ismoredifficult since this theoreticallyextends to infinity,whilst the path length is similarly awkward to define. Nevertheless, formulaehavebeenproducedforvariouscoregeometries,andaparticularlyusefulsetofformulaeforoptimum(lowest)resistanceair-coredcopperwirecoilsbasedonapaperbyA.N.Thiele[4]follows:

whereR=resistanceinΩL=inductanceinμHd=diameterofwireinmmN=numberofturnsc=coreradius(seeFigure4.21)

Figure4.21Relativebobbindimensionsforair-coredcoilsusingThieleformulae.

l=lengthofwireinm.

Theformulaearegiveninthismodifiedformbecausewireisavailableonlyina

rangeofstandarddiameters,andtheresistanceofthecoilisnotusuallycritical.Iftheresistanceisdifferentfromthatwanted,thenadifferentwirediametercanbetried.Thebestwaytousetheseequationsistodropthemintoaspreadsheetandexperiment.Ifthespreadsheethasstandardwiregauges,somuchthebetter.Experimentationsoonrevealsthatair-coredinductorshavesignificantresistanceor that they are very large. This problem of resistance is common to allinductors, and isoneof their imperfections.Air-cored inductors areusefulnotonly for loudspeaker crossovers, but also for the output filters of Digital toAnalogueConverters(DACs),wheretheresistanceisfarlessofaproblem.Itshouldbenoted thatbecauseofpracticalconsiderations(windingefficiency,variablewire diameter, etc.) the formulaecannot give exact answers, and it isthereforewise todesign5%oversize, and then remove turnswhilstmeasuringtheinductancewithacomponentbridge.Manycomponentbridgesusea1 kHzinternaloscillator.Whenmeasuringair-coredcoils,theinductivecomponentcaneasilybeswampedatlowfrequenciesbytherelativelyhighresistance,causingthebridgetogivemisleadingresults.IfitispossibletofeedsuchabridgefromanexternalsourceofAC,itshouldbefedwiththehighestfrequencythatthebridgemanufacturerallows(typically20kHz),andthiswillallowsensiblemeasurementstobetaken.

GappedCoresforACOnly

Onewaytoreduceresistancewithoutsufferinggrossdistortionis touseacoilwithamagneticcorethathasanairgap.Agappedcoresignificantlyincreasesinductance over an air-cored coil, but because the air gap is a largemagneticreluctance(analogoustomagneticresistance)inthepathofthemagneticflux,itswampsthevariationinpermeabilityofthemuchsmallermagneticresistanceofthe core, and inductance ismore nearly constant. As the gap becomes larger,inductance falls, and if the gap is infinitely large, thenwe are back to an air-cored coil. This technique was used for many years by the BBC ResearchDepartmentforinductorsinpassiveloudspeakercrossovers.We may unintentionally make an inductor with a gapped core. Many ferritecoresusedforsmallinductorsaresuppliedastwomatinghalvesthatfitaroundthecoreoncewound.Dustonthematingsurfacescausesanairgap,andifthecoresaregentlysqueezed togetherwhilst inductance ismeasured,a significantincreaseininductancewillbeseen.

GappedCoresforACandDC(PowerSupplyChokes)

If an inductor has to pass DC, it is essential that the DC current should not

saturatethecore,sincethiswoulddrasticallyreducetheinductance.Iron-coredinductorspassingDCareinvariablygappedinordertomaintaintheirinductanceuptotheirratedmaximumcurrent.However, a power supply choke must accommodate a different set ofcompromises to a loudspeaker crossover choke. Specified inductancemust bedeliveredat the ratedDCcurrent,but inductancevariationover the restof therange isnotonlypermissiblebutalsoexpected.Remembering theB/H curve,wecanexpect inductance tofallasDCcurrentrisesandsaturationapproaches(seeFigure4.22).

Figure4.22RealinductorshaveinductancethatfallswithappliedDCcurrent.

Not only doesmeasured inductance fall withDC current, but inductance alsochangeswithACexcitation.Mostcomponentbridgesonlyprovidebetween100mVRMSand1 VRMSexcitation,butpowersupplychokemanufacturersexpecttheir products to see rather more hum voltage across the products, and theydesign for those conditions, so a conventional component bridge might see asmallerinductance(seeFigure4.23).

Figure4.23RealinductorshaveinductancethatchangeswithappliedACexcitation.

Note that the choke onlymeets its specified inductancewhen a representativeACexcitationisapplied–bewarethemisleadingresultsproducedbylow-levelACexcitation.

Self-Capacitance

Ifacoilismadeofmanyturnsofwireandthereisapotentialbetweendifferentturnsandlayersofturns,thenwemustexpecttheinductortohavecapacitanceinparallelwithitsinductance(seeFigure4.24).

Figure4.24Equivalentcircuitofpracticalinductor.

Wenowhaveourfamiliarresonantcircuit,whichmeans thatasweriseabovethechoke’sself-resonant frequency, thecapacitorbegins to reduce thechoke’simpedanceandreduceitsfilteringeffect(seeFigure4.25).

Figure4.25Impedanceofachokeagainstfrequency.

Notethatalthoughthefilteringeffectdeclinespasttheresonantfrequencyof4.9kHz, the impedance is still100 kΩat20 kHz,and incombinationwitha68μFelectrolyticcapacitorhavinganESRof0.5 Ω,thiswouldtheoreticallygive105 dB of attenuation.Obviously, the higher the self-resonant frequency, thebetter it will be, and the best way to determine this frequency is to measurephase(seeFigure4.26).

Figure4.26Phasechangesabruptlyatresonance.

AsFigure4.26showed,phasechangesverysharplyatresonance,andtheeasiest

waytomeasurephaseistoarrangeacircuitthatgeneratesaLissajousfigureonananalogueoscilloscope(seeFigure4.27).

Figure4.27ConnectiontoananalogueoscilloscopeforaLissajousfiguretofindtheself-resonantfrequencyofinductor.

Theoscilloscope isused inXYmode, andas the frequencyof theoscillator isvariedandapproaches thechoke’sself-resonant frequency theLissajous figurechanges froman ellipse to a straight line.The resonant frequencycannowbereaddirectlyfromtheoscillatorormeasuredusingacounter(evencheapDVMsnowofferfrequencymeasurementtosufficientaccuracyforthismeasurement).

TransformersInaperfecttransformer,themagneticfluxoftheprimarywindingiscoupledtothe secondary winding with no loss whatsoever. Practical transformers aresomewhatdifferent.In a transformer, the losses are often divided into two distinct groups: ironlosses, socalledbecause theyaredue to imperfectionsof thecore,andcopperlosses,socalledduetoimperfectionsofthewindings.

IronLosses

Theprimarywindingon the transformerhas a finitewinding inductance, so itpresentsareactanceacrossthesupplythatdrawsacurrentevenwhenthereisnosecondary load. Rather than designing for a specific primary reactance orconsequent current, older transformers simply used ‘eight turns per volt’althoughmany contemporary iron-cored transformers (particularly toroids) useonlyfourturnspervolt.As the core is successively magnetised and demagnetised through oppositepolarities,workhastobedonetochangethealignmentofthemagneticdipoles.Thislossisknownashysteresis loss,anditmaybecalculatedbyinvestigating

thehysteresiscurvesfortheparticularcorematerialused.Becauseitisthelosscaused by changing the coremagnetisation throughone complete cycle of theappliedACwaveform,therewillbemorelossinagiventimeifmorecyclesofmagnetisationaretraversed.Hysteresislossisthereforedirectlyproportionaltofrequencyandcanonlybereducedbychoosingalowerlosscorematerial.Magneticcoresaremetal,andthereforeconductelectricity.Asfarastheprimarywinding is concerned, there is nodistinctionbetween an intentional secondarywinding connected to a load and a conductive path parallel to the primarywindingthroughthecore.Conductivepathsthroughthecorecauseeddycurrentsto flow, which, because they are short circuits, cause losses. To reduce theselosses, the core can be constructed from a stack of laminations that have hadtheirsurfaceschemicallytreatedtomaketheminsulators.Theultimateapproachtothisproblemistomakethecoreofirondustparticleswhosesurfacehasbeentreated, and then bond thesewith a ceramic to form a solid core known as aferritedustcore.Eddycurrentlossisproportionaltof2becausenotonlyisthelossproportionaltothe number of traverses of the magnetisation loop in a given time, but alsohigherfrequencieshavesmallerwavelengthsandallowmoreloopsofcurrenttoformwithin thecore.Althoughthinsteel laminationsaresatisfactoryforaudiofrequencies, ferrites are necessary for RF frequencies, and at VHF almost allcorematerialsareexcessivelylossy,andair-coredtransformersmustbeused.Primary currents due to finite primary inductance, hysteresis loss and eddycurrent loss are often combined and known as magnetising current in powertransformers and are responsible for core heating even when a load is notconnected.Notallof thefluxfromtheprimaryflowsthroughthesecondarywinding,andthis loss,combinedwithhysteresisandeddycurrent loss, isknownas leakageinductanceinaudiotransformers.Theoretically,leakageinductance(referredtotheprimary) is foundbymeasuring theprimary inductancewith thesecondaryshortcircuited. Inpractice, leakage inductance isawkward tomeasurebecausemeasurement at a single frequency is easily skewed by stray capacitances,necessitatingasweptfrequencymeasurement.Nevertheless,leakageinductanceis an important theoretical concept, since it determines the high frequencyoperatinglimitofthetransformer.Leakage inductance is dependent on the size ( q), the turns ratioN2 and thegeometryofthetransformer(k),butisindependentofμr:

Foragiven frequency,ahigherpower rating transformerwillbe larger thanalower power rating transformer and will consequently have higher leakageinductance.SinceleakageinductanceisproportionaltoN2,weshouldalways:trytokeeptheturnsratioaslowaspossible,soparallelingoutputvalvesinavalveamplifierisbeneficialbecauseitreducestheturnsratiorequired.Geometrycanbeimprovedintwofundamentalways:wecaneitherimprovetheshapeofthecore,orimproveourwindingtechnique.Standard transformers aremade with E/I cores, where each lamination of thecore is composed of an E shape and an I shape. A machine that looks (andsounds)ratherlikeacarddealerinsertslaminationsalternatelyfromeithersideof the coil so that, on alternate laminations, the orientation of the shapes isreversedtoreducetheairgapatthejoint(seeFigure4.28).

Figure4.28E/Icorelaminations’arrangementtoreduceleakageflux.

Traditionally, superior cores were made as C cores. These were made bywindingthecoreoutofacontinuousstrip,whichwasthencut inhalf,andthe

resultingfacesgroundsmooth.Thecoilswere thenwound,andthecoreswereinserted so that the ground faceswere perfectly alignedwithminimal air gap,andsteelstrapswereusedtoholdtheassemblyfirmlytogether(seeFigure4.29).

Figure4.29C-corearrangements.

TheCcorewasanexpensiveprocess,andinaccurateassemblycouldcreateanair gap, thus creating the very imperfection that the design intended to avoid.Themoremodernapproachistowindthecoreasatoroid,butnotcutit,anduseaspecialcoilwindingmachinetowindthecoilsdirectlyontothecore,resultinginaverylowleakagecore(seeFigure4.30).

Figure4.30Toroidalcorearrangement.

Incidentally, although toroids are thought of as being modern, the firsttransformer ever made was a toroid, using wire insulated with silk from hiswife’sweddingdress!(MichaelFaraday,August1831).BoththeCcoreandthetoroidhavethefurtheradvantagethatthemagneticfluxalwaysflows in thesamedirectionrelative to thegraindirectionof thecrystalstructureof thecore,whereas in theE/Icore ithas to flowacross thegrain insomepartsofthecore.ThisissignificantbecauseGrainOrientedSiliconSteel(GOSS)cantolerateahigherfluxdensitybeforesaturationinthedirectionofthegrainthanacrossthegrain.E/Icorescanthereforeonlyoperateatfluxdensities

below saturation across the grain,whereasC cores and toroids can operate atsignificantly higher flux densities, allowing core size and turns per volt to bereduced.Theworstwindinggeometryforleakageinductanceissplitchamber(seeFigure4.31).

Figure4.31Splitbobbingivesgoodprimary/secondaryisolationbuthighleakageinductance.

The geometry of a transformer can be improved by winding the primary andsecondaryoutofmany interleaving layersorsections, rather thanwindingonehalfofthebobbinwiththeprimaryandtheotherhalfwithsecondary.Increasingthenumberofsections improves thecouplingbetweenprimaryandsecondary,thusreducingLleakage,butusuallyincreasesstraycapacitance.AlthoughsectioningthewindingsisrelativelyeasyonanE/IorCcore,itisverydifficultonatoroid;moreover,windinggeometryonatoroidisquitepoor,andso it is easy to lose the benefits of the improved core by having a poor coil.Toroidal mains transformers are notorious for their leakage flux at the pointwherethewindingsexitforthisveryreason.An alternative technique for improving winding geometry is to use bifilarwinding,whereby twowires are simultaneouslywound sideby side. If oneofthesewires is part of the primary and the other is part of the secondary, thispromotes excellent coupling between the windings, and leakage inductance issignificantly reduced.The technique is cheaper than sectioning, and providingthecoilwindingmachinecancope,thereisnoreasontostopwithtwowires–threeorfourcouldbeused.Unfortunately, there are two snags to multifilar winding. Firstly, the thinpolyurethane insulation on the copper wire is easily damaged during windingand may break down if we have >100 V between the windings, making itdifficulttomakeatransformercapableofisolatingtheHTsupply.Nevertheless,the seminal50 WMcIntosh [5] amplifierusedamultifilaroutput transformeranda440 VHTsupply!Secondly, thegreatly increased capacitancebetweenprimary and secondary may resonate with the reduced leakage inductance toproducealowerresonantfrequencythanasectionedtransformer.Multifilarwindingisbestusedinsmall-signaltransformerswithaverylowturnsratio(ideally1:1),suchasthebalancedlineoutputtransformersusedinstudios.

DCMagnetisation

DCMagnetisation

IfanetDCcurrentisallowedtoflowinatransformer,itshiftstheACoperatingpointontheB/Hcurveandcausessignificantdistortionduetosaturationononehalfcycle.For thisreason,outputvalveanodecurrents inpush–pullamplifiersshouldbecarefullybalanced,andhalf-wave rectificationshouldneverbeusedonmainstransformers.AtraditionalwayofcheckingoutputvalveDCbalancein push–pull amplifiers is to measure the voltage between the anodes of theoutput valves, and adjust for zero volts. Zero voltage between anodes meansequal voltage drops, and this implies equal currents with no out-of-balancecurrent, if thewindingresistancesareequal.Checkingtheseresistancesbeforeusingthismethodisthereforeessential.Iftheresistancesareunequal,itwillbeafew tens of ohms at most, and it is perfectly permissible to add a permanentseries resistor to balance the DC resistances, allowing a correct imbalancevoltagetobemeasuredbetweentheanodes.BecauseC-coreandR-type transformershaveanegligiblegapand toroidsareessentiallygapless, theyare farmoresusceptible tocoresaturationdue toDC,particularly as all these transformers have the grain of their core materialoptimallyaligned,allowingthedesignertooperatemuchclosertosaturation.

CopperLosses

Copperwirehasresistance,andinawell-designedtransformerthelossesduetoresistanceareequalinprimaryandsecondary,andwillthereforeberelatedby:

whereNistheprimarytosecondaryturnsratio.Havingequalised copper lossesbetweenprimaryand secondaries, total copperlossesmaybetradedagainstironlossesinagiventransformerdesignsothattwotransformersmayhavedifferentproportionsof iron tocopper toachieveequalpowerratings.

ElectrostaticScreens

Capacitance between primary and secondary sections is significant in audiotransformersbecauseitismultipliedbytheturnsratioofthesectionsconcernedinamannersimilartotheMillereffectinthetriodevalve.Theproblemcanbesolvedby interposinganearthedelectrostaticscreen,whichshouldbemadeoffoil,betweentheaffectedwindings.Wenowhavecapacitancetoearth,buttheeffectofthiscapacitanceisminimal.Itismostimportantthatthetwoendsofthe

foildonotcontactelectrically,asthiswouldformashortedturn.Anelectrostatic screenbetweenprimaryandsecondary isoften fitted tomainstransformers for a rather different reason. If the insulationwas to break downbetween primary and secondary, mains voltage would be connected to thesecondary, which would be a safety hazard. By interposing an electrostaticscreen, the fault current flowsdirectly toearthandblows themains fuse, thusmaking the equipment safe.Unfortunately, such screens are usually a layer ofwire,fulfillingthesafetyrequirementbutseriouslydegradingRFperformance.A foil electrostatic screen prevents RF interference on the mains from beingcapacitivelycoupledtothefollowingcircuitry.Inaudio,thesignificanceofRFinterferencecannotbeoveremphasised,andthisissufficientincentiveforusingafoilelectrostaticscreen.Foilelectrostaticscreensareparticularlybeneficialforlow-voltagesecondariesbecausetheypreventhigh-voltagenoisefromthemainsbeingcapacitivelycoupleddirectlyintosensitivecircuitry.

Magnetostriction

Valveamplifierswithoutputtransformersmay‘sing’audiblywhenoperatedathighpower.Occasionally,thisisduetoalooselamination,butitismorelikelytobedue tomagnetostriction,which is aneffectwherebyamagneticmaterialchangesitslengthaccordingtothestrengthofthemagneticfieldpassingthroughit. Output transformers support quite strongmagnetic fields, so the effect canbecomenoticeable.Since themagnetic field isvarying, itcausesvibration,butbecausemagnetostriction is not polarity sensitive, in a push–pull amplifier thesoundthatisheardispuresecondharmonicdistortion.Magnetostrictionisinverselyproportionaltoμr,soahigher-qualitytransformerislesslikelytosufferfromthis(admittedlyminor)problem[6].

OutputTransformers,FeedbackandLoudspeakers

Itisfarmoreconvenienttoderivefeedbackfromadedicatedfeedbackwinding,orfromtheendofatappedwinding,becauseitmeansthattheusercanchangethe matching of the amplifier to the loudspeaker without having to adjustfeedback. The leak amplifiers were designed using this scheme, allowing asimplelinktodeterminematching,butitmeansthattheoutputtransformerisnotusedoptimally(seeFigure4.32).

Figure4.32Secondaryarrangementinleakoutputtransformer.

As an example, when the 4 Ω setting is chosen, only half of the secondarywinding is used, resulting in poorer leakage inductance.Worse, the feedback(whichwould ideallybeappliedat theoutput terminals)has tobecoupledviathetappedsecondarybeforebeingapplied,andthecouplingfromonepartofthesecondarytoanothercannotbeperfect.Theoptimumwaytoapplyfeedbackistoderiveitfromtheamplifieroutputterminals(orevenbetter,theloudspeakerterminals). Ideally, transformer performance should be optimised by using asmanyofthesecondarysectionsaspossibleinacarefullycontrolledway.Oldtransformerstendtohaveapairofsecondarysectionswhichareconnectedin series for 15 Ω loudspeakers and in parallel for 4 Ω loudspeakers. Thesectionsarenotnecessarilyfromthesamelayers,sothesectionshavedifferingresistancesandleakageinductances.Connectedinseries(15 Ωmatching)thisisnot a problem, but when in parallel the mismatched Thévenin sources drivecurrents into one another,which is not ideal. Better-quality transformers havefoursecondarysectionsthatcleanlygive1 Ω,4 Ω,and16 Ω,butstillhavethesameproblemasbeforeifconfiguredfor8 Ω.Whynot 16 Ω?16 Ω loudspeakerswouldnot need aparticularly low-sourceresistanceforoptimumdampingandwouldbe lessupsetby loudspeakercableresistance.Inaddition,transistoramplifierscouldbedesignedmoreeasily,valveamplifierscouldhave theirsecondarysectionsoptimisedand thereduced turnsratiowould further improve the transformer.However, anymanufacturerwhointroduced a 16 Ω loudspeaker would have that loudspeaker branded asinefficient because a given voltage would produce 3 dB less acoustic powerthanthe8 Ωdesign–readpublishedcommentsabouttheBBCLS3/5a(12 Ω).So,wearestuckwith8 Ω,andthetrendisfirmlytowards4 Ω.Althoughmodernloudspeakersarenominally8 Ω,two-waydesignsfrequently

combine a 4 Ω bass driver with an 8 Ω tweeter, so it is better to treat allloudspeakersas4 Ω– theslight lossof8 Ωmeasuredpower is insignificant,buttheboostinqualityisworthwhile.

TransformerModels

Because real transformers are such complex devices, it is usual to devisesimplified models that attempt to represent operation at low, mid and highfrequencies.Atlowfrequencies,thetransformermayberepresentedasaperfecttransformerin parallel with the primary inductance of the real transformer, driven by thenon-zeroresistanceofthesource(seeFigure4.33).

Figure4.33Transformerequivalentcircuitatlowfrequency,showingeffectofprimaryinductance.

The combination of source resistance and finite primary inductance creates ahigh-passfilterwhosecut-offfrequencyisgivenby:

Withagiventransformer,wewillobtainbetterlow-frequencyperformanceifwecanreducethesourceresistance.AnEL34pentodehasra=15 kΩ,butthesameEL34,usedasa triode,hasra=910 Ωand,usedasacathodefollower,rk<100Ω.Unfortunately, the previous model is only appropriate for small signals. In apower amplifier, output-valve operating conditions are invariably carefullymatched to its load impedance, and the reduced reactance of Lp at lowfrequencies diverts signal current from the load into Lp. At high levels, theincreasedsignalcurrent flowing intoLp saturates thecore, reducingLp, furtherincreasing signal current into Lp, leaving little current available for theloudspeakerload,solowfrequencydistortionincreasescatastrophically.Power

amplifiersthusrequirethef−3 dBfrequencyLptobedeterminedbyRLratherthanra, and the advantage of an EL34 cathode followerwould not be seen at fullpower.Oncewehavedecidedontherelevant loadresistance,weneedahighprimaryinductance, which can be achieved either by increasing primary turns, or byusingacorematerialwithahigherμr.Althoughlowfrequencyperformancecanobviouslybeimprovedbyincreasingμr,wecanalsouseincreasedμrtoimprovehigh frequency performance. Primary inductance would be maintained bywinding fewer turns, thus reducing stray capacitance, which would result inbetterhighfrequencyperformance.A better core material is preferable because the bandwidth (in octaves) of atransformerwithmatchedsourceandloadresistancesis:

Thebandwidthisdependentonthegeometryofthetransformer,andonμr,butnotonsizeornumberofturns.Allotherthingsbeingequal,acorewithhigherμrproducesatransformerofgreaterbandwidth,whichcouldbeachievedeitherbyabettercorematerial,orbyeliminatingairgaps(toroid),orboth.Anotherfactorthataffectstransformerbandwidthistheairgap:

We might have a good core material but need a large air gap to prevent itsaturating. Alternatively, single-ended amplifiers force a magnetising currentthroughtheiroutputtransformers,necessitatingaconsiderableairgap,reducingbandwidth.At mid frequencies, we can consider the losses due to the resistance of thewindings;itisusualtoreflectthesecondarycircuitintotheprimarycircuit(seeFigure4.34).

Figure4.34Transformerequivalentcircuitatmid-frequency,showingeffectofwindingresistance.

Thehighfrequencymodelismuchmorecomplex(seeFigure4.35).

Figure4.35Transformerequivalentcircuitathighfrequency,anditssimilaritytoclassicalthird-orderfilter.

Inthismodel,theprimarycircuithasbeenreflectedintothesecondary,andthesourceresistance,primaryresistanceandsecondaryresistancehavebeenlumpedtogether. Interwinding capacitance has been lumped and introduced in twopositions, and leakage inductance is also included. The resulting circuit is aclassic low-pass filter having an ultimate roll-off of 18 dB/octave, and withsuitable choice of component values this model accurately simulates a realtransformerathighfrequencies.Sincethemodelisaclassicfilter,wecanusetherulesthatapplytothesefilters.Themostimportantoftheserulesisthatperformanceiscriticallydependentonterminatingresistances.Foranormalfilter,theseterminatingresistancesarethesource and load resistance, but a transformer is also sensitive to loadcapacitance, and since fewmanufacturers provide data for the effects of loadcapacitance,it isgoodpracticetotestthetransformerwiththeexpectedsource

and load impedances and check for high frequency and low frequencyresonances.

InputTransformerLoading

Whenusingamovingcoil cartridge step-up transformer, it iswellworthwhileexperimenting to find the optimum load resistance for the transformer, beforeadjustingtheloadonthecartridge.Oncethesourceresistancetothetransformerisknown,theoptimumloadingforthe input transformer can be determined.Beware that better cartridges tend tohave higher coil resistances (because thinner wire reduces moving mass), soupgrading a cartridge could require a changeof transformer loading.Not onlywill thefrequencyresponsebeaffected,butahighercartridgeresistancecouldcausesignificantlossintheinevitablepotentialdividerformedbythecartridgeresistanceandthereflectedtransformerloadingresistance.As an example, theSowter 8055wasoriginallydesigned for a 3 Ωcartridge,anditsoptimumloadingresistancewasthenapure2.7 kΩresistance.Sincethestep-upratio is1:10andimpedancesare transformedbyaratioofn2, the3 Ωcartridgesawareflectedresistanceof27 Ω,givingatolerablelossof0.9 dB.Replacingthe3 Ωcartridgewitha10 Ωmodelincreasesthelossto2.7 dB,soafurther1.8 dBofsensitivityhasbeenlost.Thesignificanceoftheadditional1.8 dBlossisthatthenoiseattheinputoftheamplifierhasremainedconstant,sothechangeofcartridgesourceresistancehasdegradedtheS/Nratioby1.8 dB.Coincidentally,increasingthegmoftheinputvalveby50%givesanimprovementof1.8 dBinS/Nratio,butincreasinggmisalways fearfully expensive, so we must avoid unnecessary losses beforeamplification.Ifwecouldincreasetheloadingresistanceonthetransformer,thereflected resistance seen by the cartridgewould rise, and the S/N ratiowouldimprove.Unfortunately, any transformer has an high frequency resonance caused byleakage inductance and interwinding capacitances, and increasing the loadingresistance reduces damping, producing a peak in the frequency response andringingonsquarewaves.However,acarefullychosenZobelnetworkacrossthesecondarycansignificantly tametheringing.Valuesfor thenetworkareeasilyfoundbyexperiment(seeFigure4.36).

Figure4.36DeterminingZobelnetworkvaluesformoving-coiltransformer.

Thepurposeofthepotentialdividerattheoutputofthesquarewavegeneratoristwo-fold:•Wewanttodrivethetransformerfromthesameresistanceasthecartridgeplus arm wiring resistance. Typical generators do not have 10 Ω outputresistance, so the potential divider is designed to have the correct outputresistance.•Theoutputvoltageoftypicalsquarewavegeneratorsisfartoohighforthetransformer,sowecaneasilyaffordtoattenuatebyafactorof100.

Calculatingthepotentialdividerrigorouslyisunnecessarybecausephysicalcoilwinding constraints mean that cartridge coil resistances cannot be equal (5%erroristypical).Additionally,becausethepotentialdividerneedstoattenuatebya factor of 100, rout≈Rlower, so we just setRlower to be equal to the requiredresistance,andchoosethenearestconvenientvaluetomakeRupper≈100Rlower.Weknowthat the transformerwilldriveavalve thathas inputcapacitance, sothis should be calculated, or measured, using the method given later in thischapter.Although×10oscilloscopeprobes reducecapacitanceat theprobe tip,they do not eliminate it, so this capacitance must also be considered duringmeasurement. In this example, the transformer must drive an EC8010 triodewhose input capacitance has been measured to be 190 pF. The author’sTektronixP6139A×10probes present a tip capacitance of 8 pF, so a 180 pFloadingcapacitorwasused(180 pF+8 pF≈190 pF).The Zobel resistance is unlikely to be larger than that of the main loadingresistor,soa5 kΩlinearpotentiometerwasused.The variable capacitance in the Zobel network was salvaged from anirredeemablyfaultyvalveMWradio(theseused tobeplentiful,butyoumightnowneedtogotoaradiofair).Air-spacedvariablecapacitorstypicallyachieve300–500 pF with the vanes fully closed, but sections can be paralleled, if

necessary.Once the generator has been set to produce a 1 kHz square wave with anamplitude of ≈100 mV pk–pk at the output of the transformer, the Zobelresistance and capacitance can be simultaneously adjusted to give the bestpossible leading edge as viewed on the oscilloscope. In general, the resistoradjusts how much curve there is at the leading edge, whereas the capacitoradjusts the amplitude of the ringing superimposed on that curve. Finding theoptimumpointissurprisinglyeasy.Once the optimum resistance and capacitance have been set, they can becarefullydisconnectedandmeasured.YourDVMmayclaimtobeabletomakebothmeasurements,butacomponentbridgewillalmostcertainlybebetter forthecapacitancemeasurement.

WhyShouldIUseaTransformer?Withall thathasbeensaidabout the imperfectionsofmagneticcomponents, itmightbethoughtthattheyshouldbeavoidedatallcosts,particularlysincetheyareinvariablyexpensive.Anoutputtransformercanbeusedtomatchalowimpedanceloudspeakertothehigh resistance valve output stage, thereby greatly increasing efficiency. Ifmultiple secondary windings are provided, it also allows user-selectablematchingtovariousimpedanceswithouthavingtoredesigntheamplifier.An input transformer,suchasamoving-coilcartridgestep-up transformer,canstep up a small signal sufficiently that it can be amplified by the followingamplifierwithminimumnoiseduetotheamplifier.Asabonus,theprimarycanbe left floating so that any hum induced into the connecting cable from thecartridgetothetransformerisrejectedbythetransformer.(SeeChapter7forafullerexplanationofthesebenefits.)With the possibility of multiple windings, a transformer may allow novelmethods of feedback to be applied to a circuit, further improving itsperformance.This techniquehas frequentlybeenexploited inpoweramplifiers[4].Arguing the case for inter-stage transformers is rather harder. They invariablyhave to match high source and load impedances, requiring large inductancescausing large stray capacitances that reduce bandwidth. Nevertheless, whenexpenseisasecondaryconsideration,outputvalvessuchasthe845maybenefitfrombeingdrivenbyarobustdrivervalvecoupledviaacarefullyspecifiedanddesigneddrivertransformer.AtransformerisolatestheDContheprimaryfromthatonthesecondary.Thisisoftenessential!

GeneralConsiderationsinChoosingTransformersThese considerations only apply to audio transformers; power supplytransformerswillbeconsideredinChapter5.Unlessyouarebuildingastandardcircuit, forwhicha transformerhasalreadybeendesigned,youwillalmostcertainlyneedacustom-designedtransformer.Itisthereforeessentialthatyougivethedesignerasmanycluesaspossiblesotheymaymaketherightcompromisestosuityourcircuit.•Isthetransformeranoutputtransformer,orisitasmall-signaltransformer?•Whatisthemaximumsignallevel(mV)thatwillbeappliedtotheprimaryatthelowestfrequencyofinterest?Isthislevelconstantwithfrequency?Howmuchdistortioncanyoutolerateatthisfrequency/level?•Whatisthesourceresistance?•Whatprimarytosecondaryturnsratioisrequired?•What shunt resistanceand shunt capacitancewill load the secondary?Caneitherofthesebevaried,ifnecessary?•Whatfrequencyrangedoyouneedthetransformertocover?Don’tjustsay5 Hzto500 kHz ± 0.1 dBbecauseitcan’tbedone.•Doyouneedanelectrostaticscreen?• Do you need the transformer screened in a μ-metal can to reduceelectromagnetichum?•Arethereanyspecialrequirementsthatthedesigneroughttoknowabout?

If the answer to the first questionwas ‘power-output transformer’, then theseadditionalquestionsshouldbeanswered,andanannotatedcircuitdiagramoftheoutputstageisideal.•IstheoutputstageClassAorClassAB?•WhatisthequiescentDCcurrent?WhatisthemaximumDCcurrent?•What is themaximum output power, andwhat is the lowest frequency atwhichthisisrequired,foragivendistortionlevel?•Istheoutputstagepush–pullorsingle-ended?•Aretheoutputvalvestriodesorpentodes?Willyouneed‘ultra-linear’taps?Ifso,atwhatratio?•Whatprimariesandsecondariesdoyouneed?WhatDCissuperimposedon

each?•What form of physicalmounting do youwant? Open flanges, shrouds ordrop-through?

Allthesequestionsmayseemratheroff-putting,butifyoualreadyhaveaclearideaofwhatyouwant,itismuchmorelikelythatthefinishedchapterwillmeetyourexpectations.

UsesandAbusesofAudioTransformersTransformers are among the most reliable of electronic components, oftenlasting40yearsormore,but theycan bedamaged.Transformersaremadeofwire that can fail if excessive current is passed and insulation that can breakdownifithastowithstandtoomanyvolts.The most common way of destroying an output transformer is to drive theamplifier well into overload so that one output valve switches off completelywhilsttheotherishardon.Theleakageinductanceofthehalfofthetransformerassociatedwiththeswitched-offvalvetriestomaintainitscurrent,andindoingso,itproducesaverylargeprimaryvoltagecausingtheinterwindinginsulationtobreakdown:

Since d i/d t≈∞, the EMF developed is far higher than HT voltage, and it iseasily capable of punching through the transformer interwinding insulation. Ifdamp has been allowed to get at the transformer, then the (possibly paper)insulationwillalreadybeslightlyconductive,andthepossibilityofbreakdownis increased. Ingeneral,oncea transformer’s insulationhasbeendamaged, thedamageispermanent,soifthere’sapossibilitythatatransformerisdamp,dryitoutthoroughlybeforestressingit.Theauthorhas stillnotmanaged todamageanoutput transformer,evenwhendrivingamplifierstotheirfullvoltageoutputwithonlyaverysmallelectrostaticloudspeaker connected across the anodes, but the possibility should beconsidered.

GuitarAmplifiersandArcs

Sincetherateofchangeofcurrentatoverloadishigh,andoutputtransformersforguitaramplifiersaredeliberatelypoor,implyingalargeleakageinductance,asufficiently high voltage can be developed to strike an arc externally, eventhoughthetransformermaybedesignedtosurvivetheexperience.Thevoltage

neededtostrikeanarcdependspartlyonthecleanlinessofthepath,soadirty(conductive)pathlowersthevoltage,andacarbonisedtrailfromapreviousarccertainlyreducesthevoltageneeded.Although a high voltage is needed to strike an arc, once struck it can bemaintained by quite a low voltage.As an example, the xenon lamp used in asmallcinemaprojectormustbestruckbyacapacitivedischargeofthousandsofvolts,yetitmaybemaintainedbyonly26 Vat75 A.Ifanamplifierstrikesanarc from the anode, it can only maintain the arc to a place that has a lowresistance to ground because a high resistance, such as a grid leak or cathoderesistor, would limit the current and extinguish the arc. The heater pins areconnecteddirectly togroundvia theLowTension(LT)centre tap,sothemostlikely place for an external arc to strike is between anode and heater pins,becausetheonlylimitingresistanceistheHTsupply.If we know that the amplifier will be thrashed, then a possible solution(depending on the amplifier) is to insert a resistor between LT and 0V HT,perhapsa4.7 kΩ6 WW/W,inordertoextinguishthearc.However,floatingthe LT supply may now cause hum problems because of poor heater wiring(routing,dressingandconnectiontochassis).

OtherModesofDestruction

Excessivecurrentthroughanoutputvalvemaycausethermalrunawayfromgridemission,melting the internal valve structure, thus dragging sufficient currentthroughtheoutputtransformerthattheprimarywindingfails.Thesimplecureistokeepyourvalveamplifierondisplay,andifavalveanodeglowscherryred,switch it off immediately. (Output stages in valve amplifiers very rarely havefusespartlybecausethenon-linearresistanceofthefusemightcausedistortion,but mostly because a fuse would not blow sufficiently quickly to protect theoutputvalves.)Small-signal transformers are usually damagedmechanically. They are fragileand have windings of very fine wire that is easily broken. Treat them withrespect.

MagneticScreeningCans

Transformers screened in μ-metal cans must be handled carefully and not bedropped as the impact work-hardens the μ-metal screen, greatly reducing itseffectiveness (BBC1:1 transformers designed to operate at−45 dBuhaddirewarnings on their screening cans about mechanical shock) (see Figure 4.37,photoofBBCtoroidcanwithwarning).

Figure4.37Theμ-metalscreeningcanofthistransformerdemandscarefulhandling.

MagneticCoreDeterioration

Magneticcorematerialscandeterioratewithtime(thiswasastockfaultforthemains transformerof aparticularpicturemonitor), and the authorhas recentlyseenanumberofchokesandtransformerswhoseaberrantbehaviourcanonlybeexplainedbycorematerialthathasdeteriorated.YoumightwanttobearthisinmindwhenchoosingbetweenanNOSpartandaslightlymoreexpensivenewone.

ThermionicValves

HistoryThe thermionic valve was not so much invented as discovered and was aconsequence of Thomas Edison’s research into extending the longevity ofincandescent filament light bulbs. It had been observed that as the light bulbneared the end of its useful life, the glass became discoloured and darkened.(Thiseffectisnotoftenclearlyvisibleondomesticlightbulbs,butitcanbeseenonnon-quartzhalogentorchbulbsandstagelamps.)Thecauseofthedarkeningwas evaporation of the tungsten filament followed by deposition on the innersurfaceof theglass.Inanattempttocounter tungstenevaporation,aplatewasintroducedintothe(evacuated)envelope,anditwasthennoticedthatiftheplatewaspositivelychargedwithrespecttothefilament,acurrentflowedacrossthevacuum.(Lightbulbsneedavacuumbecausetheincandescenttungstenfilamentwould otherwise oxidise so rapidly that it would burn.) Glass darkening canclearlybeseenintheauthor’sEdiswan‘R’typevalve(introducedin1918,thisvalvehada6-V2.8-Wheater,yetgmwasonly0.225 mA/V)(seeFigure4.38).

Figure4.38R-typevalve;notedarkeningofenvelope.(Theetchedlegenddeclaresthisvalvetobe‘TypeapprovedbyPostmasterGeneralBBC’.)

In 1904, John Ambrose Fleming [7] went rather further, and invented a newdevicethathetermedanelectricalvalve(borrowingthetermfromthecontrolofgases)becauseitonlyallowedcurrenttoflowinonedirection.Hisdeviceusedtwo carbon filaments, one of which was heated ‘to bright incandescence ofgreater intrinsicbrilliancy than ifusedasan incandescent lamp’, although thiswasqualifiedlaterinthepatentasonlybeing≈2,000 K(thetungstenlightbulbsnowbeingphasedouttypicallyoperateat≈2,900 K).Theothercarbonfilament,orelectrode,wascold,andonceasourceofACwasconnectedbetween thesetwoelectrodes,Flemingfoundthatcurrentcouldonlyflowinonedirection.Thenew device was termed the thermionic diode because of the thermal energyrequiredtoproducetheionflow.Strictly,onlysoftvacuum(orlowpressuregas-filled)valvesrelyontheflowofgasions–hardvacuumvalvesrelyontheflowofelectrons.Althoughthediodehadgreatcuriosityvalue,andFleminghadsuggestedthatitcould be used for the detection of Hertzian (radio) waves, it was of limitedpractical use for two reasons. Firstly, carbon emits electrons reluctantly and,secondly,electronemissionisstronglydependentontemperature,whichhadtobekeptquite lowtoavoidprematurefailureof thecarbonfilament.Thesetwofactorsmeant that the carbon filamenthadonly≈0.003%of the emissionof atungsten filament at 2,900 K,necessitating a sensitivemirrorgalvanometer to

detectemission.Lee de Forest’s audion patent [8] of 1908 interposed a platinum wire in theshape of a grid iron between the heated filament and the plate, and showedexperimentallythatamplificationcouldbeachieved.Althoughthepatentrevealsthathedidnotunderstandhowitworkedatthetime,thenewdevicewasusefulandquicklyledtothecommercialbirthofradio.TheamplifyingcharacteristicsofthesoftvacuumAudionswereveryvariable,butthefarmorepredictablehardvacuumtriodesoonevolved.

Emission

All metals have free electrons within their crystal structure, so some of theelectronsmust be at the surface of themetal, but because they are negativelycharged, theyarebound thereby the electrostatic attractionbetween themandthe adjacent positively charged nuclei. However, the atoms and electrons areconstantly vibrating due to thermal energy, and if the metal is heatedsufficiently,someelectronsmaygainsufficientkineticenergytoovercometheattractiveforcesoftheatomsandescape.The heated metal in the valve is the cathode, and when this is heated to atemperaturedeterminedbytheworkfunctionofthemetal,anelectroncloudorspacechargeformsabovethesurfaceofthecathode.Becauselikechargesrepel,the cloud eventually accumulates sufficient charge to prevent other electronsescapingfromthesurface,andanequilibriumisreached.Ifweconnecttheplate,oranode,tothepositiveterminalofabattery,electronsare attracted from the cloud and are accelerated through the vacuum to becaptured by the anode. Because the electron cloud has been depleted, it nolonger repelselectronsasstrongly,somoreelectronsescape thesurfaceof thecathodetoreplenishtheelectroncloud.Current cannot flow in the opposite directionbecauseonly the heated cathodecanemitelectrons,andonlythepositiveanodecanattractelectrons.

ElectronVelocity

Wementioned that electrons were accelerated towards the anode, and this isquite literally true.At theexact instant thatanelectron leaves thecloud, ithastheoreticallyzerovelocity,butitisconstantlyacceleratedbytheelectricfieldoftheanode,andacquiresenergyproportionaltotheacceleratingvoltage:

whereE=energy

qe=electroniccharge≈1.602×10−19 C

V=acceleratingvoltage

me=massofelectron≈9.11×10−31 kg

v=electronvelocity.

Rearranging,andsolvingforelectronvelocity:

The ratio qe/ me is known as the electron charge/mass ratio and has anapproximatevalueof1.7588×1011 C/kg.Ifweapply100 Vbetweentheanodeand the cathode, the electrons will collide with the anode with a velocity of≈6×106 m/sor13millionmilesperhour.Usingthepreviousequation, itwouldappearthat512 kV(acommonnationaldistributionvoltage)wouldbesufficient toaccelerate theelectrons tobefasterthanlightspeed–whichisanimpossibility.Theflawisthatthesimpleequationassumesthatthemassoftheelectronisconstant,butatrelativistic(approachingthe speedof light) velocities, themass of the electron increases in accordancewith the Lorentz–Einstein equation [9], thus requiring an infinite voltage toaccelerateittolightspeed:

Toaccountforthis, theelegantequationgivenbyAlleyandAtwood[10]maybeused:

where

c=velocityoflightinavacuum≈2.998×108 m/s

qe/me=electroncharge-to-massratio≈1.759×1011 C/kg

V=anodevoltage.

Asanexampleof relativityathome,agoodquality televisionusingacathode

ray display tube needed a final anode voltage ≈25 kV, implying an electroncollisionvelocityof202millionmilesperhouratthetubeface,butthesimpleequationpredictsavelocity3.5%high.Note that the distance between the anode and the cathode does not feature ineitherequationbecauseaninfinitedistancewouldalsoallowaninfinitetimeforacceleration, and even if the rate of acceleration was very low, the collisionvelocitywouldstillbereached.Manyeffectswithinvalvescanbeunderstoodbyhavinganappreciationofthecollisionvelocityoftheelectronsastheyhittheanode.

TransitTime

It isoccasionallysuggested that the transit timebetweencathodeandanodeoreven between g 2 and anode is significant in audio. Transit time can becalculatedusing[11]:

whered=distancebetweenelectrodes

qe/me=electroncharge-to-massratio≈1.759×1011 C/kg

V=voltagebetweenelectrodes.

TheKT66hasaparticularlylargecathodetoanodespacing(estimatedat7 mm)andmightbeoperated (sub-optimally) at 350 V,giving a transit timeof1.26ns.Evenforvideo,1 nsisaveryshorttime,andtheexamplewasspecificallychosen to be slow, so most valves will be much faster, making transit timeentirelyirrelevanttoaudio.

IndividualElementsoftheValveStructure

TheCathodeEarlyvalvesbetrayed their lightbulborigins andweredirectlyheated usingatungstenfilamentthatwasalsothecathode.Tungstenwasusedinincandescentlightbulbsbecause ithas thehighestmeltingpointof all electrical conductors(3,695 Kor3,422 °C)andcouldthereforewithstandthe≈3,000 Ktemperaturenecessary to generate light that wasn’t obviously yellow. Although producingbrightlightwasnotactuallynecessaryforearlyvalves,itwasquicklyfoundthat

reducedcathodetemperaturecausedelectronemissiontofalldrastically,soearlyvalvesbecameknownasbrightemitters.Theemittedcurrentperunitareais:

whereT=absolutetemperatureofthecathode=°C+273.16

qe=electroniccharge≈1.602×10−19 C

φ=workfunctionofthecathodesurface(≈4.55fortungsten)

k=Boltzmann’sconstant≈1.381×10−23 J/Ke=baseofnaturallogarithms≈2.718.

(SeeAppendixforfulltheoreticalRichardson/Dushmanequation.)Theemissionefficiencyof the cathode is importantbecausenotonlydoes thefilament dissipation increase the power requirement of the equipment, but theheatmust also be lostwithout damaging any other components.We thereforewanttomaximiseelectronemissionforagivenfilamentpower,sothehistoryofthecathodeisconcernedwiththedevelopingchemistryofthecathodeemissivesurface.Thefirst improvementwas tousea thoriated tungstencathodewhichnotonlyhadimprovedemission,butalsocouldoperateatbetween1,950 Kand2,000 Krather than3,000 K.This reduced temperaturewas significant because valvesprimarilyloseheatbyradiation,andbyStefan’slaw:

whereE=powerperunitarea

σ=Stefan’sconstant≈5.67×10−8 W/K4/m2

T=absolutetemperature=°C+273.16.

Thus, 1,975 K only requires one-fifth of the heater power to overcome thelosses due to radiation compared to 3,000 K, and these valves are sometimesknown as dull emitters. Although the emission had only been doubled, thereductioninheaterpowerbyafactoroffivemeantthatthetotalimprovementinemissionefficiencywasafactoroften.The real improvement camewith the oxide-coated cathode,which operated atonly≈1,100 K,andwas100timesasefficientasthepuretungstencathode.Asanexample,evenin1929, theP215batteryvalvehadadirectlyheatedbarium

azidecoatedcathoderequiringonly2 Vat150 mA(seeFigure4.39).

Figure4.39P215directlyheatedoxide-coatedcathodevalve.

Valvemanufacturersoftenhadproprietarycathodecoatingformulations,sotheJT Baker Company manufactured the splendidly named ‘Radio Mixture 3’,which was composed of 57.3% barium carbonate, 42.2% strontium carbonateand0.5%calciumcarbonate[12].Sadly, thisconcoctionalmostcertainlybearsnorelationtotheapocryphal‘LovePotion9’.Unless the cathode is pure tungsten, the active emissive surface is only onemoleculethick,andconsequentlyfragile.The vacuum in a valve is never perfect, and there will always be stray gasmolecules between the anode and the cathode.A cold cathodeprevents anodecurrent,sozerovoltageisdroppedacrosstheanodeloadresistor,causingVatorisetothefullHTvoltage.Asthecathodewarmsfromcold,afewelectronsareattracted towards the anode, but some collide with stray gas molecules toproducepositive ionswhicharerepelledtowardsthecathode.If theonlyforceonionsbetweenthecathodeandtheanodewasrepulsionfromtheanode,spacecharge repulsion would prevent them from reaching the cathode. However,entropymotionensures that some ions alreadyhave somemomentum towardsthecathode,allowingthemtoovercomethespacecharge,andbecausetheionisamoleculehavinganucleuscomposedof (heavy)protonsandneutrons, ithas

considerablemomentumwhenitstrikesthecathodesurface.If this process of cathode bombardment occurs sufficiently often, the cathodeemissive coating can be significantly impaired, and oxide-coated cathodes areeven more vulnerable than thoriated tungsten cathodes, so if Va(pk)>2 kV isrequired, thoriated tungsten cathodes are the norm. Because pure tungstencathodes do not rely on amonomolecular layer for emission, they are almostimmunetoionbombardment.Given that the vacuumcannot be perfect,wemustminimise bombardment byestablishing the protective space charge above the cathode emissive surfacebeforeanodevoltageisapplied.Anotherproblemwithoxidecathodesiscathodepoisoning.Ifthecathodeiskeptatfulloperatingtemperature,butlittleornocurrentisdrawn,ahighresistancelayer of barium orthosilicate forms at the interface between the barium oxideemissive surface and the nickel cathode structure. The interface resistanceeventually reduces emission, but more significantly it increases the noisegeneratedbythevalvebecausethevalve’snormalshotnoisecurrentdevelopsanoisevoltageacrossthisresistance,whichisinserieswiththeinputsignal.Poisoned cathodes can occasionally be gradually recovered by operating thevalve at a high anode current.Anothermethod, often usedon the cathode raydisplaytubeusedintraditionaltelevisions,isknownasrejuvenation[13]andthisworks by temporarily increasing heater volts to heat the cathode to a highertemperature, and simultaneously drawing a large anode current. It should berealised that rejuvenation carries a risk of evaporating some of the cathodeemissive surface, and contaminating the (nearby) control grid. Inadequatecathodeactivationissometimescitedasacauseofnoise,perhapsexplainingthefactthatrejuvenationoccasionallyimprovesavalve’snoise.The final generation of colour television cameras using Plumbicon tubes usedoxidecathodesandhada‘standby’modewherebytheirheatersranathalfpower(63%heatervoltage)inordertoextendthelifeofthetubesandreducethewaitfor decent pictureswhen fully switchedon.Tobe certainof avoiding cathodestripping and cathode poisoning, the author has previously adopted the samestrategyinhisRIAAstages,especiallysinceoneofthemimmediatelysoundedfineiftheheatershadbeenleftinstandby,buttook2 htorecoverfromcoldandmeanwhilesoundedterrible.Inhindsight,itseemslikelythatleavingtheRIAAstageheatersinstandbykepttheentireelectronicssufficientlywarmtopreventcondensation and surface leakage currents causing increased noise anddistortion. (Some recording engineers argue that valve condensermicrophonessoundbetternotbecauseofthesuperiorelectronics,butsimplybecausetheheat

rising from thevalvekeeps the high impedance capsule and associatedwiringdrydespitethehumidbreathdirectedatit.)‘Standby’dissipationof8 WinanRIAAstageheaterequatesto25 Wfromthemainsonceregulatorandtransformerlosseshavebeentakenintoaccount.Overaweek,thatamountsto1.3 kWh–equivalenttorunningthehugelyprofligate‘CrystalPalace’amplifierfor2 h.Withthecurrentpriceofelectricity,thissortof extravagance can no longer be tolerated, especially since surface leakagepaths can be greatly reduced by PTFE insulators (PTFE repelswater, causingcondensation to form in isolated globules rather than wetting, joining, andmaking a conductive path). Thus, the author no longer recommends ‘standby’mode on valve heaters, and the knock-on from this is that valveHT rectifiersbecomeanecessitytoavoidcoldcathodebombardment.

ThoriatedTungstenFilamentFragilityThoriatedtungstencathodesoperateonlyslightlybelowthemeltingtemperatureof thorium (2,023 K), and to reduce the evaporation of thorium from thesurface, the tungsten filament is partly converted to tungsten carbide [14].Unfortunately, although hard tungsten carbide is brittle, so the degree ofcarbonisation is a delicate compromise between reducing thorium evaporationand fragility. Because thoriated tungsten filaments are very brittle, so valvessuchas the211,813and845shouldbehandledwithextremecareandnotbesubjectedtomechanicalshock.Unfortunately, thermal shock also kills thoriated tungsten filament valves. A1994 study of transmitter valve longevity [15] found that each off/on cyclereducedfilamentlifeby0.2%fromitsmaximumlifeof30,000 h.Thisdoesn’tsoundtoobad,butitimpliesthat500off/oncycleswilldestroythefilament,soifyouswitchedthevalveoffandoneveryday,youcouldexpectittoexpireinlessthan17months.Understandably, thebroadcasterstookadimviewofthis,andlookedtoseehowlifemightbeextended.Therearetworeasonswhytheoff/oncyclekillsthoriatedtungstenfilaments:• As the filament temperature passes through ≈900 K, the Miller–Larsoneffect causes thegrainsof themetal to reorient themselves, so that thewirebecomes thinner and longer. Worse, if a given section of the filament isslightly thinner, the increased current density causes increased localisedheating, which exacerbates the Miller–Larson effect and causes furthernecking of the filament. Eventually, this necking leads to such deep cracksthat the remaining conductivematerial has sufficiently high current densityandlocalheatingtovaporiseit,thusdestroyingthefilament.

• The resistance of a cold filament is far less than that of a hot one, andassuminganoperatingtemperatureof1,975 K,butanambienttemperatureof293 K(20 °C),theinitialcoldcurrentis8.6timeshigherthantheoperatingcurrent. The inrush current through the filament interacts with the Earth’smagnetic field to produce a small kick. Combined with the Miller–Larsoneffect, this gradually deepens the surface cracks in the brittle filament. Thedamagedonetothefilamentisproportionaltothecubeofinrushcurrent,soa‘softstart’canbeworthwhile.

If you hadbought a quartet ofNOS845s at considerable expense, youwouldhave a vested interest in avoiding the Miller–Larson effect, might want topermanentlyoperate thefilaments instandbymodeat80%offullvoltage,andonlyapplyfullvoltageatfullswitch-on,butnotethatstandbystillexpendstheemissive life at a rate of 1% compared to full filament voltage (but no anodecurrent).

DirectVersusIndirectlyHeatedCathodes

Early valves used lead–acid cells to power their directly heated cathodes, soheatervoltages insertionweremultiplesof2 V.Having to takeaheavy lead–acidbattery to the local radio shop forperiodic rechargingwas anuisance, solater valves used the household ACmains supply. Unfortunately, AC heatingcausedaudiblehumowing to the threemechanismsdescribed in the followingsubsections,rankedinorderofsignificance.TheThermalProblemThe filamenthas tobemadeof sufficiently finewire togiveahigh resistancethatcanbeheatedbyalowcurrentanddoesnotrequireexcessivelythickwiresfrom the transformer. Because the wire is so fine, the thermal mass of thefilament is low, and the temperature of the filament is partly able to track theappliedpower.Thiseffectcanbeobservedbynotingthatthethickfilamentofacarheadlightdimsslowlywhenswitchedoff,yetthefinefilamentinadomesticAC mains light bulb of the same power dims quickly. Because emission ismodulatedbyheatingpower(V2orI2), themechanismproduceshumattwicetheACmainsfrequency.TheElectrostaticProblemThevoltagedropacrossthefilamentaffectsVgkbecauseifweconsideranyonepoint tobe connected toHT0 V,otherpoints are at different (and changing)potentials.IfweconnectthecentreofthefilamenttoHT0 V,thentheendswill

be at equal and opposite voltages, so although one end of the filament emitsmoreelectrons,theotheremitsfewer.However:

The significance of the three halves power law is that the excess of electronsdrawn from themorepositive endof the filament isnot exactlynulledby thedeficiency from the opposite end. The imbalance is most apparent when the(AC)filamentsupply isatapositiveornegativepeak,so thismechanismalsoproduceshumattwiceACmainsfrequency.The thermal and electrostatic problems arise because the filament supply is asine wave. A square wave filament supply would eliminate these problems,although preventing breakthrough of the higher harmonics into the audiocircuitryviaChgwouldbeamajorheadache.

TheElectromagneticProblemThemagnetic field createdby the filamentheatingcurrent curves the flightoftheelectronssothatsomemisstheanode.WhenACisappliedtothefilament,thedirectionofcurvaturealternateswiththepolarityofthefilamentcurrent,sothismechanismproduceshumatmainsfrequency.TheIndirectlyHeatedCathodeSolutionAlthoughvariousalternativesweretried,thebestsolutiontothethreepreviousproblemswastheindirectlyheatedcathode[16],wherebytheemissivematerialwasappliedtoacoatedmetalsleevesurroundingthefilament,whichwasthentermedtheheater.Althoughnotexplicitlystatedinthepatent,thekeyideawasthatifthesleevecathodehadsufficientthermalmass,itwouldbeunabletotrackthe changing temperature of an arbitrarily thin heaterwire.Because themetalsleevedidnotpassheatercurrent,itsentiresurfacewasatthesamepotential,soitwasnamedaunipotential cathode,and this solved theelectrostaticproblem.Making thesleevefromamagneticmaterial suchasnickel tends toscreen thefilament’smagneticfield,reducingtheelectromagneticproblem.Sincethesolepurposeoftheindirectlyheatedcathodeistoreducehum,theACpowering the heater must be electrically insulated from the signals on thecathode.Unfortunately,goodelectrical insulatorsalso tend tobegood thermalinsulators,andthethermalresistanceofthealuminiumoxideelectricalinsulatormeans that theheatermustbeat1,650 K to raise thecathode to1,100 K, soindirectlyheatedcathodesneedmoreheaterpowerthandirectlyheatedcathodes.They also take longer to reach operating temperature, but for small-signalvalves, the reduction in hum is invaluable, so the slow warm-up and loss of

efficiencycanbetolerated.Thecathodeemissive surface is sprayedonto theoutside surfaceof thenickelsleeve, and the heater reverts to pure tungsten. However, the cathode sleevelookslikeananodetotheheaterfilament,andifacurrentwasallowedtoflowfrom theheater to thecathode, then thiswouldadd to the intendedcathode toanodecurrent,andhumwouldresult.Ithaspreviouslybeensupposedthatsuchacurrentwasdirectlyduetoelectronemissionfromthehot tungstenheater,andthis ideawas bolstered by the fact that superimposing a small (+10 V seemssufficient)DCvoltageontheheatersupplypreventsthehumcurrent.However,it seems more likely that electrolysis deposits a permanent conductive paththrough the porous aluminium oxide insulator and that biassing the heaterpositive prevents formation of this path. Either way, RCA [17] frequentlyrecommended +40 V as the optimum voltage between the heater and thecathode, and until more evidence arrives it seems churlish to ignore theirpracticalrecommendation.Despitealltheseeffortstoeliminatehum,theheaterfilamentcouldstillinducehum into the signal circuitry either by leakage currents, or because of theimperfectmagneticshieldingofthenickelcathodesleeve.Inafurtherefforttoreducehum, theheater filamentof theEF86waswoundasahelix inorder tocancelthemagneticfieldcausedbytheheatercurrent.Theonlywaytoeliminateheater-inducedhumistouseaDCheatersupplywithnoACcontentwhatsoever,andthisimpliesastabilisedsupply,whichhasotherbenefits.Because cathode emission is so strongly temperature dependent, it isessential that the heater voltage is correct, and Mullard quoted a maximumpermissibleheater voltagevariationof±5%,which is exceededby the currentUK legal limit for mains voltage variation (+10%, −6%). A stabilised heatersupplystabilisesthecharacteristicsofthevalve,andtheeliminationofthermalcyclingofthecathodesurfacereducesLFnoise.Asanaside,whentheauthor installedanAutomaticVoltageRegulator(AVR)to the test bench supplying his AVO VCM163 valve tester to combat mainsvoltagefluctuations,theAVRworkedhardestbetween4 pmand11 pm.IsitacoincidencethatthesoundoftheHi-Fiseemstoimproveaftermidnight?All the finalgenerationofsmall-signalvalves (exceptbatteryandelectrometervalves) use indirectly heated cathodes, and directly heated pure tungstencathodesarenowonlyusedforhighpowertransmitters.

Heater/CathodeInsulation

An indirectly heated cathode consists of a heater filament insulated by

aluminium oxide folded and slid into a tightly enclosing tubular cathode (seeFigure4.40).

Figure4.406K7heaterfilamentremovedfromcathode.Thealuminiumoxideinsulationhasbeenremovedattheapexofthehooptoexposethemuchthinnertungstenfilament.

No insulator is perfect, and they all deteriorate rapidly as temperature rises,whichisunfortunate,sincetheheater/cathodeinsulatorisred-hot.Typically,theresistivityofaluminiumoxideatthecathode’soperatingtemperatureislessthanone-millionthofitsroomtemperaturevalue.Allheater/cathodeinsulationmustthereforebeelectricallyleaky,allowingleakagecurrentstoflowbetweenheaterand cathode. Even worse, if the insulation is contaminated, this imperfectionproduces 1/ f noise. Irritatingly, one of the worst offenders for poorheater/cathodeinsulationis theotherwiseexcellent12B4-A,so thisvalvemustbe screened to exclude those samples with poor (hot) insulation if noise iscritical.Heaterpowercouldbereduced,andthevalvecouldbemademoreefficient,byreducingthethicknessoftheheater/cathodeinsulation,andthisisexactlywhatwasdone in the transition from the InternationalOctalbasedgeneration to thelaterB9Ageneration,butthiscompromiseselectricalheater/cathodeinsulation.Increasing the voltage across the heater/cathode insulation increases leakagecurrents.AlthoughVkh(max)isspecifiedondatasheetsasbeinganywherefrom90 Vto150 V(exceptforsomeruggedisedand‘P’seriesTVvalves),thisisavery ‘soft’ limit, since it is usually given at an arbitrary leakage current.Nevertheless, a sufficiently high voltagewill punch through the insulation torupturetheheater.Heaterfailureduetoheater/cathodeinsulationbreakdownisuncommon,but it ismost likely incathodefollowerswithhigh-signalvoltagesoroutputstageswithdistributedloads(suchastheMcIntoshdesign).

CathodeTemperatureConsiderations

BecauseoftheRichardson/Dushmannequation,electronemission,andthereforeanodecharacteristics,arecriticallydependentoncathodetemperature.Providedthatanodedissipationissufficientlylowthatitdoesnotfurtherheatthecathode,cathodetemperatureisrelatedtoheaterpower(P)by:

Szepesi [18] also found that the oxide-coated cathode of theTungsramHL4Gproducedminimumnoisewhenoperatedat≈1,200 Kandthata60 Kdropincathodetemperaturecausedbya25%dropinheatervoltagedoubledthenoisepower.Operatingoxide-coatedcathodesathigherheatervoltagesdramaticallyshortenslife because it increases evaporation of the emissive material, so Vh≯105%.Thus, long life, low noise and stable anode characteristics demand heatersuppliesstabilisedatthecorrectvoltage.

HeatersandtheirSupplies

Itisusualtosupplypowertoparallelheatersinfromaconstantvoltagesource(typically6.3 V),orseriesheatersfromaconstantcurrentsource(typically300mA).Ifeithertypeofsupplydriftsfromitsnominalvalue,undesirablechangesinanodecharacteristicsoccur.Although6.3 Vregulatorsareeasilymade,linearregulators become increasingly inefficient as load current rises, and unlesscarefullydesignedandconstructed,switchedmoderegulatorscanbeelectricallynoisy.Bycomparison,a300 mAconstantcurrentsupplyfeedingapureseriesheaterchainiseasilyandefficientlyimplemented.Valvemanufacturersoftenspecifyseriesorparallelheaters,butisthereactuallyany fundamental difference between the filaments of the two types, and couldwe use 6.3 V heaters (of equal current requirements) in a constant currentchain?Some 6.3 V valveswere tested to see if therewas any significant differencebetween thebehaviourof theirheaters.Thevalvesweredeliberatelychosen tobe as different as possible to magnify any difference between heaters. The12AT7was selected tobeonewhoseheater flashedwhiteat switch-on (Table4.3).

Table4.3PercentageofNormalisedHeaterCurrentAgainstHeaterVoltageforParallel(6.3 V)HeatersHeater

voltage(V)CV402412AT7

(0.30 A)MullardECC83

(0.29 A)Raytheon5842

(0.30 A)GE6BX7(1.45 A)

MullardEL84(0.79 A)

MullardEL34(1.475 A) Mean 1σ

6.30 100 100 100 100 100 100 100 0

1σ=Standarddeviation.

6.00 97 97 100 97 96 97 97.3 1.375.50 92 93 93 93 92 93 92.7 0.525.00 87 90 90 88 87 87 88.2 1.474.50 83 83 83 83 82 85 83.2 0.984.00 77 78 80 78 77 78 78.0 1.103.50 70 66 73 72 72 73 71.0 2.683.00 67 60 67 66 67 67 65.7 2.802.50 58 62 60 61 60 60 60.2 1.332.00 52 55 53 54 51 53 53.0 1.411.50 42 45 47 45 43 44 44.3 1.751.00 30 34 37 37 32 34 34.0 2.760.50 20 21 20 26 19 20 21.0 2.53

Withinthelimitsofexperimentalerror(whichworsenedsignificantlytowards1V), the heater currents are in very close agreement, suggesting that parallelheatervalveshaveessentiallysimilarfilaments.Thisisbroadlytobeexpected,sincetungstenistheonlypracticalfilamentmaterial.APL508wasthentestedsettoitscorrectcurrent(300 mA),thevoltageatthatcurrent was measured, and a series of measurements was taken, which werenormalised to 6.3 V and compared with the mean currents from Table 4.3(Table4.4).

Table4.4PercentageComparisonofCurrentHeaterValve(PL508)withMeanCurrentofVoltageHeaterValvesVoltage 6.3 6.0 5.5 5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5Mean 100 97 93 88 83 78 71 66 60 53 44 34 21PL508 100 97 93 88 83 78 71 66 60 54 45 35 23

A somewhat improvedmeasurement techniquewas availablewhen the PL508wastested;nevertheless,thecorrelationbetweenthisandtheparallelheatersisremarkable.Thereappearstobenosignificantdifferencebetweenthefilamentsin valves specified for series or parallel heaters, and provided that individualheatersconsumetheircorrectpower,thereseemstobenoreasonwhyweshouldnotmixthetwotypesatwill.ThistechniquewillbeusedintheEC8010RIAAstagedescribedinChapter7.As a further test, the heater current of an EL34 was investigated at 0.5%intervalswithina±5%nominalvoltagerange,andtheresultswereplottedasagraph.Anextremelyclosefittoastraightlinewasobserved,indicatingthattheheaterbehavesasaconstantresistanceoverthisverylimitedrange.SinceP=I2RandP=V2/R,twoconclusionsemerge.Firstly, parallel chains should be constant voltage (Thévenin) regulated, andserieschainsshouldbeconstantcurrent(Norton)regulated.Secondly, we should not mix topologies – series/parallel heater chains causeerrors–becauseeachheaternolongerseesaperfectThéveninorNortonsource.

Theauthorinvestigatedhisstockandfoundthatall24ofhis6SN7and12SN7doubletriodeshavetheirheatersinternallywiredinparallel(exceptforasingleRCA12SN7),whereashis14 (12.6 V)14N7uses two6.3-Vheaterswired inseries.Thesignificanceof thisobservation is that14N7shouldbemorestablewithconstantcurrentheating,whereas6SN7and12SN7shouldbemorestablewithconstantvoltage.As amore insidious example, a double triode initially tested on a valve testerwith 6.3 V parallel heaters, and found to have perfectly matched anodecharacteristics between sections, would be mismatched by configuring theheatersinseriesunlesstheheaterswerealsoperfectlymatched.Matchingshouldcloselyreplicatetheproposedconditionsofuse.

CurrentHoggingandHeaterPower

Having established that valve heaters are essentially the same, is the series orparallel chain best in terms of heater power regulation? Fortunately, althoughparallel connectionwith a Thévenin source is rather better in terms of powerregulationand thermal runaway, the filament/cathode losesmostof itsheatbyradiation,whichisproportionaltothefourthpowerofabsolutetemperature,sothisisaveryeffectiveregulatingelement.It has been suggested that valves intended by the manufacturer for constantvoltageheatingcouldexhibitvoltagehogging(analogoustocurrenthogginginparallel power transistors) when connected in a series string and powered byconstantcurrent.Thehypothesisisthatifonevalvestartswithalargervoltagethan another, it must be absorbingmore power (P= IV, and I has been heldconstant),andifitisabsorbingmorepower,itsfilamenttemperaturemustrise,causingitsresistancetorise,makingitabsorbevenmorepowerandcausingittohogheatervoltage.TheauthortestedanEC8010(with315 Ωparallelresistortodraw20 mAandcorrecttotalcurrentto300 mA)inserieswitha6J5GTtoseeiftherewasanyevidenceofcurrenthoggingoccuring(seeFigure4.41).

Figure4.41Heatervoltagesoftwodissimilarvalvesfedinseriesfromaconstantcurrentsource.

Asmightbeexpectedfromtwoentirelydifferentvalves,thevoltageacrosseachvalveiscompletelydifferentatswitch-on,buttheygentlyconvergeandafter45ssettletoverynearlyequalvalues,withnoevidenceofcurrenthogging.However,inanotherseriesoftests,theauthormonitoredheaterpowerforapairof valves of the same type but selected for a large difference in their heaterpowers.Thevalveswere first connected as a series string anddriven constantcurrentatthemanufacturer’sratedcurrentandtheirheatervoltagesloggedat1sintervalsfor120 sfromswitch-on,andthenthepairsweredrivenindividuallyconstantvoltageattherated6.3 V(measuredatthepins)andbothvoltageandcurrentloggedat1 sintervalsfor120 s.Foreachvalve,thedisparityinpowerdissipationbetweenthepairwascalculatedforbothconstantcurrentheatingandconstantvoltageheating(Table4.5).

Table4.5ComparisonofConstantVoltageandConstantCurrentHeatingValvetype Constantvoltage(%) Constantcurrent(%) Ratio

KT88(1.6 A) 3.8 11 2.96J5GT(0.3 A) 2.6 4.8 1.9

The tabulated results tell us two things. Firstly, constant current heatingexacerbates differences between valves, almost doubling the 6J5GT disparityand almost trebling the KT88 disparity. Secondly, it seems that the problembecomesworsewithhigherheaterpowers–itwouldnotbeagoodideatouseseriesKT88heaters.Constant current 300 mA series heater chains have a number of advantages

comparedtoconventional6.3 VDCregulatedsuppliesforparallelheaters:

•Theassumedlinearregulatorismoreefficient.•Theyareinherentlyproofagainstaccidentalshortoropencircuits.•Thethermalshocktothevalveheatersatcoldswitch-oniseliminated.•IndividualheaterresistancescanbeusedaspartofastagedRadioFrequencyInterference(RFI)filter.•Heaterwiringresistancebecomesirrelevant(acomplexpre-amplifierusingOctalvalves,perhapsconsuming6.3 Vat>5 A,wouldrequirethickheaterwiring).

Thedisadvantagesofseriesheaterchainsare:•Any failure iscatastrophicandaffectsallvalves in thechain.Havingsaidthat, the author has had a total of two heater failures in 30 years (one self-inflictedbyfloutingVhk(max)).Sadly,thesecondfailurewasinaseriesheaterchain,andtheconsequentialdamagewashorrendous.• Constant current heating exacerbates differences between valves – whichmightbeaprobleminadifferentialpair.

HeaterVoltageandCurrent

Typical indirectly heated valves require approximately 1 min to reach 99%heater temperature from cold, or 40 s when preheated at 80% current (63%voltage).Whendrivenfromaconstantcurrentsource,heaterterminalvoltageisaverysensitivemeasureofheater(andbyimplication)cathodetemperature.AnInternationalServicemaster14N7(Ih=300 mA)wastestedbya4½digitDVMsettologheatervoltageat5 sintervals.Theresultswerenormalisedto100%ofthefinalheatervoltageandarepresentedintheaccompanyingtable(Table4.6).

Table4.6HeaterVoltageAgainstTimeWhenDrivenbyaConstantCurrentTime(s) Vh(%)

0 22.625 36.2810 46.6015 58.9320 78.7525 89.2930 93.1435 95.2440 96.8745 98.06

50 98.8055 99.1960 99.3890 99.54120 99.70150 99.80180 99.87210 99.93240 99.98270 100

AscanbeseenfromTable4.6,althoughthevalveoperatescorrectlywithin60s, a considerably longer time is required before the heater/cathode reachesthermal equillibrium. Since emission, and therefore valve operation, istemperature dependent, we cannot expect stable operation until 5 min afterswitch-on.The most marked changes occur during the first minute of operation, so theheater voltage over the first 50 s of a selection of different types was testedusing an HP54600B oscilloscope set to 20% Vh/div vertically and 5 s/divhorizontally(seeFigure4.42).

Figure4.42Heatervoltageagainsttimeforvariousvalvesfedfromaconstantcurrentsource.

Ascanbeseen,allthevalveswarmatdifferentrates,hencethemanufacturer’scaveatsaboutseriesheaterchains.Without changing oscilloscope settings, a Brimar ECC88 was preheated with80%heatercurrent,andtheeffectof thiswascomparedwithheatingthesamevalvefromcold,andthisshowedthatpreheatingreducedwarm-uptimefrom40sto<10 s(seeFigure4.43).

Figure4.43Heatervoltageagainsttimefromconstantcurrentsource.Uppertrace:Preheated.Lowertrace:Fromcold.

TheControlGrid

Thecontrolgridiswoundfromstiff,finewire(oftentungsten)asahelixaroundthe cathode, and it is most effective close to the cathode surface, where thevelocityoftheelectronsisless,thanneartheanode,bywhichtimetheelectronshaveacquiredconsiderablemomentumandarenotsoeasilyrepelled.Therefore,eveninavalvehavingasuccessionofgrids,thecontrolgridisalwaysthegridnearesttothecathode.Thepitchofthegridwindinganditspositioningrelativetotheanodeandcathodeinfluencegmandμ(seeFigure4.44).

Figure4.44Theeffectofvalvegeometryonμandgm.

As a practical example of the concepts shown in the diagram, two dissectedvalveshavingcomparablemutualconductancewereinspectedunderatravellingmicroscope.The6080(μ=2)hadagridpitchof≈1.64 mmperturn,whereastheECC81(μ=65)hadapitchof≈0.16 mmperturn.As an extreme example of the effect of anode–cathode spacing on μ, goodqualityvalvetelevisionsregulatedtheirextrahightension(EHT)supplybecausethis avoided changes in picture size with brightness. Because their EHT wastypically15 kV, series regulatorscouldnotbeused (heater/cathode insulationand efficiency problems), so shunt regulatorswere necessary. No valve has aperfect vacuum, so an increased anode–cathode spacing was needed to avoidarcing,resultinginhumungousμ(1050forthePD500).Increasinggmrequiresthatthegridbemovedclosertothecathode,butifhighμis also required, then the grid winding pitch must be very fine, necessitatingextremelyfinewireforauniformfield.Thus,theWE416C(gm≈65 mA/Vandμ≈250)wasspecifiedtohaveagridwithapitchof1,000turnsperinch(0.0254mm),using0.0003″(12 μm)diameterwire,spaced0.0005″(20 μm)fromthecathode[19].Becausethecontrolgridissoclosetothecathode,averysmallmovementofthegrid has a significant effect on the flow of electrons, and this is the cause ofvalvemicrophony.

GridCurrent

Althoughthecontrolgridisnormallyahigh-resistancepoint,itcanpasspositiveornegativegridcurrent.Ifwechargethegridpositivelywithrespecttothecathode,thegridreducestherepulsive effect of the space charge on electron emission at the surface of thecathode,andassistsinpullingelectronsawayfromthesurfaceofthecathode.Amuchhigher anode current flows, but some electrons are captured by the gridand flow out into the grid circuit, resulting in positive grid current, whichdrasticallyreducesinputresistance.ThisiswhyClassAB2outputstages,whichoperatewithpositivegridcurrent,areinvariablyprecededbyapowerdriver.

ThermalRunawayduetoGridCurrent

If the grid is allowed to emit electrons, negative grid current results, anddependingonthevalueofthegrid-leakresistorandbiassing,thepotentialofthegridmayrise(loweringVgk),causinganincreaseinanodecurrent,andfurther

heatingthevalve.Theemissivematerialofthecathodethenbeginstoevaporate,contaminating the grid and increasing grid emission. At worst, the grid maybecomesohotthatitslumpsandtouchesthecathode,completingthedestructionof the valve, but permanently increased valve noise is inevitable even if thevalveisnotactuallydestroyed.

GridEmission

Cathodestrippinghasbeenmentionedearlierasaproblemforthecathode,butthestrippedcathodematerialmustgosomewhere.Thecontrolgridisnearesttothe cathode, so this sputtering process contaminates itwith emissivematerial,greatlyincreasingthelikelihoodofgridemission.The Richardson/Dushmann equation (see Appendix) shows that there are twowaysinwhichtheemissionofanuncontaminatedgridmaybeminimised:•Reducegridtemperature:Powervalvescooltheircontrolgridbywindingiton thick copper axial supporting wires that conduct the heat to radiantheatsinks at their ends. Note that a hot anode inevitably increases gridtemperature.•Increasegridworkfunction:Electronemissionisproportionaltotheinversepower of work function, so selecting a grid material with increased workfunctionreducesgridemission(Table4.7).

Table4.7ComparisonofEmissionforDifferentGridMaterialsMetal φ Relativeemissionat1,100 K(%)

Tungsten 4.55 100Gold 5.28 0.05Platinum 5.63 0.001

As can be seen, a slight change inwork functionmakes a huge difference toemission.Platinumgivesbyfar thebestperformance,butapureplatinumgridwouldbeexpensiveandtooweaktoberigid.Onepracticalsolutionwastouseplatinum-cladmolybdenumwire (25%platinumbyweight [20]),buteven thiswasexpensive.Conversely,thinlygold-platingagridischeap,sothistechniqueiscommon(6080,6545P).

Frame-GridValves

Ifahorizontalbraceisweldedfromoneverticalcontrolgridsupportrodtotheotheratboth topandbottom,aframeisformed,so theseareknownasframe-gridvalves.Theadvantageofthisconstructionisthatthegridwirecannowbetensionedacrosstheframe,greatlyreducingsag,whichenablesfarmoreprecise

grid-cathode positioning of eachwire, allowing closer spacing to the cathode,whichincreasesgm.Asanexample,theframe-gridE88CCcomfortablyachievesgm=10 mA/V,whereasthetraditionalconstructionoftheotherwisecomparableECC82strugglestobetter2 mA/V.

Variable-μGridsandDistortion

Variable-μvalvesarealsoknownasremotecut-offvalves,whichreferstothegentlecurveoftheirmutualcharacteristics,requiringanunusuallylargenegativegrid voltage to reduce Ia to 0.Radio receivers have to copewith a very largedynamic range of RF signals because theymay be tuned from a strong localsignaltoaweakdistantsignal.Toallowsufficientgainfortheweaksignal,butavoidoverloadonthestrongsignal,theRFgainofthereceiverismadevariableby anAutomaticGainControl (AGC) system.Typically, theAGC affects thegain of two or three valves simultaneously, and because the total gain is theproductofindividualgains,eachvalveonlyneedstochangeitsgainbyasmallamountforthetotalgaintochangesignificantly.Thecontrolgridisdeliberatelywoundwithanunevenpitch(whichcausesμandgmtochangewithVa),sothesevalvesareknownasvariable-μtriodesorpentodes(seeFigure4.45).

Figure4.45Controlgridof6K7variable-μpentode.Notethedeliberatedeviationsfromconstantpitchwindinginthecentreandaquarterofthewayinfromeachend.

Althoughvariable-μvalvesaredesignedtochangetheirgainwithVa,thisisnota problem at RF because the signals are so small compared to audio, anddistortionisproportionaltoamplitude.Inanaudiotriode,distortionisdominatedbythevariationofrawithIa,butoncetheloadlineisflattened(RL>>ra)tolowerdistortion,werelyonconstantμ,sotheevennessofthegridpitchbecomesimportant.Mechanically,thegridwireiswoundandswagedintoguideslotscutintothegridsupportrodswhosepositionwasdeterminedbyaleadscrew.

Asthe leadscrewwears,backlashdevelopsand thepositionof theguideslotsbecomeslessprecise,resultinginanunevengridwinding.Backlashismoreofaproblemwithfinergridpitches(high-μvalves),soitismoredifficulttomakealow-distortionhigh-μvalvethanalow-μvalve.Reducingbacklashandtighteningproductiontolerancestoreducevariationofμare not insurmountable problems – they just costmoney, so this specificationwould be driven by the application. Fortuitously, it appears that the CV1988(military6SN7) required lowvariationofμ, so ithas lowerdistortion than thecommercial6SN7.

OtherGrids

Tetrodes and pentodes have a helical screen grid (g 2) wound concentricallybetweenthecontrolgridandtheanode,soaproportionofthecathodecurrentisacceleratedintothescreengrid,causingitstemperaturetorise.Ifthescreengridis coated with zirconium, this not only helps cooling by radiation, but alsoabsorbsresidualgas,sothescreengridassiststhegetterinmaintainingagoodvacuum.Beam tetrodes have beam-forming plates rather than a helical wire grid (seeFigure4.46).

Figure4.46Beam-formingplatesandcathode/gridstructureofQQV07-50VHFdualbeamtetrode.

Electronsareonlyweaklyattractedtothesuppressorgrid(g3)inapentode,sothisgriddoesnotself-heat.

TheAnode

Theanode isconstantlybombardedbyhighvelocityelectrons.Although theseelectrons have very little mass, their high velocity means that they possessconsiderablekineticenergy,whichisconvertedintoheatwhentheyarestoppedby the anode. An important specification for a valve is therefore the anodedissipation, because a hot anode heats the grid, causing grid emission. Asecondary effect is that a hot anode releases gas, a phenomenon known asoutgassing,whichcontaminatesthevacuum.Occasionally,someearlyvalvesusedcoarselywovenwiremeshanodes,whichwas claimed to ‘prevent the grid becoming overheated by reflectedradiation’[21](seeFigure4.47).

Figure4.47TruemeshanodeofaPhilco37.

Themeshanodeideahasbeenrecentlyresurrected,althoughthe‘meshanode’300B is actually pressed from metal sheet having rectangular holes punchedthroughit(seeFigure4.48).

Figure4.48Punchedplate‘mesh’anode300B.

Theanodedissipatesheatbyradiation,and tomaximiseradiatingarea,anodesoftenhavefins.Anotherwaytoimprovethelossofheatbyradiationistocolourtheanodeblackbycoatingthenickelanodewithgraphite.Evenbetter,the813transmitting tetrode and 6528 series regulator dual triode use solid graphiteanodesbecausetheydonotwarpathighanodetemperatures.Themanufacturerofthe6528madeavirtueoutoftheveryhotgraphiteanodebycoatingitwithzirconium,which has a great affinity for hydrogen, nitrogen and oxygen onceheatedabove800 K(incipientredheat).Theanode’s surroundingsmustbe cool andcapableof absorbing radiantheat.Otherwise, theywill emit or reflect heat back to the anode,which is perfectlycolouredtoabsorbradiantheat, thusraisinganodetemperature.Chrome-platedoutputtransformers,etc.,maylooknice,buttheycouldraiseanodetemperature.The worst possible surroundings for a valve would be a concentric chrome-platedcylinder,sincethiswouldfocustheradiantheatbacktotheanode.TheEF86low-noisepentodehasanelectrostaticscreensurroundingitsanodetoreducehum,andinsomeexamplesisformedfromashinymetalsheet,butthisshould not be confused with the anode. This screen severely restricts anodecooling,but thegmof theEF86 isquite lowanyway, sooperating it at ahighcurrent(whichwouldincreasegm,butalsoincreasesPa)wouldbepointless.TheEF86 typically operates with a lowPa, so the electrostatic screen does not a

causeacoolingproblem.Becauseelectronscollidewiththeanodeathighvelocity,thereisapossibilityofdislodging more than one electron from the anode surface for each electronstrike–aneffectknownassecondaryemission.Ifthesecondariesbarelyleftthesurfaceof theanodebefore returning, thiswouldnotbeaproblem,but if theystray any distance, they affect the electric field between the cathode and theanode,causingdistortion.TherelativelevelofthisemissionisdeterminedbytheSecondaryEmissionRatio(SER)ofthematerialconcerned.NickelhasafairlylowSER(≈1.3)and, togetherwith itsmalleability, this iswhy it iscommonlyused for anodes and other pressed sheet valve electrodes. The SER of anelectrode can be dramatically reduced by zirconium plating or by graphitisingthesurface(coatingitwithcolloidalgraphite).GraphitehasaverylowSER,butisratherfragile,soitcanonlybeusedinquitethick (>1 mm) structures. Moulded graphite anodes have increased thermalinertia,allowingPa(peak)>>Pa(continuous),sotheyarepopularintransmittervalvessuch as the 813, 211 and 845. The Mullard QV08/100 has a massive anodestructureformedoutoftwographiteslabs≈8 mmthick,makingananodethatisverytolerantofmomentaryoverloads(seeFigure4.49).

Figure4.49GraphiteslabanodeofQV08/100tetrode.

TheVacuumandIonisationNoise

TheVacuumandIonisationNoise

Thequalityofthevacuumwithinthevalveiscriticalbecauseinitiallyunchargedgasmoleculesinthevalvearelikelytobestruckbyhighvelocityelectronsontheirwaytotheanode,possiblydislodgingelectronstocreatepositivegasions.Positively charged ions are repelled from the anode, but are attracted to thegrid/cathode structure, whereupon they are immediately discharged by abalancing number of electrons flowing up from the external paths to ground.Since theformationof ionsand theirsubsequentdischargeby thegrid/cathodestructureisrandom,itcreatesrandomnoisecurrentsleadingtoionisationnoise.Ionisation noise currents become a problem only when they flow through anexternal resistance such as a grid-leak resistor. They then develop a voltageacross that resistance in accordance with Ohm’s law, and because valves arevoltage-operated devices ( Va or Ia∝ Vgk), the ionisation noise voltage isamplified.Ifthegridresistancewaszero,theionisationcurrentwouldbeunabletodevelopanoisevoltage.Low-noise input stages use a high- μ valve, so that subsequent stages do notdegradethenoiseperformance,butahigh-μvalveimpliesfinegridpitch,whichgreatlyincreasestheprobabilityofionsstrikingthegridratherthanthecathode.SinceRg, the grid-leak resistor, is invariably quite a high value, a significantnoise voltage can be developed and amplified. Because the grid effectivelyscreens the cathode, very few ions strike the cathode, so cathode ionisationcurrent is greatly reduced, and because even an undecoupled Rk has a lowresistance to ground comparedwith the grid-leak resistor, this further reducesanynoisevoltagedeveloped in the cathode circuit. Ionisationnoise in high-μstagesisthusdominatedbygridionisationnoisecurrentandcanbeminimisedbyalowsourceimpedancetogroundataudiofrequencies,sotransformerinputcoupling reduces the effects of ionisation noise currents at low frequenciescompared with capacitor coupling. (At very low frequencies, Zsec≈ RDC(sec),which is quite low, whereasXC≈∞, so capacitor coupling producesmore 1/ fnoise.)Output stages tend to use low- μ valves to minimise Miller capacitance andpreserve bandwidth, but low- μ valves have a coarse grid pitch, biassing theprobability of ion strike in favour of the cathode. Low-μ valves operatewithhigh bias voltages (Vgk), requiring high values ofRk. The combination of anincreasedproportionofionisationcurrentandhighRkmeansthatlow-μvalvesshould not leave their cathodes undecoupled if the effects of ionisation noisecurrentsaretobeminimised.A good vacuum is referred to as being hard, whereas a poor vacuum is soft.

Therefore, valves are sometimes described as having ‘gone soft’. Duringmanufacturing,theairinthevalveispumpedout,butsomeairwillremainthatcannotberemovedbypumps,andtheremaininggasisremovedbythegetter.

TheGetter

Gasmoleculesaretrappedintheintersticesofthemetalparts–notdissolved,soheatingtoredheatcanforcethemout,justbeforethegetterisflashed.Thegetterisametalstructureoftenfittednearthetopofthevalve,coatedwithahighly volatile powder (usually a barium compound similar to the cathodeemissivesurface).Oncethevalvehasbeensealedandasmuchgasaspossiblehasbeenpumpedout,thegetterisheatedandthepowderexplodes,consumingthe remaining gas. The force of the explosion throwsmolten barium onto theinsidesurfaceoftheenvelopetogivethefamiliarmirroredcoatingatthetopofthe valve. The explosion is initiated electrically, either by directly passing aheating current through the getter’s metallic supporting structure (metalenvelope valves), or by shaping the getter as a short-circuited turn and usingtransformeraction to induce theheatingcurrent fromanexternalRFsourceat≈450 kHz(glassenvelopevalves).Althoughsomeofthegettermaterialisdeactivatedbytheexplosion,thegettermustcontinuetoconsumegasmoleculesthroughoutthelifeofthevalvebecausegascontinuouslypermeates thevacuum,eithervia leaksat thesealswhere theleads leave the envelope, or by outgassing from hot structures. The rate of achemicalreactiondoubleswitheach10 °Criseintemperature,somostvalvesthermallybondthegettertothehotanodewithathickwire.Becausetheanodeisnotataconstanttemperatureoveritsentiresurface,andthewirehasthermalresistance,somevalvesmountgettersviashortstubsontothehottestpartsoftheanode. Ifbondedwithonlyonestub, themassof thegettercombinedwith thespringofthestubcanformamechanicallyresonantsystemwithaveryhighQ,sosomespecialqualityvalvessupporttheirgetterswithtwostubstoreducetheQ,andhencemicrophony.To be consumed by the getter, the gas molecules must touch it, but this isensured by entropy, and provided the heater reaches operating temperaturebeforeHTisappliedtotheanode,itshouldbeeffective.Softvalvescanoftenbespottedbythegentleblueglowneartheglassenvelope,whichisduetothecollisionofionisedgasmoleculeswiththeglass.ThisshouldnotbeconfusedwiththebluefluorescencethatcanbeseenontheinnersurfaceoftheanodeinvalvessuchastheEL84,andwhichisperfectlynormal.Valvesstoredfordecades inacoldwarehousemayhavean imperfectvacuum

because the getter was too cold to be fully effective. Fortunately, 24 h in adomesticovenat100 °Cwarmsthegetterandwilloftenclearresidualgas[22],butbewarethat thephenolicbasesofOctalvalvescaneasilybedamagedbyahighertemperature.Whenfirstused,evennewvalvesshouldhavetheirheaterspoweredfora leasthalfanhourbeforeapplyingHT.Althoughafewhoursofelectricalusealsoclearsthegas, thepreviousmethodsavoidthedamagingionbombardmentsufferedbythecathodeuntilthegetterhascleanedthevacuum.Occasionally,ratherthanairgentlyseepinginthroughtheKovaralloyglasstometal seals at the valve’s pins, a severely overheated anode may releasesufficient gas (known as outgassing) to poison the cathode and turn the gettersputtering from silver/brown to an almost transparent brown. Long-termoverheating results in stains on the anode, so the combination of stains andnearlytransparentgettersputteringmayrevealthedamageevenbeforethe‘gas’testonavalvetester(seeFigure4.50).

Figure 4.50 The right-hand valve of this pair has almost lost its gettering due to outgassing caused by catastrophic anodeoverheating.

TheMicaWafersandEnvelopeTemperature

The electrode structure, heatsinks and getter are supported and held rigidly inpositionbyinsulatingmicawafersatthetopandbottomoftheanodestructure.

If this mica is not a perfect insulator, then leakage current paths will form,perhapsfromtheanodetothecontrolgrid,whichwouldcausenoiseinasmall-signalvalve,butcouldcausedestructioninapowervalve.Whenthegetterisexploded,somemoltenmetalmaystrikethemicawaferandmakeitslightlyconductive.Tolengthentheleakagecurrentpathsandincreasetheirresistance,slotsarecutinthewaferbetweenthecontrolgridandtheanode.Alternatively,thegettermaybepositionedsuchthatitislesslikelytosprayontothe mica wafers, or the electrode supporting wafers may be shielded by asacrificialmicawaferormetalplate.Thedesignersof theKT88notonlyusedall of the previous techniques to reduce leakage, but also made the electrodesupporting wafers undersize, so that they did not touch the (assumedcontaminated)envelope(seeFigure4.51).

Figure4.51ViewofGECKT88;notethemeasurestakentoreduceleakagecurrents.

Osrammadeabig fuss aboutquality control, perhaps justifiably– theirKT88toleratesahigheranodevoltagethanamodernone.Even if the mica wafers have not been contaminated with conductive gettermaterial,micaisnotaperfectinsulator,andlikeallinsulatorsitsresistancefallswith increasing temperature. The Sony C-800G studio condenser microphoneusedaPeltiereffectheatpump tocool theenvelopeof itspre-amplifiervalve.Sincethemicawafersareincontactwiththeenvelope,theyarealsocooled,andit seems probable that the reduction in leakage currents through the wafers,together with reduced anode temperature and consequent outgassing is

responsibleforthereportedimprovementinnoise[23].Notonlydoesreducedenvelopetemperaturereducenoise,butitalsoimprovesvalve life. To directly quote the ‘Brimar Valves Components Group MobileExhibition’(November1959)manual,‘Theuseofclose-fittingscreeningcansofhigh thermal conductivity in intimate thermal contactwith a large area of thebulb, in conjunction with an adequate heat sink, can materially reduce theoperatingbulbtemperatureandveryconsiderablyimprovethelifeofthevalve.’Contrast this with a further comment from the same source, ‘The use ofscreening canswhich are not in thermal contactwith the valvemay seriouslyinterferewiththecoolingofthevalve.’Ahot envelope implies a hot anode, and because themicawafers support theanode,theanodeconductsheatdirectlytothewafers.Thewaferscanbeheatedby an excessively hot anode to the point that they outgaswater vapour (micaunavoidably contains water), which is particularly poisonous to oxide-coatedcathodes[24].Micas can also poison cathodes because of vibration. A vibrating electrodechafesitssupportholesinthemicas,producingfinemicadust[25].Weightforweight, dust has a far greater surface area than a solid block, so it readilyreleaseswatervapour.Ceramicsupportwafersarepopularintransmittingvalvessuchasthe845,andin ruggedised valves such as the 6384, because it avoids the water vapourproblem.

ValveSockets–LossesandNoise

Theauthorhas agoodvarietyofB9Avalve sockets inboth chassismountingand PCB types ranging from phenolic through ceramic to PTFE, so theirfrequency-dependent losses were investigated. After considerable testing, ittranspired that the ceramic and PTFE typeswere essentially indistinguishable,butthatothertypeshadmeasurabledefects(seeFigure4.52).

Figure4.52Leakageresistanceagainstfrequencyfordifferentvalvesocketinsulatingmaterials.

Acleartrendisapparent–ifyoucan’tuseaPTFEorceramicsocket,getasfarawayfromblackaspossible(blackiscarbon,whichisconductive)becauseDCleakagecurrents(especiallyfromanodetogrid)implynoiseand/ordistortioninhighimpedancecircuits.

ValveBasesandtheLoktal™Base

Octalvalvesrequireaninsulatingbaseintowhichhollowbrasspinsareriveted,sotheauthorinvestigatedtheanodetogrid-leakageresistanceof44triodes(seeFigure4.53).

Figure4.53Averageanode togrid leakage resistanceagainst frequency fordifferentvalvebase insulatingmaterials (Number inbracketsreferstothenumberofsamplestested.)

Theresultsaresimilartothevalvesocketcomparison,withtheworstbasebeingthe black phenolic Pinnacle 6J5GT – which is an interesting result since thistriodeperformedverywellintheauthor’sdistortiontests.Clearly,thePinnacle6J5GTismoresuitedtohighsignallevelswheredistortionisimportantthantosmall signal levels from high impedances where anode to grid leakage andresultingnoiseisimportant.However,theclearwinnerinthiscomparisonistheSylvaniaJAN7N7,whichhasaLoktal™base.Despite its technical superiority over the established octal base, the Loktal™base introduced by Sylvania in 1938 was an unpopular diversion and anevolutionarydeadend,sincetheresultingvalvewaslittlesmallerthananOctalvalve.Toproduceavalve that couldoperateup to225 MHz (7A4versus theotherwiseequivalent6J5),capacitances,inductancesandleakagepathshadtobereduced. Eliminating the glass pinch within the valve and bringing electrodesupport wires directly to the pins shortened the valve, which reduced internalstray capacitances and lead inductance. Eliminating the phenolic base reducedleakagebetweenpins,andtheadditionofanearthedmetalbasethroughwhichthe pins protruded both screened and electrically guarded individual pins.Thecentralmetalspigotnotonlyprovidedkeyingtoensurecorrectorientation,butalso had a ring that locked the valve into the base once inserted. To avoidtrademark infringement, competing companies changed the nomenclature to‘Loctal’,orreferredtothemas‘Lock-in’valvesanddesignatedthebaseB8G.For high quality audio, Loctal valves are excellent, since their electrodeconstruction(andconsequentdistortion)isthesameastheOctalgeneration,butthey have the obvious technical superiority of the Loctal base. Since Loctalvalvesweredesignedforuseabove100 MHz(whensocketlossesbecomeverysignificant),PTFE-insulatedLoctalbasesweremade,andarestillavailable.The 1939 Sylvania manual misleadingly specifies Loktal™ heater voltage asbeing7 Vor14 Vfor130 Vline,allowingthemtousethenew‘7’and‘14’prefixesfortheirtypedesignation,butthisisdirectlyequivalentto6.3 Vor12.6Vfor117 V–theirnominallinevoltage,sothesevalvesactuallyhavestandardheaters.Thecontrivedprefixesweresimplyamarketingrusetodistinguishthenewbase.Brimar[26]notedthatleakagecurrentsinthebaseareacauseofnoise,andoncepoorinsulatorshavebeeneliminated,theonlywaytoreduceleakagecurrentsisto lengthen the leakagepath.Thus, triodes requiring lowgridcurrent lengthenthe leakage path by bringing their grid out through the top of the valve(ME1400,EC1000),orincludeacentralnippleinsidetheglassbuttonbaseforthegridconnection(ME1401).

TheGlassEnvelopeandthePins

TheGlassEnvelopeandthePins

The envelope maintains the vacuum within the valve; careless handling willcrack thevalve,andairwillenter.Theeasiestway tocrack theenvelope is tobend the pins whilst attempting to insert the valve into a new socket. It istherefore a good practice to plug old valves into the new sockets of a newamplifier,andtesttheamplifierbeforeinsertingtheexpensivenewvalves.Thisthenspreadsthefingersofthesocketslightly,andthenewvalvescanbeinsertedwithout fear of damage. A hidden problem is that repeated plugging andunplugging can createmicro-fractures in the glass near the pins, allowing justsufficientgastoleakintothevalvetosubtlydegradethevacuum,andincreaseionisation noise (for this reason, the British Standards Institution [27]warnedagainst repeated testing of special quality valves). A terminally damagedenvelope is easily spotted because the mirror coating due to the getter turnswhite.Iftheenvelopeisallowedtoaccumulatefluff,itwillbethermallyinsulated,andthe valve will run hotter, with all the dire consequences that entails. Valvesshouldbecleanandshinytopromotelonglife.Notallelectronsacceleratedtowardstheanodearecaptured,andsoachargecanbuild up on the inside surface of the (insulating) glass envelope. Coating theglasswithgraphiterendersitconductive,andconnectingittothecathodeallowsthechargetobedrainedaway.Conversely,theinternalglassnipplearoundeachpin on a button base lengthens paths and reduces leakage currents betweenadjacentpins.The pins aremade ofKovar, which is an iron–nickel–cobalt alloy having thesamecoefficientof thermalexpansionas theglassenvelopeinorder that leaksdonot occur at the seals as thevalvewarms. If storedunderdampconditionsKovar can rust, so valves should ideally be stored in evacuated plastic bags.LoctalvalvesweretheearliestvalvestobeintroducedwithKovarpins,andtheirunpopularityatthetimemeansthata50-year-oldNOSvalveisnotuncommon,sobewareof thisproblem.Ifyouhaveagoodstockofvalves,store theminawarm,dryplace–notinashedorgarage.On some valves, the pinsmay be gold-plated, but this platingwill be quicklyremoved by repeated plugging and unplugging.Gold-plated pins used to be asign of quality (although Brimar did not always bother to gold-plate theirexcellentE88CC),but somemodernvalvemanufacturers cheerfullygold-plateselected valves sourced by their standard production line, whereas traditionalspecial quality (Mullard) or trustworthy (Brimar) valves were consciouslydesigned/producedtobebetter,ratherthanselectedfromastandardproduction

line.Althoughgoldiscorrosionresistantandassistsinachievingagoodcontactwiththe socket, silver has better conductivity ( ρ=1.47×10 −8 Ω/m compared with2.05×10−8 Ω/m for gold and1.54×10−8 Ω/m for copper).As frequency rises,skineffectcausesconductiontooccurprincipallyatthesurfaceoftheconductor,so the MUSA video connector originated at Post Office telecommunicationsexchange London MUSeum A was silver-plated to improve conductivity.Similarly, transmittingvalves intended for use atVHF sometimes have silver-platedpins.Sadly,unattendedsilvercorrodesquitebadly.

PCBMaterials

Glass Reinforced Plastic (GRP) boards are slightly less than ideal for valveaudiobecauseofleakageresistance.Theleakageoccursbecausetheepoxyresindoesnotalwayssealperfectlytotheglassfibresandsurfacetensiondrawswatervapourintotheresultinggaps,nevertobereleased.Manyyearsago,theauthorbuilt circuits on Synthetic Resin Bonded Paper (SRBP) and felt that theysoundedbetterthanthesamecircuitbuiltonGRP,butatthetimehecouldnotseeanyengineeringreasonbehindit,andputitdowntoimagination.ThecrucialdifferencebetweenGRPandSRBPisthatSRBPisporousoveritsentiresurfaceandnot just at its edges.SRBPcan therefore losewatervapourover its entiresurfaceasitheats,whereasaGRPboardcanlosewatervapouronlyatitsedges.A warm SRBP board could therefore actually be less leaky (even thoughnominallyapoorermaterial) thanawarmGRPboard.Becausewater ispolar,theproblemofdielectricleakagebecomesevenmoreacuteathighfrequencies,somicrowaveand>200 MHzoscilloscopedesignershaveavoidedthematerialfordecades,preferringtousePTFE.

References[1]Scroggie,MG,Radioandelectroniclaboratoryhandbook.8thed.(

1971)Iliffe;P475.[2]Grover,FW,BullBurStandsVII(1911)495.[3]In:(Editors:Hughes,LEC;Holland,FW)Electronicengineer’sreference

book3rded.(1967)Iliffe.[4]Thiele,AN,Air-coredinductorsforaudio,JAudioEngSoc24(June(5))(

1976)374.[5]McIntosh,FH;Gow,GJ,Descriptionandanalysisofanew50-wattamplifier

circuit,AudioEngDecember(1949).

[6]Sowter,GAV,Softmagneticmaterialsforaudiotransformers:history,production,andapplications,JAudioEngSoc35(October(10))(1987)760.

[7]Improvementsininstrumentsfordetectingandmeasuringalternatingelectriccurrents.BritishPatent24,850;1904.

[8]USPatent879,532;18February1908.[9]vonArdenne,M,Cathode-raytubes.(1939)Pitman,NewYork;P4.[10]Alley,CL;Atwood,KW,Electronicengineering.(1962)Wiley,NewYork.[11]vanderZiel,A,Noise,sources,characterization,measurement.(

1970)Prentice-Hall;P101.[12]Rosebury,F,Handbookofelectrontubeandvacuumtechniques.(

1965)Addison-Wesley.[13]Upton,LS,Therejuvenationofvacuumtubes,OldTimer’sBulletin

December(1973).[14]Spangenberg,K,Vacuumtubes.1sted.(1948)McGraw-Hill;P41.[15]JohnsonW.TechniquestoExtendtheServiceLifeofHigh-PowerVacuum

Tubes.In:NABEngineeringConferenceProceedings.NationalAssociationofBroadcasters;1994.pp.285–93.

[16]Improvementsincathodestructuresforvacuumthermionictubes.BritishPatent209,415;1924.

[17]RCA.Receivingtubemanual,TechnicalSeriesRC-19;1959.[18]Szepesi,Z,Thetemperatureresponseoftheshoteffectofvalveswith

oxide-coatedcathode,WirelessEngineerFebruary(1939)67–70.[19]416Cvalvedatasheet.WesternElectric;1971.[20]Knoll,M,Materialsandprocessesofelectrondevices.(1959)Springer-

Verlag;(assistedbyBKazan.[21]HendersonFE.Introductiontovalves.2nded.WirelessWorld;1943.[22]Jones,M,Newlifeforoldvalves,ElectronWorldNovember(2000)

863–867.[23]Spencer-Allen,K,Chillfactor,StudioSoundNovember(1992)56–59.[24]Rowe,EG;Welch,P,Developmentsintrustworthy-valvetechniques,Electr

CommunSeptember(1954)172–188.[25]6384valvedatasheet.BendixCorporation.[26]BrimarapplicationreportVAD/508.36BR7;October1951.[27]Theuseofelectronicvalves.BritishStandardCodeofPracticeCP1005.

BSI;1962.

RecommendedFurtherReading•Eastman,AV,Fundamentalsofvacuumtubes.3rded.(1949)McGraw-Hill;

Verylittleonaudiobutgoodforthefundamentalphysicsbehinddeviceoperation.

•Chaffee,EL,Theoryofthermionicvacuumtubes.(1933)McGraw-Hill;Therearetwosuperbbooksthatmajorontheelectronphysicsneededtodesignvalves,andthisistheolder(butmoreeasilyobtainable)one.Brushupyourmathematicsandphysics.

•Spangenberg,KA,Vacuumtubes.(1948)McGraw-Hill;Thisistheotherelectronphysicsbook.Verywide-ranging,itincludesspecialtubessuchasklystrons,magnetrons,photomultipliers,anddisplaytubes.Nevertheless,thereisstillplentyofphysicspertainingtoaudiovalves.Superb,butrare.

•Reimann,AL,Thermionicemission.(1934)Chapman&Hall;ReimannworkedforMarconi-Osramanditshows.Lighteronmathematicsthantheprevioustwobooks,thisbookisprimarilyaboutthepracticalproblemsofmanufacturingvalvesandparticularlythechemistry.

•Vyse,B;Jessop,G,ThesagaofMarconiOsramvalve.(2000)Vyse;Writtenbytwoex-Marconi-Osramemployees,butfromamoremodernperspectiveandmorehistorythanphysics,thisisafascinatingreadbecauseitdetailsvalvedevelopmentandputsitintocontext.

•Knoll,M,Materialsandprocessesofelectrondevices.(1959)Springer-Verlag;(assistedbyBKazan).Thisisoneofthelastbookswrittenaboutvalvemanufactureandthereforecontainsallthesignificantinnovations.Ifyoueverwantedtoknowwhichmaterialswereusedwhere,andwhy,thisbookhastheanswer,andwillprobablyansweranysupplementaryquestions.Superb.

•Tomer,RB,Gettingthemostoutofvacuumtubes.(1960)Sams;ReprintedbyAudioAmateurPress(2000).Oneoftheveryfewbookswrittenonthereliabilityofvalvesandshouldbereadbyalldesigners.Itsslimnessbeliesitsworth.

•Theuseofelectronicvalves.BritishStandardCodeofPracticeCP1005(1962).Nottheworld’smostexcitingpamphlet,butusefulforcautionsonvalveuse.ReadinconjunctionwithTomer.

•Thrower,KR,HistoryoftheBritishradiovalveto1940.(1992)MMAInternational;Doeswhatitsaysonthetin.Nophysics,butagreatdealof

historyandanexposéoftheshenanigansemployedbythevalvemanufacturingcartelstomanipulatethemarket.

Chapter5.PowerSupplies

ValveamplifiersneedaDCHighTension(HT)supplyandoneormoreheater,orLowTension(LT)supplies,whichmaybeACorDC.Often,thesuppliesforthe pre-amplifier and power amplifier will be derived from the same powersupply,whichisfrequentlyintegraltothepoweramplifier,butthisneednotbeso.TheadventofPowerSupplyUnitDesignerVersion2(PSUD2)freewarein2003hastransformedthedesignoflinearsupplies,butanunderstandingoftheunderlyingprinciplesenablesmuchfasterconvergencetoanoptimumdesign.

Inthischapter,wewillidentifythemajorblocksofapowersupply,seehowtodesignthem,andthendesignacompletesupply.

TheMajorBlocksThere are two fundamental types of power supply: linear and switchers (seeFigure5.1).

Figure5.1Comparisonoflinearandswitcherpowersupplies.

In a switcher, the ACmains input is rectified, switched at a high frequency,typically >50 kHz, transformed, rectified, and smoothed; regulation is part ofthe switching element.Switchers are small, light and efficient.Their design ishighly specialised, and early designs generated copiousRadioFrequency (RF)noise, but designs conforming to modern Electro-Magnetic Compatibility(EMC)standardsaresurprisinglyquietandcanbeusefulforheatersupplies.Bycontrast,alinearsupplytransformsthe50 Hzor60 HzACmainsdirectly,requiring a bulky mains transformer. This is then rectified by valves orsemiconductors, smoothed by large capacitors, and possibly even largerinductors, and then regulated if necessary. Linear supplies are heavy andinefficient,buteasilydesignedandlownoise.Valveamplifiersuselotsofthem,sowehadbetterknowhowtodesignthem.Power supplies aredesigned from theoutputback to the input.Since they aredesigned after the amplification stages, it is tempting to think of them as anafterthought; indeed, somecommercial products reflect this attitude. It ismostimportanttorealisethatanamplifierismerelyamodulatorandcontrolstheflowofenergyfromthepowersupplytotheload.Ifthepowersupplyispoorandhasinsufficient energy to meet the amplifier’s peak demands, then the mostbeautifullydesignedamplifierwillbejunk.

RectificationandSmoothingAlthoughwemaynothavea regulatoron theoutputof thesupply,wealwayshaverectificationandsmoothing.Thetwofunctionsareinextricablylinkedanddetermine the specification of the mains transformer, so this is usually thestartingpointfordesign.SinceweneedtorectifythesinusoidalACleavingthetransformer with maximum efficiency, we will only consider full-waverectification.Half-waverectificationisnotonlyinefficient(becauseitonlyusesalternatehalf-cycles),butalsocausesDC to flow through the transformer,andevensmallDCcurrentscancausecoresaturation.Asaturatedcoreislossyandproducesleakageflux,whichcaninducehumcurrentsintonearbycircuitry.

ChoiceofRectifiers/Diodes

Therearetwoformsoffull-waverectification:thecentre-tappedrectifierandthebridgerectifier(seeFigure5.2).

Figure5.2Full-waverectification.

The bridge rectifier is the usual modern topology because it economises ontransformer windings. The centre-tapped rectifier was traditional in valvecircuitsbecauseiteconomisedonrectifiers(whichwereexpensive).WhenweconsiderHTsuppliesproducingVDC<1 kV,wehaveachoicebetweensilicon and hard vacuum thermionic rectifiers. The GZ34 was the ubiquitousdual diode rectifier, but if we’re designing from scratch, the single diodesintended for use in television line scan circuits are cheaper and better, butbeware that although the Novar (North American) and Magnoval (European)basesaresuperficially identical,plugging the1 mmpinsof the6CL3 into the1.3 mmreceptaclesofaMagnovalsocketguaranteesarcingandunreliability.Cathode ray tubes for television needed large deflections (120°, or more) tominimise thedepthof the tubeandusedmagneticdeflection, so linescanwascurrent drive, rather than voltage (as in electrostatic deflection analogue

oscilloscopes). Applying a constant current to an inductor (the line scan coil)causesavoltageramp,producingtherequiredlinearhorizontalsweep.Becauseflyback had to occur in <12 μs (rather than 52 μs for active picture), acorrespondingly larger negative current was required. However, this largernegativecurrentwaseffectivelyahighamplitudepulse,anditexcitedallsortsofresonances.Oneearlysolutionwastodamptheresonancesusingaresistor,butthatcouldwaste20 Wofpower.Themoreelegantapproachwastodeliberatelyexcite one half-cycle of resonance and use it as the flyback pulse (who caresabout linearity during flyback?), and then use a diode to clamp the followinghalf-cycle. This eliminated the power wasted in the damping resistor, so theclampingdiodebecameknowninEuropeasanefficiencydiode,butadamperdiodeintheUSA.Examplessuitableforaudiouseare6CL3/6CK3(USA)andPY500A(Europe).Sadly,valverectifiersareinefficient.Notonlydotheyneedaheatersupply,butthey also drop tens of HT volts across themselves and increase the supply’soutput resistance. They are fragile in terms of ripple current (which we willinvestigateinamoment),sothereisamaximumvalueofcapacitancetheycantolerate, and even they need a minimum total resistance in series with eachanodetolimitthisripplecurrent:

whereRs=secondaryresistance

Rp=primaryresistance

n=secondary-to-primaryturnsratio.

AlthoughTable5.1allowsforquickcomparison,fordetaileddesignweshouldrefertoamanufacturer’sdatasheetorfullanalysis.

Table5.1ComparisonofCommonHard-VacuumRectifierValves

aMullarddidnotspecifyC(max)fortheGZ37,butia(pk)=750 mAforboththeGZ34andGZ37,soC(max)=60 μFmaybeassumed.

bPerdiode,afull-waverectifierwoulddoublethisvalue.

IDC(max)(mA) Rseries(Vout=300 V)(Ω) C(max)(μF) Iheater Vheater(V)

EZ90/6×4 70 520 16 600 mA 6.3EZ80/6V4 90 215 50 600 mA 6.3EZ81/6CA4 150 190 50 1 A 6.3GZ34/5AR4 250 75 60 1.9 A 5

GZ37 250 75 60a 2.8 A 5

6CL3/6CK3 250b – – 1.2 Ab 6.3

PY500A 440b – – 300 mA 42b

TheunpopularEZ90isonlyreallysuitableforpre-amplifiersbutisverycheap.EZ80andEZ81arecheapandareidealforpre-amplifiersorsmallmonopoweramplifiers.NewOldStock (NOS)MullardGZ34 and even the current-hungryGZ37arenowscarce,inflatingprices.Apairof6CL3/6CK3isfarcheaperthanaGZ34–anddon’t forget theevencheaper12CL3/12CK3,but thepricepaidfortheirhigherratingsisincreasedheaterpowerconsumption.ThePY500Ahasto be used carefully because its peak current rating is lower than might beexpected.Indirectlyheatedrectifiers(EZ8*andEZ9*series)aredesignedtooperatefromthesame6.3 Vheatersupplyasthesignalvalves,butthismeansthatVhk≈300V,whichappliesseverestress to theheater/cathode insulation, implyingnoisecurrentsfromtherectifier’scathodeintothegroundedcommonheatersupply.Iflow heater noise is paramount, we could transfer the stress from the fragileheater/cathode insulation to themore robustmains transformer by providing adedicatedrectifierheaterwindingtiedtotherectifiercathode,sotheGZ3*seriesforcesthisdesigndecisionbyinternallytyingtheindirectlyheatedcathodetotheheater.Hardvacuumvalve rectifiershaveonlyoneclearadvantageoversiliconvalverectifiers,butthisadvantagemaybesufficienttomakeustoleratetheirfoibles.Thewarm-uprisetime(timetakentochangefrom10%to90%)oftheiroutputvoltage when fully loaded ≈5 s, which greatly reduces the inrush current toelectrolytic capacitors in comparisonwith semiconductor rectifiers (see Figure5.3).

Figure5.3GentleriseofHTsuppliedbyEZ81rectifierwith120-mAload.

Devotees of hard vacuumvalve rectifiers point out that the valve switches onandoffmorecleanlythansiliconvalverectifiers,thusexcitingfewerresonancesin the power supply, but the author’s experience is that both types of rectifierproduce switching spikes, and it is the smoothing/snubbing arrangements thatareimportant.Ifthereisanimprovementduetovalverectifiers,itismorelikelybecauseoftheirenforcedlowripplecurrent.Whichever rectifier topologywe choose, wemust ensure that it is capable ofwithstanding the stresses imposed upon it by the surrounding circuit. Whenconsidering low-frequency rectification derived from themains,we need onlyspecifythevoltageandcurrentratings.However,neitheroftheseratingsisquiteasstraightforwardasitmightseem(seeFigure5.4).

Figure5.4Effectofcapacitoronrectifierratings.

Thediagramshowsa centre-tapped rectifier using silicondiodes to rectify the300–0–300 V RMS secondary. The off-load voltage at the reservoir capacitorwillbethepeakACvoltagelessdiodedrop:

Note that this ismuch higher than if a valve rectifier had been used – silicondiodesandvalverectifiersarenotdirectlyinterchangeable,althoughforashortperiodsolidstateplug-inreplacementsweremade(seeFigure5.5).

Figure5.5Solid-stateplug-inreplacementforvalverectifier.

Thediodevoltageratingthatconcernsusisthereversevoltagerating,knownasVRRM (Reverse Repetitive Maximum), also known historically as PIV (PeakInverseVolts).Agoodsafetyfactortoallowformainsspikesistwicethepeakincomingvoltage,whichiswhythe5 A1,200 VSTTA512Fsilicondiodeissousefulforvalveelectronics(Table5.2).

Table5.2ComparisonofDiodeVRRMRatingsNeededforFull-WaveRectificationDioderating(VRRM/VRMS) Vf

Centre-tapped 2√2 1Bridge √2 2

When rectifyinghighvoltages, thecentre-tapped rectifierhas thedisadvantagethat it needs diodes havingdouble theVRRM rating.As an example, a 300–0–300-V transformer with centre-tapped rectifier would require diodes having

VRRM>849 V,butasingle300 Vwindingplusbridge rectifiercouldproducethesameoutputvoltage,andwouldonlyrequirediodeshavingVRRM>424 V.ItiscomparativelyeasytomanufactureahardvacuumrectifierwithahighVRRMrating,socentre-tappedrectifierstendtobevalve,whereasbridgerectifierstendtousesilicon.Wecanstack‘n’silicondiodesinseriestomultiplyVRRMby‘n’ifnecessary,but unmatched diode ‘off’ capacitances could cause one diode’s VRRM to beexceeded, causing failure. This problem can be avoided by adding a parallelcapacitanceof about10 times thediode’s low-voltage ‘off’ capacitance acrosseach diode so that individual reverse voltages are defined by the (perhaps 5%tolerance) external capacitor rather than the (rather looser) internal diodecapacitance. Thus, the 1,200 V STTA512Fwould require a 4.7 nF 1,200 Vfilmcapacitortoswampits≈600 pFlow-voltage‘off’capacitance.Although most popular in valve electronics, the centre-tapped rectifier isoccasionally useful in low-voltage/high-current silicon circuits because of thelowerforwarddiodedrop;only1 Vf,comparedto2 Vfforthebridge.Valves such as GZ34, EZ81, EZ80, etc. that are intended for use in centre-tapped rectifiers naturally require a centre-tapped transformer, but a hybridvalve/semiconductorrectifiercircumventsthisproblem[1](seeFigure5.6).

Figure5.6Hybridvalve/semiconductorrectifier.

When the diode feeds a reservoir capacitor, current pulsesmany times greaterthantheDCloadcurrentflow.Fortunately,modernsilicondiodesaredesignedwith thesepeaks inmind,andit isusuallysufficient tochooseacurrentratingforeachdiodeequaltotheDCloadcurrentdividedbythenumberofpolaritiesused.Thus full-wave rectificationallowsahalvingofdiode ratingbecause theload current is shared between the diodes of the two polarities, whereas half-waverectificationforcestheloadcurrenttobesuppliedfromasinglediode.Ifyou are lucky enough to have three-phase mains (Germany), you can further

dividebythenumberofphases,allowingsix6CL3/6CK3todeliver1.5 A.

RectifiersToBeAvoided(Gas)

Thefirstgasincommonusagewas(poisonous)mercuryvapour[2],butitwassupplanted by xenon (a noble gas, and therefore non-poisonous).Despite this,the soft blue glow of mercury vapour rectifiers has recently become mildlyfashionable.Because the valve is filledwith a lowpressure gas, as an electron acceleratesawayfromtheheatedoxide-coatedcathode,itislikelytostrikeagasmolecule,displacing a second electron. The two electrons accelerate towards the anode,andtheprocessrepeats.Itiseasytoseethatthisprocesscouldoccurmanytimesbeforetheanodecapturesalltheelectronsgeneratedbyasingleelectronleavingthecathode.Thismechanismofgasamplification reducessloperesistanceandforwarddropcomparedtohard-vacuumrectifiers,makingthemusefulathighercurrents.Rectificationreliesonvapour,yetmercuryvapourquicklycondensesasmetallicdroplets,soitmustbeevaporatedbytheheaterandthecorrectvapourpressurereachedbeforeHTcanbesafelyapplied,asshowninTable5.3.

Table5.3DelaysNeededbyMercuryVapourRectifiersPre-HeatTime Ediswan[3] Mullard[4]

Afterstorage/mechanicaldisturbance >15 min >30 minDay-to-day >60 s >60 s

Toavoidflashback,mercuryvapourrectifiersaretypicallyonlyratedtooperatebetween20 °Cand60 °C,althoughsomecanonly tolerate≤50 °C, soa fancouldbeneededtodispersehotairfromothercomponents.Unfortunately,gasamplificationisnotentirelyabonus.Eachgasmoleculethatreleasesanelectronbecomesapositivelychargedionandisacceleratedtowardsthecathode,whereuponitisdischargedbyanelectron.Buteventhelightestgasionconsistsof aproton (1,836 times themassof anelectron), sogas ions areslow,andmorecomplexionsareheavierandslower.Imagineanelectronstrikingagasmoleculeclosetothesurfaceoftheanodeanddisplacing an electron so that the two electrons almost immediately reach theanode,buttheionstillhastoreachthecathodetobedischargedbyanelectron.Thus,anychangeinVathatwouldswitchavacuumvalveoffisdelayedbythetransit time of gas ions from anode to cathode because these ions determinewhenthelastelectronisemittedfromthecathode,sogasvalvesswitchofffarslower than they switch on due to the charge storage caused by the lowermobilityoftheheavyions.

One practical consequence of the slow switch-off or current overshoot of gasvalves is that theyare likely tooscillate if the anode lead isnot snubbedwithlossyferritebeadsorRFchokes,andtheymayneedtobeenclosedbyametalscreeningcan.Thebestwaytodetectoscillationisnotwithanoscilloscope,butbymovinganAMradionearbyandlisteningforabuzzastheradioapproachestherectifier.As Table 5.4 shows, mercury vapour rectifiers exhibit most of the nastierdisadvantagesofsiliconandvalvesthenaddsomeuniquelytheirown,buttheydoproduceaprettyblueglow.Ifabsolutelynecessary,perhapsanequallyprettyeffectcouldbeobtainedbyfittingablueLEDinthebaseofa6CK3/6CL3?

Table5.4SummaryofMercuryVapourRectifierFeaturesDisadvantages Advantages

Mercuryvapourispoisonous PrettyblueglowThat(poisonous)mercuryvapouriscontainedbyafragileglassenvelope SloperesistancecomparabletosiliconNeedsheatersupplyNeedsdelaybeforeHTcanbesafelyappliedChargestorageduetoslowionsmaycauseoscillationLimitedtemperaturerangeThatprettyblueglowincludesultravioletlight,whichcandamageeyesight

RectifiersToBeAvoided(Selenium)

The author recently had the dubious privilege of testing an InternationalRectifier E150L 130 V 150 mA selenium rectifier. (Note that this is anAmerican device, so the similarity to European Pro-Electron numbering ispurely coincidental.) The device begins to turn on at about 4.5 V but has aforward drop of 15.8 V at its rated current of 150 mA; this is slightly betterthananEZ81(valve)at thesamecurrent(19.8 V),but theEZ81has10timesthereversevoltagerating!Thereversecurrentisbestnottalkedaboutinpolitecompany;7.92 mAat100 V implies≈10 mAat the ratedvoltageof130 V(seeFigure5.7).

Figure5.7E130Lseleniumrectifierforwardcurrentforappliedforwardvoltage.

Thesedevicesarerecognisablebythesquarefinsneedednotjusttodissipatethepowerwasted inforwardmode– thepowerdissipatedwhen thedeviceshouldbeoffisalsosignificant(10 mA×130 V=1.3 W!).Selenium rectifiers fail short-circuit and cause wholesale smelly destructionwhentheydoso.Takethemoutbeforetheytakeoutthemainstransformer,butbeware that their replacement will almost certainly need some added seriesresistancetomaintaintheoriginaldesignvoltage.

RectifiersToBeAvoided(CopperOxide)

Theforwardcharacteristicsofcopperoxideareonlyalittleworsethanthoseofsilicon, which is why they were used for low voltages.When tested, reversecurrentofaWB1/6 Arectifierwas10 μAat0.5 Vbutroseto1.14 mAat60V,notquiteasalarmingasselenium,butalongwayfromsilicon.Copperoxiderectifiers arenotoften seenbut look like a collectionof stackedwasherson acentralscrew.

RFInterference/Spikes

Rectifiersareswitches.Althoughthefollowingargumentimpliesaresistiveloadon the rectifier, the results are also valid for the loadpresentedby a reservoircapacitor.As the inputACwaveformrises through0 V,oneormorediodeswill switchon,andstayswitchedonuntilthewaveformfallsthrough0 V,whentheother

diode,ordiodes,switchon.Alldiodesneedaminimumforwardbiasbeforetheycan conduct, even if it is only the 0.7 V required by silicon.Thismeans thatthere is a dead zone symmetrically about 0 Vwhere no diodes conduct. Thetransformer,which is inductive,hasbeenswitchedoff, and it tries tomaintainthecurrent flow,but indoing so, it generates a spikeofElectroMotiveForce(EMF):

Fortunately, diodes don’t switch quite as abruptly as postulated and there areusuallyplentyofstraycapacitanceswithinthetransformertopreventthisEMFfromrisingveryfar,butifweareunlucky,theshockappliedtothesystemcanexcite a resonance resulting in a damped train of oscillations. Using a searchcoil,theauthoronceobserved100 Hzrepetitionrateburstsof200 kHzleakingfromamainstransformerforthisveryreason.Happily,theproblemcanusuallybe cured by bypassing each individual rectifier diode with a 4.7 nF filmcapacitor having a voltage rating equal to the diode VRRM rating. Veryoccasionally it may be necessary to add a series resistor to each snubbingcapacitortopreventringing.Whetherweuseabridgerectifieroracentre-tappedrectifier,westillapplythesamewaveformtothesucceedingcircuit.Thewaveform,althoughitisofonlyonepolarity, isnotasmoothDC.The functionof thesmoothingelement is toreducetheripple,eithertoasatisfactorylevel,ortoalevelsuchthataregulatorcancopewithit.

TheSingleReservoirCapacitorApproach

The simplest way of smoothing the output of the rectifier is to connect areservoircapacitoracrossit,andfeedtheloadfromthisreservoir(seeFigure5.8).

Figure5.8Powersupplyusingreservoircapacitor.

Assumingnoloadcurrent,thecapacitormustchargetothefullpeakvalueoftheACleavingthetransformer(Vsec×√2).

RippleVoltage

Theoutputoftherectifiertopsupthechargeinthecapacitoreverycycle,sothatatthepeakofthewaveform,thecapacitorisfullycharged.Thevoltagefromthetransformer then falls away sharply, so the rectifier diodes switch off. Loadcurrent is now supplied purely from the capacitor, which dischargesexponentially into the (assumed resistive) load until the transformer outputvoltage rises sufficiently to recharge the capacitor and restart the cycle (seeFigure5.9).

Figure5.9Ripplevoltageacrossreservoircapacitorcausedbycharge/dischargecycle.

Althoughthereservoircapacitor theoreticallydischargesexponentially, foranypracticalvaluethedischargecurvemaybetakentobeastraightline.(Iftheloadis a series regulator, the discharge curve truly is a straight line because anycircuit that supplies a constant load current with a regulated constant voltagewith negligible wasted current must be a constant current sink.) Given thisapproximation,itiseasytocalculatewhattheoutputripplevoltagewillbe.Thechargestoredinacapacitoris:

Thetotalcharge,duetoacurrentI,flowingfortimetis:

Wecancombinetheseequations:

Rearranging:

This equation gives the voltage change on the capacitor due to the capacitor

supplyingcurrentI,fortimet.Ifmainsfrequencyis50 Hz,theneachhalf-cycleis 0.01 s. If we nowmake another approximation, and say that the capacitorsuppliescurrentallofthetime,thent=0.01 s.Wenowhaveausefulequation:

It might be thought that this equation is of little use, since two sweepingapproximationswere used to derive it, but as the reservoir capacitor is nearlyalwaysanelectrolyticcapacitor,whosetolerancecouldbe±20%,wewouldneeda very inaccurate equation before it approached the error introduced bycomponenttolerances!WecannowcalculatetheripplevoltageattheoutputofourexamplecircuitinFigure5.8,whichhada68 μFcapacitorandaloadcurrentof120 mA:

whichisabout5%offullvoltage,agooddesignchoice.Thepreviousmethodproducessensibleresultsprovidedthattheripplevoltageisbetween5%and20%ofthetotalvoltage(itisunusualtoallowripplevoltagetoriseabovethislimit).

TheEffectofRippleVoltageonOutputVoltage

Thereservoircapacitorchargestothevoltagepeaksleavingtherectifier,sotheripplevoltageissubtractedfromthisandreducestheoutputvoltage.TheoutputvoltageVoutcanbeconsideredtobemadeupoftwocomponents:VDCwhichispure DC and Vripple which is the superimposed AC ripple voltage. ThesignificanceofmakingthisdistinctionisthatsubsequentfilteringblockstheACcomponenttoleaveonlytheDCcomponent.

TheACripplevoltageswingssymmetricallyaboutVDCand,atitspositivepeak,reachesVpeak,therefore:

Consideringourpreviousexample,whichhadVripple=18 VandVpeak=325 V,theDCvoltagethatwouldbeseenaftersubsequentperfectACfilteringwouldbe:

Summarising,VDCisalwaysreducedbyafactorofhalftheripplevoltage.

RippleCurrentandConductionAngle

Now thatwehave looked at ripple voltage,weneed to look at ripple current.Thisisthecurrentrequiredbythecapacitortofullyrechargeiteveryhalf-cycle.Todothis,weneedtofindtheconductionangle,whichisthehalfportionofthecycle forwhich the diodes are switched on and the capacitor is charging (seeFigure5.10).

Figure5.10Determinationofconductionanglefromripplevoltage.

Todothis,weworkbackwardsfromthetimethatthecapacitorisfullycharged.Weknowtheripplevoltage,sowecanfindtheabsolutevoltageonthecapacitorattheinstantthatthediodesswitchon.Theinstantaneousvoltageattheoutputoftherectifier(ignoringthepolarity)is:

Attheinstantthatthediodesswitchon,thecapacitorvoltagemustbe:

Rearranging:

Ifwenowputsomefiguresintothisequationfromourearlierexample(Figure5.8),rememberingtoworkinradians,andnotdegrees:

Notethat50 Hzwasusedintheaboveequationdespitethefactthatfull-waverectification of 50 Hz produces 100 Hz ripple. The reason is that full-waverectificationsimplyinvertsthepolarityofalternatehalf-cycles,sotheshapeandtimingofeachhalf-cyclepertainstotheoriginalACfrequency.Thecapacitordrawscurrentfromthemainstransformeronlyfor1 msinevery10 ms, or 10%of the time.We should therefore expect this ripple current toconsistofshort,highcurrentpulses(seeFigure5.11).

Figure5.11Ripplecurrentwaveform.

Wecannowfindtheripplecurrentusingtherelationship:

ButweneedanexpressionfordV/dt,sowestartwithouroriginalexpression:

Differentiating:

Andsubstituting:

Ifwenowputsomevaluesintothisequation:

whichisafactorof18greaterthanthe120 mAloadcurrent!Quickcheck:Chargeisequaltocurrentmultipliedbytime,whichwouldbeareaonagraphofcurrentagainsttime.Ifthecapacitorhastochargeinatenthofthetimethatittakestodischarge,thenitisreasonabletosupposethatitwillrequire

10 times thecurrent (Q= It).Thisbringsus to1.2 A.However,weobservedearlier that the shapeof the chargingpulse isnot rectangular, andbecause theareaunderthispulseissmallerthanthatofarectangleofequivalentheightandwidth,thisaccountsforthefinaldifferenceinthetwoanswers.Summarising,theanswerisunexpectedlylarge,butbelievable.Inpractice,peakripplecurrentisreducedby:•Transformercoresaturation• Series resistance made up of diode slope resistance, capacitor EffectiveSeriesResistance(ESR),wiringresistanceandtransformerwindingresistance(secondaryandreflectedprimary).

Asaresultofthesefactors,peakripplecurrentistypicallybetweenfourandsixtimes theDC loadcurrent.Asameasuredexample, a transformerwith siliconbridge rectifier and capacitor input filter producing 108 V DC loaded by aresistordrawing35 mADCdrewIripple(pk)=160 mA,aratioof4.6:1.Valve rectifiers have far higher internal resistance than silicon rectifiers andusually need additional series resistance in deference to their limited ripplecurrent ratings, so their ratio of Iripple/ IDC is even lower. A DC 50 MHzTektronix TCP202 current probewas used to investigate a 300 VHT powersupplyusingaGZ34tofeedits47 μFpolypropylenereservoircapacitorandtheload current of 88 mA DC caused Iripple(pk)=340.3 mA, a ratio of 3.9:1 (seeFigure5.12).

Figure5.12Capturedreservoircapacitorwaveformsdueto88 mAloadcurrent.Uppertrace(Ch1):currentwaveform(Ipk=340mA).Lowertrace(Ch2):ripplevoltage(13 Vpk–pk).

Theripplecurrentpulsescontainharmonicsof100 Hzthattheoreticallyextendinto low RF. Fast Fourier Transform (FFT) mode was selected on theoscilloscope,allowingspectrumanalysisofthereservoircapacitorripplecurrent(seeFigure5.13).

Figure5.13Spectrumofreservoircapacitorripplecurrent.

The spectrum sweeps linearly from DC (left) to 1.25 kHz (right), so thedominant 100 Hz fundamental can be clearly seen, followed by a train ofharmonics.Althoughthe20μA/divlinearverticalscaleofthisFFTimpliesthattheharmonicsdieawayrapidly, logarithmicscalingrevealed thatharmonicsat2.5 kHz were only 45 dB below those at 100 Hz. Audio engineers mightcomplainaboutmainsnoise,buttheirpowersuppliesarenotinnocent.

TransformerCoreSaturation

Toroidaltransformersaremoresusceptibletocoresaturationasadirectresultoftheir more nearly perfect magnetic design. Whether mains or audio, powertransformer cores are normallymade ofGrainOrientedSiliconSteel (GOSS),whichhastheadvantageofallowingahigherfluxdensityinthedirectionofthegrain.TraditionalstackedEIcoresareunabletotakefulladvantageofthis,sincethereisalwaysaregionwherethefluxisatrightanglestothegrain,butCcores

and toroidshaveall their fluxalignedwith thegrainandcanoperatecloser tosaturation (permitting a smaller core), so this is why toroids are smaller andcheaper.Consequently, toroidssaturatesharply,whereasEIcoreshaveamuchgentlerlimit.Transformercoresaturationisundesirablebecauseitreleasesaleakagefieldofmagneticfluxtoinducecurrentsinnearbycircuitry.Evenworse,thissaturationhappenscyclically(100 Hzor120 Hz)andsoproducesburstsofinterferencewith harmonics extending to radio frequencies. Sharper saturation produces agreaterproportionofhigherharmonicsintheleakagefield.Thisisnotmerelyanapocryphaltaleofwoe.Manyyearsago,theauthortorehishairoutsearchingforthesourceof(video)huminapicturemonitor,onlytofindthatthecausewasasaturatingmainstoroidinducinghumdirectlyintotheneckofthepicturetube.

ChoosingtheReservoirCapacitorandTransformer

Ifwehavedesignedoursupplytohavearipplevoltageof5%ofsupplyvoltage,then for 90% of the time the transformer is disconnected, and the outputresistanceof thepower supply is determinedpurelyby the capacitorESRandassociated outputwiring resistance. This iswhy changing reservoir capacitorsfrom general purpose types to high ripple current types produces a noticeableeffectonthesoundofanamplifier;theyhavealowerESR(butahigherprice).The transformer/rectifier/capacitor combination is a non-linear system. ThismakesitsbehaviourconsiderablymorecomplexthantheidealThéveninsource,soweneedtoinvestigateitoverdifferentperiodsoftime.In the short term (less than one charging cycle), the output resistance of thesupplyisequaltocapacitorESRpluswiringresistances.Thiswillbetrueevenfor very high current transient demands,whichmay appear in each and everychargingcycle,providedthattheydonotsignificantlydepletethechargeonthecapacitor.Allthatisrequiredisthatthecapacitorshouldbeabletosourcethesetransientcurrents.Tobeabletodothis,thecapacitorneedsalowESR,notjustatmainsfrequencies,butalsoup toat least40 kHz,becauseaClassBpoweroutputstagecausesarectified(andthereforefrequencydoubled)versionoftheaudiosignaltoappearonthepowersupplyrails.(SeeChapter6forexplanationofClassB.)Wecancopewiththisrequirementbyusinganelectrolyticcapacitordesignedforuseinswitchedmodepowersuppliesasthemainreservoir.A power amplifier may significantly deplete the charge in the reservoircapacitor, causing output voltage to fall either by drawing a sustained highcurrent,duetoacontinuousfullpowersine-wavetest,orbyreproducingashort,

butloud,sound–suchasabassdrum.Supplyingaconstantloadisrelativelyeasy,becauseweknowexactlyhowmuchcurrentwillbedrawn,andwesimplydesignforthatcurrent.Iftheripplevoltageforasensibleripplecurrentishigherthanwewouldlike,thenwesimplyaddaregulatortoremoveit.Thedifficultiesstartwhenwewanttosupplyachangingload.Itmightseemthatifthepoweramplifierisratedat50 Wcontinuousinto8 Ω,thenallwehavetodoistocalculatewhatloadcurrentthatimplies,anddesignforthatcurrent.Thedrawbacks of this approach are more easily demonstrated using a transistoramplifier,where the load isdirectlycoupled to theoutputstageand thepowersupplyisverysimple(seeFigure5.14).

Figure5.14Typicalpowersupplyfortransistoramplifier.

Consideringour50 W8 Ωexample:

Therefore,forasinewave:

Butwehavetosupplythepeakcurrent,whichis√2greater,at3.5 A:

But we have to supply the peak voltage, which is √2 greater, at 28.3 V.Transistor amplifiers can typically swing towithin about a volt of rail, sowemightjusttolerate±29 Vrails,andapowersupplycapableofdelivering±29 Vat3.5 Aisimplied.Wethereforeneed203 Wperchanneland406 Wfora50Wstereoamplifier!This is avery large andexpensivepower supply, andwewouldneedsomeastonishinglygoodreasonsforusingit.Thekeytotheproblemlies intheclassof theoutputstage.If theoutputstageoperatesinClassA,thenthequiescentcurrentequalsthepeakcurrentrequiredatmaximumpoweroutput,inthiscase,3.5 A.Ifeachchannelgenuinelydrawsaconstant3.5 Afromthe±29 Vpowersupply,thenwereallydoneedthe406Wpowersupply.TheclassicKrellKSA5050 Wstereoamplifierdrew300 Wfrom themainsat idle [5] , suggesting that itwasn’tquite trueClassA,but itwascertainlyfarcloserthanmostClassApretenders.The reservoir capacitor valuewas easy to determine using our earlier formulaand5%ripplevoltagecriterion,butthetransformerisquiteadifferentmatter.Itis possible todetermine the requirementsof the transformer exactly, using thegraphsoriginally devisedbySchade [6] . In practice, the required transformerinformationmaynotbeavailable,soapracticalruleofthumbistomaketheVAratingofthetransformeratleastequaltotherequiredoutputpower.Ifourexamplestereo50 WamplifieroutputstagebecomesClassB,theneachchannel still supplies 3.5 A to the load on the crests of the sinewave, but atother points in the cycle the required current from the power supply ismuchlower.Theeffectofthereservoircapacitoristoaveragethefluctuatingcurrentdemand,andforafull-waverectifiedsinewave:

Theaveragesupplycurrentis2.2 A,soa250 VAtransformerwouldbechosen.Wecouldfurtherarguethattheamplifierdoesnotoperateatfullpowerall thetimeandthattheshorttermmusicalpeaksrequiringmaximumoutputpowerdonotlastlong.Asmallertransformercouldthereforebeused,sincethereservoircapacitorcouldsupplythepeakcurrents.Thisisaveryseductiveargument,andmanycommercialamplifiermanufacturershavebeenpersuadedby it, since£1extraoncomponentcostgenerallyadds£4–5totheretailprice.We do not have to work to such tight commercial considerations and, withinreason,thebiggerthemainstransformer,thebetteritis.

Back-to-BackMainsTransformersforHTSupplies

Thisideapopsupfromtimetotimeasacheapwayofobtainingthehighvoltageneeded for the HT supply. As an example, a 240 V:6 V mains transformerprovides 6 V to the valve heaters (5% low, but perhaps tolerable) and anidentical240 V:6 Vtransformerisconnectedwithits6 Vwindingacrossthefirsttransformer’s6 Vwinding,withtheintentionofproducinganisolated240V to be rectified for the HT. If transformers were ideal, then using onetransformer to step down followed by another to step up would be fine.However…Thefirstproblemis thatapractical240 V:6 Vtransformerdoesnothave the40:1turnsratioexpectedofanidealtransformer.Thetransformermanufacturerknows that therewill be resistive losses in the primary and secondary, so theturns ratio is reduced toensure that the ratedsecondaryvoltageappearsat fullload current. Transformers having a low VA rating invariably have poorregulation.Regulationisdefinedas:

Very small transformersmay have regulation as bad as 20%. In otherwords,their turns ratio has had to be reduced by 20% to ensure that they deliver therated secondary voltage at full load current. Thus, our example 240 V:6 Vtransformermightactuallyhaveaturnsratioof32:1,sowhenwetrytostep6 Vbackupto240 V,weonlyget192 V.Worse,that192 Vistheoff-loadvoltageandfallsby20%atfullloadcurrent,soinsteadofseeing192 V,wewouldonlysee154 Vatfullloadcurrent.The second problem is to dowithmagnetising current. Although the ratio bywhicha transformerstepsup(orstepsdown)avoltageisdictatedbythe turnsratio betweenprimary and secondary, this implies that so long as youhad theright ratio, you could use as many or as few turns as you liked. Imagine atransformerwitha secondarynotconnected toanything. If the secondary isn’tconnected to anything,we can simply throw it away.We are now leftwith achoke across the mains having a reactance (due to the transformer’s primaryinductance):

Wehaveavoltageacrossthisreactance,soacurrentmustflowthatisinverselyproportional to the reactance (V/XL= I), and this is generally known as themagnetising current. Inductance is proportional to the square of turns, so themoreturnswehaveontheprimary,thehigherthereactance,andthelowerthemagnetisingcurrent.Thekeyissueisthatthehigherthemagnetisingcurrent,the

morepoweriswastedasheatinthewireandthecore.It might seem that the ideal would be to use as many turns as possible tomaximise primary inductance and thusminimisemagnetising current, but thinwirehasahigherresistanceandwouldcausehigherresistivelosseswhenaloadcurrent was drawn. Thus, the primary inductance of a transformer must be acarefulbalanceofanumberoffactorstomaximiseefficiency.Large transformers (anything bigger than a domestic washing machine) arecarefullydesignedtobe>99%efficient,butsmalltransformersaredesignedtobecheap.Theupshotisthatasmalltransformermightbesoinefficientanddrawsuchalargemagnetisingcurrentthatconnectingtwotransformersback-to-backcouldoverloadthefirstsimplyduetothemagnetisingcurrentofthesecond.The author used a Tektronix P6302 50 MHz current probe and associatedAM503amplifierconnectedtoaTDS3032oscilloscopetomeasuretransformermagnetisingcurrentfrom240 VRMSmains.A30 VAtoroiddrewanegligiblemagnetisingcurrentof1.5 mARMS(albeitverydistorted),whereasa20 VAEIdrew a magnetising current of 24 mA RMS – equivalent to 5.8 VA. Thus,althoughthetoroidwouldbeeminentlysuitableforback-to-backconnection,apairoftheEItransformerswouldreducethefirsttransformer’sVAratingto14VA.Thesituationbecamefarcicalwithaverysmall6 V250 mA(1.5 VA)EItransformer that drewaverydistortedmagnetising current of 19.6 mARMS –equivalentto4.7 VA,soback-to-backconnectionofapairofthesetransformerswouldgrosslyoverloadthefirst(seeFigure5.15).

Figure5.15Highlydistortedmagnetisingcurrentdrawnby1.5-VAtransformer.

Summarising, connecting transformers back-to-back might appear to beconvenient, but it relies on the second transformer having a lowmagnetisingcurrent(suggestingatoroid)toavoidoverloadingthefirst transformer,andtheoutputvoltagewillalwaysbesignificantlylowerthanmainsvoltage.Ifyouonlyneeda small current,betterqualitybathroomstrip lights includea≈20 VAsplitbobbinisolatingtransformerfortheirshaversocket,andthisisamuch better solution. When measured, the turns ratio of such a 20 VAtransformersteppedupby1:1.09 inorder toovercomeits full load losses,andtheratioofthewindingresistanceswasidentical,implyingthatthesamegaugeofwirewasusedforprimaryasforsecondary.Thisimpliesthatifyouwantedavoltage lower than 240 V, this split bobbin transformer could safely have itsprimary and secondary interchanged so that instead of the turns ratiocompensatingforlosses,itwouldstepdowntogive≈200 Vatfullloadcurrent.

VoltageMultipliers

Sometimes the mains transformer we are forced to use can’t produce a highenoughvoltage, andoneof the cheapest andmostpopularwaysofgeneratinghigh voltages at relatively low currents is the classic diode/capacitor voltagemultiplier.Multipliersaremostcommonwhereaconstantandnegligiblecurrentisrequired,suchasthepolarisingbiasrequiredbyelectrostaticloudspeakers(≈5kV).

The voltage multiplier was invented [7] in 1920 by the Swiss physicist H.GreinacherforpolarisingionisationchambersandaSwisspatent[8]grantedin1922,butnobodyseemedtotakemuchnotice.However,10yearslaterin1932,J.D.CockcroftandE.T.S.Waltonpublishedapaper[9]describingtheuseofa125 kV voltagemultiplier identical toGreinacher’s for accelerating hydrogenions to split the lithium atom’s nucleus. Perhaps the glamour of splitting theatommeant that thepatentexaminerswerenotasdiligentas theyshouldhavebeen,forCockcroftandWaltonweregrantedUK[10]andUS[11]patentsforthe multiplier. Certainly, splitting the atom later won them the 1951 Nobelphysics prize, and the attendant voltage multiplier has become incorrectlyassociatedwiththem.Themultiplier,oftenknownasaladderorcascode,canbeextendedindefinitely,witheachsteptheoreticallyadding√2 Vin(RMS)totheoutput,butitsregulationisvery poor.Each diode needs a voltage rating>√2 Vin(RMS).Unfortunately, allbut the lowestcapacitormustberatedat>2√2 Vin(RMS).Additionally,becausesucceeding capacitors are charged by rectifier switching that partly dischargesthelowestcapacitor, thiscapacitormustbeofahighervaluetoreducevoltagedrop(seeFigure5.16).

Figure5.16Greinachervoltagemultiplier.

AlthoughvoltagemultiplierswereinitiallyusedforgeneratingEHT,theycanbeusefulforprovidingnegativegridbias,andthediminutiveRogersCadetstereopower amplifier even used a voltage doubler for its main HT. There are twoforms(seeFigure5.17).

Figure5.17Non-floatingandfloatingvoltagedoublers.

The non-floating doubler is a truncated Greinacher multiplier. It can beconnected in parallel with a conventional centre-tapped rectifier/transformercombination allowing a subsidiary (higher voltage) HT to be developed –perhapsforpolarisingadedicatedhigh-frequencyelectrostaticloudspeaker.The advantage of the floating doubler is that it uses two identical capacitors,each rated at half the output voltage, but the diodes must be rated at >2√2Vin(RMS).Becauseeachcapacitorisonlychargedonalternatehalf-cycles,ripplevoltage isdoubledcompared toaconventional full-wave rectifier.Because theripplevoltagesof the twocapacitors are in series, a furtherdoublingof ripplevoltage occurs. Thus, for a given ripple voltage, the floating doubler requireseachcapacitortohavefourtimesthecapacitanceneededbyaconventionalfull-waverectifier.

TheChokeInputPowerSupply

Chokeinputpowersupplieswereverypopularintheheydayofvalveamplifiersbecauseeveniflargevaluecapacitorshadbeenavailable,theripplecurrenttheywouldhavedrawnwouldhavedestroyedtherectifiersofthetime,sochokeshadtobeusedforsmoothing(seeFigure5.18).

Figure5.18Chokeinputpowersupply.

Ifwecouldmakeachokeinputsupplyhavingachokeofinfiniteinductance,themains transformer currentwouldbe identical to theDC loadcurrent.Practicalsupplies do not quite achieve this ideal, so the transformer current is acombination of DC load current and a somewhat smaller, nearly sinusoidalcurrentdrawnbythechoke.Nevertheless,thechokeinputpowersupplyhasthegreat advantage that it draws a very nearly continuous current from themainstransformerratherthanaseriesofhighcurrentpulses.Tounderstandwhythisisso,weneedtoconsidertheoutputwaveformoftherectifierindetail(seeFigure5.19).

Figure5.19Full-waverectifiedACsinewave.

Thiswaveformisafull-waverectifiedsinewave,butbecauseithasundergoneanon-linear process (rectification), the frequencies present in thiswaveform arenotthesameaswentintotherectifier.Fourieranalysisrevealsthattheresultoffull-waverectificationofasinewaveis:

NotethatVin(RMS)isthevoltagebeforerectification.Thepreviousequationisamathematicalwayofexpressinganinfiniteseries,butforourpurposesitissimplertopresenttheinformationasfollows:

This shows us that a full-wave rectified sine wave is made up of a DCcomponent corresponding to 0.90 Vin(RMS), plus a series of decaying evenharmonicsoftheinputfrequency(f)beforerectification.ThechokehassuchahighreactancetotheseACtermsthatonlytheDCcomponentreachestheload.The output voltage of a choke input power supply is therefore 0.90 Vin(RMS),ratherthan√2 Vin(RMS)forthecapacitorinputsupply.

MinimumLoadCurrentforaChokeInputSupply

Chokeinputpowersuppliesrequireaminimumloadcurrenttobedrawnbeforethey operate correctly. If less than this current is drawn, the circuit reverts topulsechargingofthecapacitor,andtheoutputvoltagerisestoamaximumof√2Vin(RMS).Theabsoluteminimumcurrentthatshouldbedrawnis:

In practice, the inductance of any power supply choke varieswith the currentthrough it, so it is wise to draw rather more current than this, and a handyapproximation(appropriatefor50 Hzor60 Hzmains)is:

Choke input supplies invariably feed a capacitor, and the minimum currentrequirement is therefore important, since insufficient current could cause thevoltageacross thecapacitor to rise to≈157%ofnominalvoltage,whichmightdestroy it. The traditional way of dealing with this problem was to use aswingingchoke,whosesmallairgapcausedhighinductanceatlowcurrentsthatfell as current increased, and although these became unfashionable after the1960s,theyhavereturned–justlikeflaresandplatformshoes.Once the minimum current has been exceeded, the output ripple becomesconstant with load current and because for any practical power supply filter,XL>>XC, the simple potential divider’s attenuation can be approximated to aratio:

whereω=2πf.Ifweconsiderthatonlytheamplitudeofthesecondharmonicissignificant,wecan incorporate its 0.6 factor from the Fourier series we saw earlier anddeterminethepeakripplevoltage:

Itismoreusualtoworkwithpeak-to-peakripplevoltages(becausethey’remucheasier tomeasure on an oscilloscope), and thewaveform is sinusoidal soVpk–pk=2 Vpk:

IfwenowchangetheequationtoacceptcapacitancedirectlyinμFandinclude100 Hzor120 Hzripplefrequencies:

where L is in H, C in μF and Vin(RMS) is the mains transformer secondaryvoltage.Strictly,thefactorof2inthe60 Hzapproximationshouldbe2.1,butitis not unusual for an iron-cored choke’s inductance to vary by 50% or moredependingonDCandACcurrent,andthetoleranceofanelectrolyticcapacitoris likely to be ±20%, so the 5% error that allows an easily rememberedapproximationisinsignificant.Moreimportantly,theapproximationsagreewellwithmeasurementandPSUD2predictions.

CurrentRatingoftheChoke

Although a choke of infinite inductance would allow both choke and mainstransformertohaveacurrentratingequaltothemaximumDCloadcurrent,theyactually have to support a somewhat higher current, and it is particularlyimportant that thechokeiscorrectlyrated.Remember that thechokegeneratesmagneticfluxinitscoreproportionaltothecurrentpassingthroughthecoil,butiftoomuchmagnetisingforceisapplied,thecoresaturates,causinginductancetofalltozero.Since the output of the rectifier comprises a DC component and an ACcomponent,itisthesummationofthesecomponentsthatdeterminesthecurrentratingof thechoke.TheDCcomponent issimplythe loadcurrent,but theACcomponentrequiresalittlemorethought.Becausethechokeisfollowedbyacapacitor,whichisashort-circuittoAC,theentireACcomponent leaving the rectifier isdevelopedacross the reactanceofthechoke,causinganACcurrenttoflow.OnceweknowtheACvoltageacrossthechoke,wecaneasilycalculatethecurrent.As previously mentioned, the AC component is dominated by the secondharmonic, so we can simplify the calculation to deal exclusively with this

component.TheinstantaneousACvoltageacrossthechokeistherefore:

wherefisthesecondharmonicofmainsfrequency.Thereactanceofthechokeis:

Using Ohm’s law to combine the two equations, the instantaneous currentthroughthechokeis:

We are only concernedwith themaximum current, which occurs when cos(2πft)=1,sothisfactorcanberemoved,leaving:

Itwasstatedthatonlythesecondharmonicwassignificant,butthisassumptionshouldnowbeexamined.ReferringtotheFourierseries,thefourthharmonicis20%(0.12/0.6)ofthevoltageofthesecondharmonic.Thedoubledreactanceofthechokeatthefourthharmonichalvesthechokecurrent,resultinginafourthharmoniccurrentthatisonly10%ofthesecondharmonic,sotheapproximationisfair,butthereisroomforimprovement.The sum of the AC currents drawn by each of the Fourier terms, up to andincluding the eighth harmonic,was investigated to find themaximumpositivepeak.(ThenegativepeakisirrelevantsincewhenaddedtotheDCloadcurrent,it reduces the total peak current.) The result of this exercise modified theequationto:

ButthetotalpeakcurrentflowingthroughthechokeisthesumoftheACpeakcurrentandtheDCloadcurrent:

Asanexample,aClassApoweramplifierusingapairofpush–pull845valvesrequires a raw HT of 1,100 V at 218 mA, and a 10 H 350 mA choke isavailable,butisthisadequate?Thetransformersupplyingthechokeinputfilterhas an output voltage of 1,224 VRMS.Using the previously derived equationandassuming50 Hzmains:

Thetotalpeakcurrentis324 mA,sothe350 mAratedchokeisjustadequate,but the example shows that choke AC current can be surprisingly high,particularlywhenhighHTvoltagesarecontemplated.As a sweeping generalisation, chokes for HT choke input supplies generallyneedtobe≥15 H,otherwisetheACcurrentbecomescrippling,andthequickestway of determining a choke’s suitability for a choke input supply is either tomodelitinPSUD2,ortoputallthechokeequationsintoaspreadsheet.

MainsTransformerCurrentRatingforaChokeInputSupply

Thepeakchokecurrentmustbesuppliedbythetransformer,sothetransformershould be rated appropriately. However, since transformer ratings assumeresistiveloadsandsinewaves,theircurrentratingsareRMSofsinewave,andtheycandeliverapeakcurrentof√2thisvalue,sothepreviousexamplewouldrequire a transformerwith anRMS sinewave current rating of 229 mA (324mApk).Thisissufficientlyclose(5%error)totheDCloadcurrentof218 mAthatacommonapproximationistoassumethatthetransformershouldhaveanACRMScurrentratingequaltotheDCloadcurrent.

CurrentSpikesandSnubbers

Choke input power supplies are not perfect and have two main problems,electricalswitchingspikesandmechanicalvibration.Althoughwesaidearlier that thechoke inputpowersupplydrewacontinuouscurrent from the mains transformer, this cannot be exactly true. Since therectifier diodes require a certain voltage across them before they switch on(irrespectiveofwhethertheyarethermionicorsemiconductor),theremustbeatime, as the inputwaveform crosses through zero volts,when neither diode isswitched on. The current drawn from the transformer is therefore not quitecontinuous andmustmomentarily fall to zero. The chokewill try tomaintaincurrentand,indoingso,willdevelopanEMF:

Inanyfull-waverectifier,thediodesswitchoffattwicemainsfrequency,andatthatinstant,di/dt=∞,sotheoreticallyinfinitevoltagespikesareproducedwitharepetitionrateoftwicemainsfrequency(seeFigure5.20).

Figure5.20Extremechokeringingcausedbyrectifierswitchingwithoutloadcurrent.

Although drawing a significant load current greatly damps the ringing of thechoke,thecurrentwaveformstillhasaglitch(seeFigure5.21).

Figure5.21Withoutsnubber(butwithloadcurrent).Uppertrace(Ch1):transformerloadcurrent.Lowertrace(Ch2):inputvoltagetorectifier.

Traditionally, a resistor/capacitor snubber network was connected across thechoketoprotecttheinter-windinginsulationofthemainstransformerfromthespikes(seeFigure5.22a).

Figure5.22Traditionalandimprovedchokesnubbernetworks.

Although fitting the traditional10 nF+10 kΩsnubberacross thechoke tamesthevoltagespikes,itdegradeshigh-frequencyfilteringandworsenstheglitchinthecurrentwaveform(seeFigure5.23).

Figure5.23With10 nF+10 kΩsnubber.Uppertrace(Ch1):transformerloadcurrent.Lowertrace(Ch2):inputvoltagetorectifier.Notetheworsenedcurrentwaveform.

Asnubbingmethodthatsignificantlyimproveshigh-frequencyfilteringistofit

back-to-backcapacitorsacrossthechoke,withtheircentretapconnectedto0 V,andusetheinternalresistanceofthechokeasthesnubbingresistance.OptimumhighfrequencyfilteringisobtainedbychoosingC1sothatitresonateswiththeleakage inductanceof themains transformerat thesamefrequencyas theself-resonanceofthechoke,butthisseemsnottobecritical,andcuriously220 nFisoftenapracticalvalueforbothHTandLTsupplies(seeFigure5.22b).The modified snubber network removes the voltage spikes withoutcompromising high frequency filtering or adding glitches to the currentwaveform(seeFigure5.24).

Figure5.24With220 nFback-to-backsnubber.Uppertrace(Ch1):transformerloadcurrent.Lowertrace(Ch2):inputvoltagetorectifier.Notethecompleteabsenceofglitches.

Asmentionedpreviously,theentireACcomponentattheoutputoftherectifierisacross thechoke. InChapter4 ,weobserved thatoutput transformerscould‘sing’due to loose laminationsormagnetostriction, and the same is truehere.The choke couldbuzz at twicemains frequency, and if it has any looseparts,such as a loose screening can, it will rattle loudly. Even worse, the choke isboltedtoaresonantsoundingboard(thechassis),whichwillamplifythebuzz.Theauthorhasrecentlyinvestigatedanumberofchokeinputpowersupplies.Abuzzing choke implies core saturation.Unfortunately, it seems that iron corescandeteriorateover thedecades, reducing inductance,which increases theACcurrent,perhapstothepointofsaturation,thuscausingbuzz.Ifyoumustuseoldchokes(andtransformers),checkthemforbuzzunderloadbeforedrillingholes

inthechassis.

IntermediateMode:TheRegionBetweenChokeInputand

CapacitorInput

For a given input voltage, a choke input supply produces the lowest outputvoltage (0.90 Vin(RMS)) because only the DC component from the rectifierreachestheload,whereasacapacitorinputsupplywithCreservoir=∞achievesthemaximum(√2 Vin(RMS))becauseitcanusetheACcomponent.Anotherwayoflookingatachoke inputsupply is toconsider it tobeacapacitor inputsupplywhereCreservoir=0.Wenowseethatchangingreservoircapacitorvaluecouldbeausefulwayofadjustingoutputvoltagebetween0.90 Vin(RMS)and√2 Vin(RMS),thus allowing a previously unsuitable transformer secondary to provide therequiredoutputvoltagewithoutwastingpowerinaresistor(seeFigure5.25).

Figure5.25Intermediatemode:theeffectofreservoircapacitanceonoutputvoltageandDCoutputresistance.

Thismodelledexampleshowsthatareservoircapacitorofbetween1 μFand10μFisneededtooperateinintermediatemode,andthisisfairlytypical.Notingthecriticaldependenceofoutputvoltageonreservoirvalue,aplasticcapacitor(rather than an electrolytic) is necessary to ensure that the practical capacitormatchesthemodelledvalue.Fortunately,thehighpeakvoltageappearingacrossthe reservoir capacitor tends to force a polypropylene type, guaranteeing asufficientlyclosetolerance.DC output resistance of a supply is important because it shows how outputvoltage changeswith load current (AC output impedancewill be investigated

shortly). The graph shows the lowest DC output resistance when the supplyoperatesinchokeinputmode(Creservoir=0),andasomewhathigherDCoutputresistance in capacitor input mode ( Creservoir=∞), but note that the cost ofintermediate mode is significantly higher DC output resistance than either ofthese.Theimplicationof the intermediatemode’shighDCoutputresistanceisthatitisbestsuitedtoconstantcurrentloadssuchasregulatorsorpre-amplifierswherethesignalcurrentissosmallthatitcannotmodulatethesupply.AlthoughintermediatemodehasahighDCoutputresistance,itisefficientbecauseaddingarealseries resistance to theoutputofacapacitor inputsupply toproduce thesameoutputvoltagewouldwastepower.Notethatbecauseintermediatemodeusesanundersizedreservoircapacitor,thatcapacitorhasasubstantialripplevoltageacrossit(whichisn’taproblem),butitmeansthatthefollowingchokemustalsohaveasubstantialripplevoltageacrossit,implyingsignificantACcurrentinadditiontotheDCloadcurrent.Thus,justlike the choke input power supply, we must ensure that our choke has anadequatecurrentratingtocopewiththesumofthesecurrentswithoutsaturating.It would be nice if intermediate mode had one equation for predicting therequiredreservoircapacitorvalueforaparticularHTvoltageandanotherforthepeak choke current, but we contravene the assumptions made earlier forcapacitor input smoothing and do not consider theDC component leaving therectifier. The only way of determining the required value of the reservoircapacitor is to determine it experimentally – start with a 5 μF reservoir andadjust it upordownuntil the requiredHTvoltage is achievedat the expectedload current.Having found the capacitor value, the chokepeak current canbedetermined.Eventheauthordoesnothaveadecadecapacitanceboxhavinganadequate voltage rating (and 1–10 μF range), let alone a large selection ofchokes,but theexperiment iseasilydoneasacomputer simulation.PSUD2 isidealforthetask,butbewarethatintermediatemodemaytakeconsiderabletimefor its output voltage to reach its final value, so a long simulation time isessential(50 sisgenerallyadequate).

PSUD2

PSUD2 by Duncan Munro is a power supply simulation freeware that hasbecomethedefactostandardforsimulatingthetraditionallinearpowersuppliesused in valve amplifiers. The software can simulate all combinations of LCRsuppliesandgivesagraphicaldisplayofchosenvoltagesorcurrents.PSUD2iseasilyused,soratherthanexplainitsfulloperation,theauthorwillsimplytouchontwoimportantpoints.

Most commercialmains transformers operate just above the knee of theB/Hcurve,andthismeansthatripplecurrentislimitedbycoresaturationtofourtosix times DC load current. Simulations like PSUD2 necessarily use a simpletransformermodelthatcan’ttakeaccountofsaturation,soittypicallypredictsaslightlyhigherripplecurrent(perhapsseventimesDCloadcurrent).Whenthereal-world transformer saturates and limits ripple current, the effect is to veryslightlylowertheDCloadvoltagecomparedtothePSUD2prediction.PSUD2hasafeaturethatseemstrivial,yetallowsunprecedentedunderstandingofthesupplybeingsimulated.PSUD2cancheckthelowfrequencystabilityofasupply.Checkinglowfrequencystabilityisimportantbecause,aswewillseeinamoment, it is easy to accidentally design a supply that rings like a subsonicbell. Low frequency stability is checked using the ‘stepped load’ command,which is invoked using the ‘edit’ command on the load to select a constantcurrentload(seeFigure5.26).

Figure5.26InvokingthesteppedcurrentfeatureinPSUD2.

Astepincurrentof10:1willcertainlyprovokeanyresonances,andthesewillbeseenascapacitorvoltageringing.Notethatthetimewhenthestepoccurscanbeset, so it should be some time after the supply has completed its switch-ontransient.Thus,amulti-sectionfilterwithcurrenttapsateachsectionshouldsetstepped loads at each current tap butwith different timings (1 s intervals areuseful), and thenmonitor each capacitor voltage.Ringing at one section oftenleaksintoothersections,sowhenanunstablesection’sloadsteps,itwillcauseparticularlybadringing,revealingtheproblematicsection.Ifweover-dampthefilters, thepowersupplywillbeslowtorespondtochangesinloadcurrent,soweideallywantalittlelessthancriticaldampingbutnooscillation.Thus,each

oftheprogrammedcurrentstepsshouldcausecapacitorvoltagestochangewithafastexponentialcurvebutwithoutringing(seeFigure5.27).

Figure5.27Awell-designedsupplyrespondstocurrentstepchangeswithoutringing.

However, should one of the LC sections have too high a Q (caused in thisinstance by reducing the series resistance of its choke from400 Ω to 40 Ω),ringing occurs which is lightly coupled into the voltage of the other tap (seeFigure5.28).

Figure5.28Anunstablesectioncauseslowfrequencyringing.

Althougha220 nFcapacitorisfrequentlyadequateforsnubbinghighfrequencyringingofthechokeinachokeinputsupply,itmaynotbelargeenoughtodamptheLowFrequencyresonanceformedbythecombinationofthechokeandthefollowingreservoircapacitor,andthisisbestcheckedusingPSUD2.Theexactvaluecanbequitecritical;whensettostepfrom20 mAto80 mAafter0.9 sandviewedfor1 safterareportingdelayof1 s,changingthesnubberfrom500nF to 600 nF completely eliminated the ringing in oneHT supply.Althoughlarger values ensure freedom fromLowFrequency ringing, they also slug theresponseofthesupplytoacurrentstep,soit’sworthusingasnubberonlyalittlelarger than the theoretical required value. In practice, the theoretical value isunlikelytobeapreferredvalue,sothenextpreferredvalueupwilldonicely.

We could iteratively optimise a design by randomly changing all values inPSUD2untilweobtaintherequiredresult,butthisislikelytobeveryslow.Theearlier analysis of rectification and LC filters greatly speeds optimisationbecauseitallowsustomakeinitialestimatesofallrequiredvaluesandputthemintoPSUD2.Further,theanalysisalsogaveusanunderstandingofwhichpeakcurrents and voltages should be checked in PSUD2 to avoid overloadingcomponentsandhowtoavoidlow-frequencyinstability.

BroadbandResponseofPracticalLCFilters

So far, our investigation of rectification and filtering has focussed on thebehaviouratripplefrequencyanditsharmonics,butwenowneedtobroadenouroutlook to include behaviour fromDC to low radio frequencies. To attenuatelow(≈100 Hz)frequenciessignificantly,anLCfilterwithalargeinductanceisrequired,whichinevitablyhasinternalshuntcapacitance.Conversely, thefiltercapacitor has series inductance and resistance (ESR), and these hiddencomponentsmeanthatanypracticalLCfilterhasafrequencyresponsethatmaybedividedintofourmainregions.(Althoughsurprisinglysmooth,thefollowinggraphisaresultofpracticalmeasurementsofanLCfilter.SeeFigure5.29.)

Figure5.29MeasuredfrequencyresponseofLCfilter(20 H50 mA,120 μF400 Vpolypropylene).

Region1This is the only region we can directly control, so it is well worthy ofinvestigation.Apart from losses due toDC resistance, the low-pass filter does

notattenuatefrequenciesbelowtheLowFrequencyresonance:

We aim to position the (hopefully) subsonic resonance as low as possible bymaking L andC large because every octave by which we can lower fres(LowFrequency) produces an additional 12 dB of filtering. If fres(Low Frequency)hasQ>0.707, anLowFrequency peak results in the response of the filter, so it isusefultocheckQ:

whereL=inductanceofchokeRDC=DCresistanceofchoke

C=capacitanceoffiltercapacitor.

Ideally, the resonance should be critically damped ( Q=0.5), which can beachieved by adding external series resistance to the choke. Strictly, the loadresistance across the capacitor also damps the resonance, and this may betransformedintoanotionalextrachokeseriesresistanceusing:

However, thedampingeffectof the load resistance isusuallynegligible.Evenworse,aseriesvoltageregulatorisaconstantcurrent,orinfinite,ACloadtothesmoothingcircuitry,soitaddsnodampingwhatsoever.A typical traditional example:A choke input supplymight use a 15 H chokehaving 260 Ω internal resistance coupled to an 8 μF capacitor, resulting infres(LowFrequency)=15 HzandQ=5.3.ThisQ is toohigh,and fres(LowFrequency) istooneartheaudioband,buttheadditional2.5 kΩseriesresistancerequiredtoachieve critical damping would waste HT voltage and greatly increase powersupplyoutputresistance.Abetteralternativewouldreplacethe8 μFcapacitorwitha120 μFpolypropylene,since thiswouldgive fres(LowFrequency)=3.75 HzandQ=1.36,andthisQmightbeacceptable.NotethatreducingQbyincreasingCisnotaseffectiveasincreasingRbecauseCisinsidethesquareroottermoftheQequation,sowhensimulatinginPSUD2,expecttheneedtoincreasefiltercapacitancesignificantlyifyoucan’ttolerateincreasedchokeresistance.Region2

Region2Thereactanceofthechokedoublesforeachoctaveriseinfrequency,whilstthereactanceofthereservoircapacitorhalves,producingthefamiliar12 dB/octaveslope.PSUD2worksinthetimeratherthanfrequencydomain,sowedon’tseethisdirectly,butthereportedvaluesofrippletellushowwellwearefilteringatourchosenripplefrequency.Note that PSUD2 has no understanding of the next two concepts, so bothconceptsmustbecheckedmanually.Region3Thechoke’sinternalshuntcapacitancebeginstotakeeffect.Oncethereactanceof the shunt capacitance is equal to the inductive reactance of the choke, thechokeresonates,sothisregionmaybedefinedasbeginningatfres(highfrequency).Above this self-resonant frequency (3–15 kHz for a typical HT choke), thechoke’s shunt capacitance forms a potential dividerwith the filter capacitancewhoselossisconstantwithfrequency:

Region4Theseriesinductanceofthefiltercapacitorbecomessignificant,andthisformsahiddenhigh-passfilterinconjunctionwiththeshuntcapacitanceofthechoke,sotheoutputnoiseofthepracticalfilterrisesat12 dB/octave.All of theprevious concepts canbe simplifiedby considering an idealisedLCfilter response to bemade up of three straight lines having freedom tomoveeitherverticallyorhorizontally(seeFigure5.30).

Figure5.30ConceptualmodelofuniversalLCfilter.

• Line A falls at 12 dB/octave, and slides horizontally to the left as the

productofchokeinductanceandfiltercapacitanceincreases.• Line B falls vertically as the ratio of filter capacitance and choke shuntcapacitance increases, intercepting line A at the choke’s self-resonantfrequency.Capacitancebetween adjacentwinding layers of the choke couldbe reduced by vertical sectioning or by interposing earthed electrostaticscreens.•LineC rises at 12 dB/octave, and slides horizontally to the right as filtercapacitor series inductance falls, intercepting line B at the capacitor’s self-resonant frequency.Mostmoderncapacitorshaveseries inductancebetween10 nHand100 nH,so if thisvalue isknown, their self-resonant frequencycanbecalculatedusingthestandardresonanceequation.Conversely, if theirself-resonantfrequencyisknown,seriesinductancecanbecalculated.Sadly,the two preceding statements are not true for an electrolytic capacitor – thecapacitance of an electrolytic capacitor at self-resonance is likely to bebetween25%and50%lowerthanitsDCvalue.

Unfortunately, filter capacitor ESR also complicates the issue and can easilymasktheplateauoflineB.TheintersectionoflinesBandCcanbeviewedastheresponseofanLCfilter,butplottedupsidedown.Thus,toavoiddegradingthe plateau, theQ of the capacitor’s self-resonant frequency should be >1/√2(unusually, we want the filter’s response to be underdamped at its resonantfrequency).Remembering:

RearrangingandinsertingourQrequirement:

Thus, a 100 μF filter capacitor having a typical series inductance of 20 nHwouldrequireESR<18 mΩ.The modelled filter compares the effect of the measured parameters of threedifferentfiltercapacitorsincombinationwithaWoden51700choke(20 H,365Ωand95 pF)(seeFigure5.31andTable5.5).

Figure5.31ModelledcomparisonofamplitudeagainstfrequencyresponseofLCfilterusingthreedifferentcapacitors.

Table5.5CapacitorValuesandParasiticComponentsoftheModelledFilterofFigure5.31C

(μF)ESR(mΩ)

Lseries(nH)

(A)100-μF450-V159seriesBCComponentsPCBmountingsnap-inaluminiumelectrolyticcapacitor 95 300 16

(B)120-μF400-VAnsarmetallisedpolypropylene 120 35 200(C)100-μF400-VAnsarmetallisedpolypropylenewithKelvinconnection 100 7 ≈5.5

Asexpected,theelectrolyticcapacitorfailstoachievethefilteringplateauduetoits significantESR.CapacitorBhad thepotential tooffer excellentbroadbandfiltering,but itsESRandseries inductancewerebadlycompromisedbyan ill-consideredmechanicalrequirementtohavebothleads(knownastails)exitfromthesameend,enforcinganadditional120 mmlengthononetail.Capacitor C with its Kelvin connection was from the second batch speciallymade for the author by suppression devices of clitheroe but will doubtlessbecomeastandardpart.Note thatnotonlydoescapacitorCeasilyachieve thefiltering plateau, but also that its minimal series inductance maintains thatplateautothehighestfrequency.Eachendofthecapacitorhastwoindependenttails from the tin/zinc layer connecting to the plates: one tail is used for thesourceofcurrentandtheotherfortheload(seeFigure5.32).

Figure5.32Kelvinconnectionmovesleadinductancetoapositioninthecircuitwhereitnolongermatters.

The significance of the Kelvin connection is that from the point of view offiltering incoming interference, tail inductance (typically 0.75 nH/mm) andresistance are no longer relevant, and filtering is determined purely by theresidual inductance and resistance of the foils. This connection is also usefulwhen the capacitor is used as a reservoir capacitor because it enables idealseparation of ripple current from load current. Most importantly, if a plasticcapacitorhastobeused(usuallybecauseoftherequiredvoltagerating)Kelvinconnectionoffersasignificantreductionofmains-borneinterferencebetween10kHzand1 MHzatinsignificantadditionalcost.ThemodelledKelvin connection showsa significant improvement, but does itmatchreality?(seeFigure5.33).

Figure5.33ComparisonofmodelledandmeasuredLCfilterusingcapacitorhavingKelvinconnection.

As can be seen, the match isn’t quite perfect, with meter noise causing ashallower null at the choke’s self-resonant frequency than modelled, but thegeneralcorrespondenceisexcellent,andmatchingthemodeltothemeasurementwas the only practical way of determining the Kelvin capacitor’s seriesinductance and ESR. More importantly, the hypothesised improved high-frequencyfilteringoftheKelvinconnectionwasconfirmed.Summarising, the ideal practical LC filter achieves the plateau of line B andmaintains it to a high frequency. The limiting factors are choke self-resonantfrequency,filtercapacitorESRandLseries,sotheidealLCfilterusesacapacitorhavingaKelvinconnection.

EstimationofWide-BandLCResponse

The significance of the LC model is that once we know the self-resonantfrequency of the iron choke, we also know where the filter’s attenuationbecomesconstant.Further,sinceweknowthatthelinedowntotheself-resonantfrequencyfallsat12 dB/octave(or40 dB/decade,ifyouprefer),weknowthemaximum high-frequency attenuation. It is easy to measure a choke’s self-resonant frequencyusinganoscillatorandanoscilloscope,but that takes time,andwemightneedaquick ‘downanddirty’ estimation.Theauthormeasuredthe self-resonant frequencyofanumberofHTchokesandplotted this againsttheirinductance(seeFigure5.34).

Figure5.34Self-resonantfrequencyagainststatedinductanceforanumberofiron-coredpowersupplychokes.

Thegraphshowsthatwecanestimateachoke’sself-resonantfrequencyasbeing20 divided by the square root of its inductance. As an example, if we werewondering about the suitability of a 16 H choke, we could estimate its self-resonantfrequencyasbeing5 kHz.Further,wecouldnotethatfrom100 Hzto5 kHzisroughlyfive-and-a-halfoctaves,sowewouldknowthatthemaximumattenuation compared to 100 Hzwould be 5.5×12≈66 dB. Ifwe had alreadysimulatedthechokeandaccompanyingcapacitorinPSUD2,wewouldknowtheexpectedrippleat100 Hz,sowewouldnowhaveanestimateofthenoiseattheline B plateau. Obviously, if we knew the exact values of all the parasiticcomponents in ourLC filter, we couldmodel it in T/spice.However, it takestimeandalittlecaretodeterminethesevaluestoanydegreeofaccuracy,soifwearehappywitharesultaccurateto±6 dB,anestimationisfine.

SectionedRCFilters

WemighthavecarefullydesignedthefirststageofanHTpowersupply(chokeorcapacitorinput)withtheavailablepartssothatitproduces2 Vpk–pkofripple,yet we might need ripple <1 m Vpk–pk, but could afford to drop some DCvoltage.Thus,weneedafilterthatcanattenuatetheripplebyafactorof>2,000.SinceanRC filter isapotentialdivider, theattenuation isR/Xc (provided thatthis ratio is reasonably large). Suppose that in our example,we can tolerate 2kΩ of resistance, soXc=2 kΩ/2,000=1 Ω. Since the ripple frequency is 100Hz,wefindtherequiredcapacitanceusing:

This is a very large capacitor and represents a brute force solution to theproblem. A more efficient alternative is to make a filter out of a cascade ofsectionseachusingasmallerresistorandcapacitor(seeFigure5.35).

Figure5.35SectioningtheRCfilterleavestotalresistanceandcapacitanceunchanged,butincreasesattenuationbecauseultimateslopeincreasesfrom6 dB/octaveto24 dB/octave.

Theproblemistodeterminehowmanysectionsareideal.Fortunately,Scroggie[12] (writing as ‘Cathode Ray’) has already investigated this problem andproducedTable5.6.

Table5.6CascadedSectionCoefficients(afterScroggie)

SomevaluesinTable5.6differfromtheoriginalreferencebecauseScroggiedidnothavethebenefitofaspreadsheettoaccuratelycalculatehisvalues.

No.ofsections 2πfCR(Rtotal/Xc) AttenuationRCinkΩ·μFpersection

100 Hz 120 Hz1 16 16 25.5 21.22 45.6 130 18.1 15.13 90 997 15.9 13.34 149 7,520 14.8 12.45 223 56,400 14.2 11.86 311 420,000 13.8 11.5

To understand Table 5.6 using our previous example, we need attenuation>2,000, so the first number of sections that can exceed this in the attenuationcolumn is n=4. If the resistance must total 2 kΩ, each section must be 2kΩ/4=500 Ω.Tofindtheindividualcapacitancerequired,weusethe100 HzRC column. The capacitance required is 14.8/0.5=29.6 μF. In practice, wewouldprobablyuse470 Ωresistorsand33 μFcapacitors.Thekeypointisnotjustthatthefour33 μFcapacitorsarelikelytobemuchcheaper(andsmaller)thanasingle≈1,590 μFcapacitor,butthatthesectionedfilterpromisesalmostfour times the attenuation. PSUD2 can analyse multiple RC filters, so thecombinationofScroggie’stableandaPSUD2simulationcanbeveryeffective.Alternatively,youmighthavealargebagof22 μFcapacitors,andenoughroomtousefour,butmustuse2.5 kΩofseriesresistance.Howcanthecapacitorsbebestusedtoattenuate100 Hzripple?Connectingthefourcapacitorsinparallelgivesatotalcapacitanceof88 μF,sotheratioofRtotal/Xc=138.Inspectingthe

Rtotal/ Xc column, 90 is the first solution exceeded by 138, so three sectionsshouldbeused.Eachresistanceis thus2.5 kΩ/3=833 Ω.Ifweonlyusethreesections,ourtotalratioR/Xcisreducedbyafactorof3/4,soitfallsto104,butthisisstilloptimumwiththreesectionsandgivesanattenuationof997,whereasusing fourparallel 22 μFcapacitorswith a2.5 kΩseries resistorwouldonlyhavegivenanattenuationof138.Ourfactorofimprovementis7,yetwehaveusedonefewercapacitor(savingspace).

RegulatorsThe best way of improving a power supply is to use a voltage regulator. Avoltage regulator is a real-world approximation of aThévenin source; it has afixed output voltage and an output resistance that approaches zero. A trueThéveninsourceimpliesinfinitecurrentcapacity,whereasthesupplythatfeedsa regulatorhas limitedcurrentcapacity. It is therefore important to realise thatthe regulator can only simulate a Thévenin source over a limited range ofoperation,sowemustensurethatweremainwithinthisrangeunderallpossibleoperatingconditions.Allvoltageregulatorsarebasedonthepotentialdivider.Eithertheupperorthelowerlegofthedividerismadecontrollableinsomeway,andbythismeans,theoutputvoltagecanbevaried(seeFigure5.36).

Figure5.36Relationshipbetweenvoltageregulatorsandthepotentialdivider.

Iftheupperelementismadecontrollable,thentheregulatorisknownasaseriesregulatorbecausethecontrolledelementis inserieswiththeload.If thelowerlegofthedivideriscontrolled,thentheregulatorisknownasashuntregulatorbecause this element is shunted by the load. Shunt regulators are usuallyinefficient compared to series regulators, and their design has to be carefullytailoredtotheirload,buttheyhavetheadvantagethattheycanbothsourceandsinkcurrent.

TheFundamentalSeriesRegulator

ThefundamentalelementsofaseriesvoltageregulatorareshowninFigure5.37.

Figure5.37Fundamentalseriesregulator.

Thecircuitshownusessemiconductors,butavalveversioncouldequallywellbe built. The error amplifier amplifies the difference between the referencevoltageandafractionoftheoutputvoltageandcontrolstheseriespasstransistorsuchthatastableoutputvoltageisachieved.Thecircuitdependsforitsoperationonnegativefeedback.WesawinChapter1thatwhenfeedbackisapplied,inputandoutputresistanceschangebyratioofthefeedback factor (1+ βA0). Voltage regulators rely on shunt-derived feedbackreducingtheoutputresistanceofthesystembytheratioofthefeedbackfactor.Suppose initially that the regulator is working and that there is 10 V at theoutput.Bypotentialdivideraction,theremustbe5 Vontheinvertinginputofthe operational amplifier. The voltage reference is holding the non-invertinginput at5 V.The seriespass transistor is anemitter follower fedby theerroramplifier,andhas10 Vonitsemitter,sothebasemustbeat10.7 V.Supposenow that theoutput voltage falls for some reason.Thevoltage at themidpointofthepotentialdividernowfalls,butthevoltagereferencemaintains5V.Theerroramplifiernowhasahighervoltageonitsnon-invertinginputthanonitsinvertinginput,anditsoutputvoltagemustrise.Ifthevoltageonthebaseof the transistor rises, its emitter voltagemust also rise. The circuit thereforeopposesthereductioninoutputvoltage.Sincethesameargumentworksinreverseforariseinoutputvoltage,itfollowsthat the circuit is stable and that the output voltage is determined by thecombinationofthepotentialdividerandthereferencevoltage.Ifweredrawtheregulator,wecanseethatitissimplyanon-invertingamplifierwhosegainissetby the potential divider and that it amplifies the reference voltage (see Figure5.38).

Figure5.38Seriesregulatorredrawntoshowkinshiptonon-invertingamplifier.

Byinspection,theoutputvoltageistherefore:

Sincetheerroramplifiersimplyamplifiesthereferencevoltage,anynoiseonthereferencewillalsobeamplified,andweshouldfeeditfromascleanasupplyaspossible.Although theargumentseems likeasnakechasing itsowntail, ifwefeed the reference from the output of the supply (which is clean), then thereferencewillbeclean,andtheoutputofthesupplywillalsobeclean.Itmightbe thought thatsupplying thecurrent for the referencevoltage fromtheoutputvoltagewouldcauseinstability,butthisisnotaprobleminpractice.It should be noted that all regulators need an input voltage higher than theiroutput voltage. The minimum allowable difference between these voltagesbefore the regulator fails tooperatecorrectly isknownas thedrop-outvoltage(becausetheregulator‘dropsout’ofregulation).Withthisparticulardesignitisonly a few volts, but drop-out voltage for a valve version could be 40 V ormore.

TheTwo-TransistorSeriesRegulator

The two-transistor series regulator is a very common and useful circuit (seeFigure5.39).

Figure5.39Basictwo-transistornegativeregulator.

This circuit is popular because of its extreme cheapness, but despite that, itsperformance is reallyquitegood.Q2, theseriespass transistor, is fedfromthecollector of Q1, a common emitter amplifier. The emitter of Q1 is held at aconstantvoltagebythevoltagereference,whilstitsbaseisfedafractionoftheoutputvoltageby thepotentialdivider. If theoutputvoltagerises,Q1turnsonharder,drawingmorecurrent,itscollectorvoltage(connectedtothebaseofQ2)falls,causingtheemittervoltageofQ2(whichistheoutputvoltage)tofall,thuscounteractingtheinitialerror.This circuit is ideal for use as a bias voltage regulator in a power amplifierbecauseweoftenneedtodropmorevoltsthananICregulatorwouldtolerate.Aspresented,thecircuitcanonlysupply50 mAofoutputcurrentbecausethebasecurrentforQ2isstolenfromthecollectorcurrentofQ1.Ifweincreasedthecollector current of Q1, Q2 could steal more, and output current could beincreased, but a better solution would be to replace Q2 with a Darlingtontransistor, which would need less base current. Alternatively, Q2 could be apowerMOSFET,butitwouldneedagate-stopperresistorof≈100 Ωsoldereddirectlytoitsgatepin.The Zener diode passes 12 mA, which is quite sufficient to ensure that itoperatescorrectly,andhasastableoutputvoltagewithminimumnoise.A6.2 VZenerhasbeenchosenbecauseithaslowesttemperaturecoefficientandlowestsloperesistance,butitstillproducessomenoise,soitisbypassedbythe47 μFcapacitor.

TheSpeed-UpCapacitor[13]

This capacitor is connected across the far resistor of the potential divider. Itspurpose is to increase the amount of negative feedback available at AC, andtherebyreducehumandnoise.Sinceanylinearregulatorcanbeconsideredtobecomposedofanop-ampenclosedbya feedback loop,agenericgraphmaybedrawn(seeFigure5.40a).

Figure5.40Theeffectofthespeed-upcapacitoronripplerejection.

Theop-ampgainisacombinationofDCopen-loopgainandgainthatfallsat6dB/octave with frequency. The gain within the hatched area is available forattenuatingincomingripple,soripplereductionismaximisedby:•MaximisingDCopen-loopgain• Maximising low frequency corner frequency (741: fcorner≈20 Hz; 5534:fcorner≈1 kHz)

•MinimisingtheratioofDCoutputvoltagetoreferencevoltage.

Althoughweneed theop-amptohave thecorrectgainatDCtoset theoutputvoltage correctly, the gain below the hatched area is wasted. The speed-upcapacitoraimstorecoversomeofthiswastedgain(seeFigure5.40b).Atfirstsight,itwouldseemthatf−3dBshouldbeplacedsufficientlylowthatallof the previously wasted gain is recovered. However, an oversized speed-upcapacitorslugstheresponseoftheregulatortochangesinloadcurrent.The maximum value for this capacitor is found by first calculating the ACThéveninresistancethatitsees:

Rememberingthat

andalsothat

we find that for this circuit, with hfe=200 and Ic=2 mA, hie≈2.9 kΩ. So theThéveninresistanceseenbythecapacitoris≈1.8 kΩ.We would like the capacitor to have a significant effect on the lowest ripplefrequencytobeattenuated,whichis100 Hz(120 HzUS).ThepotentialdividerchainandcapacitorisastepequaliserwhoseeffectontheregulatorissimilartothatusedfortheRIAA3,180 μs/318 μspairinginChapter7.Wecouldmakethe reactance of the capacitor at the lowest ripple frequency equal to theThévenin resistance at the tappingof thepotential divider,whichwouldmeanthataninfinitelylargecapacitorcouldonlyimproveripplereductionbyafurther3 dB:

Thenearest value is 1 μF.This is quite a small capacitor, and the author hasseen many similar circuits with oversized capacitors and, indeed, built onehimself. The subjective effect of the oversize capacitor was to create a bassboomthatwasincorrectlythoughtatthetimetobeduetoroomacousticswhenitwasreallyduetothesluggishrecoveryofthepowersupplytotransients.Attheoppositelimit,wecouldsetthereactanceofthecapacitorrelativetothetotalresistanceofthedividerchain.Thesmallercapacitorwouldonlygivea3dB improvement inhumcompared toachainwithout a capacitor,but its lowfrequency transient response would be better than a regulator using a largercapacitor.Thevalueofthespeed-upcapacitorisacompromisebetweenhumreductionandregulatorlowfrequencytransientresponse,sothereisn’ta‘correct’answerhereotherthanthatthecapacitorshouldbesmall.Youmightevenwanttodetermineits final value by listening because different loudspeakers (with different lowfrequencydamping)canpreferdifferentvalues.

CompensatingforRegulatorOutputInductance

Theregulatoralsohasacapacitoracross itsoutput.Asshown inFigure5.40 ,thegainoftheerroramplifierfallswithfrequencyduetoMillereffectandstraycapacitances, so the amount of gain available for reducing output impedancefalls.If(1+βA0)hasfallen,thentheoutputimpedancemustrise,andtheeffectis that output impedance rises with frequency. A perfect Thévenin source in

serieswith an inductorwould look identical, and for this reason the output ofregulatorsisoftendescribedasbeinginductiveathighfrequencies.Theoutputcapacitormaintainsalowoutputimpedanceathighfrequencies.

AVariableBiasVoltageRegulator

Weoftenneedabiasvoltageregulatortobevariablebetweencertainlimits.Inthis example,wewill look at a grid bias regulator needed for an 845 directlyheated triode. Perusal of RCA anode characteristics ( circa 1933) indicated agridbiasvoltageof−125 V,butmodernvalvesdonotmatchtheoriginalcurvesexactly,andwemustequaliseanodecurrentsinthis(push–pull)outputstagetoavoid saturating the output transformer with an unbalanced DC current andcausing distortion. A range of ±25 V on either side of the nominal −125 Vseemsreasonable,buthowdowedesignaregulatortofulfilthisrequirement?Fortunately,since it suppliesapartof thecircuitwhere thesignalvoltagesarevery high (up to 90 VRMS), the regulator need not have an impeccable noiseperformance,andavalanchediodesareperfectlyacceptable(seeFigure5.41).

Figure5.41Adjustable−125 Vbiasregulator.

Ahigher-voltagereferenceallowsthefinishedcircuit tohavebetterregulation,but we must still allow a reasonable voltage between the collector and theemitterofthecontroltransistor.Inpractice,areferencevoltageofabouthalfthemaximumoutputvoltage isusuallyagoodchoice, and75 V referencediodesareavailable.Thereferencediodeholdstheemitterofthetransistorat−75 V,andVbe=0.7 V,sothebaseofthetransistorwillbeheldatafixedpotentialof−75.7 V.Sincethebaseof the transistor isconnected to thewiperof thepotentialdivider, the

wipermustalsobeheldat−75.7 V,nomatterwhatoutputvoltage is set.Wecan now calculate the required attenuation of the potential divider for the twoextremedesigncases:

By choosing a convenient value for the variable resistor in themiddle of thepotential divider, we now have enough information to calculate the requiredresistors on either side.A lowvalueof variable resistorwould require a largecurrent to flow in the potential divider, whereas too high a value will causeerrors due to the (small) base current drawn by the transistor. A goodengineeringprinciple is that thepotentialdividerchainshouldpass roughly10timestheexpectedbasecurrent,soa50 kΩvariableresistorwasaconvenientstandardvalueforthisexample.Whenthewiperofthevariableresistorissettoproducethelargestvoltageattheregulatoroutput, it isconnecteddirectly to thegroundedresistor (x),andviceversa.Usingthestandardpotentialdividerequation,for−150 V:

Andsimilarlyfor−100 V:

We now have two equations that can be solved, either simultaneously or bysubstitution, togive thevaluesof the fixed resistorsx andy. In thisparticularcase, the values fell out very conveniently to give x=100 kΩ and y=47 kΩ,wherexistheupperpotentialdividerresistorandyisthelowerpotentialdividerresistor.Asa finalnote,biassuppliesand their regulatorsdrawvery littlecurrent fromtheirtransformer,soalowcurrentwindingisused.Lowcurrentwindingstendtohaveverypoorregulation,andbecausetheirfull-loadcurrentisrarelydrawn,so the actual voltage at the theoretical−170 Vpoint could easily be−180 Vwhenmeasured.

The317ICVoltageRegulator

Although the two-transistor regulator is the ideal choice for a bias regulatorbecause of its high voltage drop capability, once we need higher currents at

lowervoltagesitslimitationsquicklybecomeapparent.It is perfectly possible to build a voltage regulator using a handful ofcomponents including an operational amplifier, a voltage reference, varioustransistors,resistorsandcapacitors.Withcare, thecircuitcanbemadetoworkalmostaswellasanICregulatorandonlycostsaboutthreetimesasmuch.WeneednotfeelguiltyaboutusingICregulators.The317isastandarddevicethatismadebyallthemajorICmanufacturers[14].LinearTechnology[15]makesanupgradedversionofthe317,theLT317,butthe only difference is that the guaranteed tolerance of the voltage reference istighter.Acommercialdesigncould therefore set itsoutputvoltageusing fixedresistorsratherthanavariableresistor,thussavingmoney,becausenotonlyarevariable resistors expensive tobuy, theyalsohave tobeadjusted (whichcostsmoney). We do not often have to worry about such considerations, so thestandard317isfine.The317incorporatesallofthefundamentalelementsofaseriesregulatorinonethree-terminalpackage,andweonlyneedtoaddanexternalpotentialdividertoproduceanadjustableregulator(seeFigure5.42).

Figure5.42Basic317regulatorcircuit.

Oneendof thevoltage reference isconnected to theOUT terminal,whilst theotherisaninputtotheerroramplifier.TheotherinputoftheerroramplifieristheADJ terminal. The 317 therefore strives tomaintain a voltage equal to itsreferencevoltage(1.25 V)betweentheOUTandADJterminals.AllwehavetodoistosetourpotentialdividersothatthevoltageatthetapisVout=1.25 V,andthe317willdotherest.Indatasheetsforthe317,youwill invariablyfindthattheupperresistorofthepotentialdivideris240 Ω.Thereasonforthisisthatthe317mustpass5 mAbefore it can regulate reliably. If the potential divider passes 5 mA, then this

ensuresthatthedeviceisabletoregulateevenifthereisnoexternalload.The317sources≈50 μAofbiascurrenttotheoppositerailfromtheADJpin,whichthereforeflowsdownthelowerlegofthepotentialdivider.Normally,thisis negligible, but if you are designing a high voltage regulator, and choose alowerpotentialdividercurrent,thiswillneedtobetakenintoaccount.The manufacturers’ data sheets generally show a regulator with the ADJ pinbypassed to ground by a 10 μF electrolytic, which improves ripple rejectionfrom60 dBto80 dBat100 Hz.Thisisthespeed-upcapacitorthatweaddedtothe two-transistor regulator, but because the reference voltage is tied to Vout,ratherthanground,thespeed-upcapacitorconnectstoground,ratherthanVout.Wecouldthereforeusethemethodderivedearliertocheckwhether10 μFisareasonable value of capacitor. The ADJ pin is an input to an operationalamplifier, so we can treat it as infinite input resistance, and we are onlyconcernedwiththeexternalresistorvalues.Ifweweretouseanupperresistorof240 Ω,anda2.7 kΩlowerresistortosetanoutputvoltageof≈15 V,thenthemaximum value would be 7.2 μF, so a 10 μF electrolytic capacitor is areasonablechoice,althoughtheauthorwouldprobablyprefer6.8 μFifhehadoneinstock.Justlikethetwo-transistorregulator,theoutputofthe317isinductive,andthemanufacturer’s output impedance curves suggest that the output impedance isequivalentto≈2.2 μHinserieswith2.7 mΩwhensettoproduce10 V,sotheyrecommend a 1 μF tantalum bead output bypass capacitor, as shown in theequivalentcircuit(seeFigure5.43).

Figure5.43ACThéveninequivalentof317plus1μFbypasscapacitor.

Assuming that the tantalum capacitor had zero ESR (!), the only dampingresistance would be the 2.7 mΩ of the 317, so we have an underdamped

resonantcircuit,andwecancalculateitsQ:

Wiring resistancewill reduce thisQ considerably, but it will not reduce it toQ=0.5,whichwouldbecriticallydamped.Thiswouldnotmattergreatlybecausewewouldbeunabletoexcitethecircuitfromtheoutput(anyexternalexcitationwouldbeshort-circuitedbythecapacitor).Ifwenowconcedethatthecapacitorisnotperfect,wemaybeunluckyenoughtobeabletoexcitetheresonance,andthe circuit could become unstable. Rearranging the formula, 3 Ω criticallydampstheresonance,andtheICmanufacturersrecommend2.7 Ωinserieswiththetantalumcapacitor.The author measured a couple of 1.5 μF tantalum bead capacitors randomlypickedfromhispartsbinandfoundonehadanESRof4.8 Ω,whilsttheothermeasured2.7 Ω–negatinganyneedfortheseries2.7 Ωresistor.Itdoesseemthat tantalum bead capacitors have very variable ESR not just betweenmanufacturers, but also between sampleswithin batches, so data sheets eitherneed to be read carefully or should be measured before use. An aluminiumelectrolytic capacitor plus series resistorwould be a cheaper and less variablealternative.

The317asanHTRegulator

Becausethe317isafloatingregulator,thereisnoreasonwhyitshouldnotbeusedtoregulatea400 VHTsupply.However,becausethe317canonlytolerate37 V from input to output, it needs support circuitry for protection [16] (seeFigure5.44).

Figure5.44Maidahigh-voltageregulator(reproducedbykindpermissionofNationalSemiconductor).

The317isprecededbyahighvoltagetransistorDarlingtonpairwhosesoleaimin life is to protect the 317 by maintaining 6.2 V−2 V BE−0.1 ILOAD(mA)between its IN andOUT terminals.Unfortunately, the voltagedrop across the100 Ω resistor in this particular circuit means that the 317 drops out ofregulationonceloadcurrent>20 mA.TheDarlingtonpaircaneasilycopewithvariationsinmainsvoltage,butitshouldnotbethoughtthatthiscircuitisproofagainstashort-circuitwhenusedattypicalvalvevoltages.Accidentallyshort-circuitingaregulatorofthistypewithanoscilloscopeproberesultsinanalmightybang,andallthesiliconisdestroyed.Theauthorknows.The lowerarmof thepotentialdivider isbypassed,buthasa resistor in serieswith the capacitor to improve low frequency transient response by raising thelower f−3dB frequency of the step equaliser, and a diode has been addedallegedly to discharge the capacitor in the event of an output short-circuit(althoughtheauthor’sexperiencewasthatitdidn’tactuallyhelp).VariantsoftheMaidacircuitareverypopularasHTregulators,andtheauthorhasusedmanyover theyears (see theCrystalPalaceamplifier inChapter6 ),butthecircuitisfragile,andwewillseelaterthatitispossibletodobetter.

ValveVoltageRegulators

Valvevoltageregulatorshavealwaysbeenveryrare,andwewillnowseewhy(seeFigure5.45).

Figure5.45Basicvalvevoltageregulator.

The circuit is directly analogous to the two-transistor regulator; it simply hasvalvesandhighervoltages.Thesiliconreferencediodehasbeenreplacedbya

gasreferencethatholdsthecathodeoftheEF86stableat85 V,whilstthegridisfedfromthepotentialdivider.Theseriespasselementisa6080doubletriode(Pa(max)=13 W),whichwasspecificallydesignedforuseinseriesregulatorsandcanpasshighcurrentsatlowanodevoltages.Avalverectifierisused,andindeferencetoitslimitedripplecurrentcapacity,an 8 μF paper/foil capacitor has been chosen for the reservoir, although apolypropylene capacitor (≤60 μF for this rectifier) would be physicallypractical. This results in considerable ripple voltage which is filtered by thefollowingLCcombination.Unlesstheg2resistorvalueiscarefullychosen,theperformanceoftheregulatorisslightlycompromisedbyfeedingg2oftheEF86fromtherawsupply,butiffedfromtheregulatedsupply,thereisadangerthatthecircuitmightsimplysulkandnotswitchon.ThegainoftheEF86is≈100,andabove≈100 Hzthisgainisavailableforreducingtheoutputresistanceofthe6080,whosegm≈7 mA/V,sork≈200 Ω (including the effect of the external 100 Ω Ra). The regulatorthereforeachievesanoutputresistanceof≈2 Ω.Eachvalvehasitscathodefloatingaboveground,implyingthreeseparateheatersupplies(gasreferencesarecoldcathodevalves).The6080datasheetspecifiesVhk(max)=300 V,soifVregulated<300 V,the6080heatercouldbepoweredfroma grounded heater supply. The EF86 could be supplied by a grounded heatersupply, but this is putting quite a strain on the heater to cathode insulation;stressingheater/cathodeinsulationisnotrecommendedbecauseitreducesvalvelifeexpectancyandincreasestheirnoise.TheEF86issomewhatnoisy(2 μV),butthisnoiseisswampedbythe60 μVnoisefromthe85A2(bothMullard-statedvalues).Eventhebettervalvessuchasthe 85A2 are notorious for voltage jumps, an effect whereby the referencevoltage jumps by typically 5 mV if the operating current changes. Sadly,smaller random jumps occur even with a constant current, as shown by thecaptured trace of a Mullard M8223 150 V special quality gas stabiliseroperatingat20 mA(seeFigure5.46).

Figure5.46VoltagestepsinM8223gasreference.

Theoscilloscope trace requires careful interpretationbecause it is precededby75 dB(≈×5,600)ofACcoupledgain,soinformationcanonlybegleanedfromedges,notDC levels.The trace showsapositivepulsedue to apositive jumpcloselyfollowedbyanegativepulseduetoanegativejump.Asmeasuredbytheoscilloscope, theamplitudeof thepositivepulse is17.7 V,butas theNE5532op-ampprecedingithas±18 Vrails,itcanbeassumedthatitwasclippedandthattheoriginaljumpexceeded3.2 mV.However,thenegativestepat−9.4 Vwouldnothavebeenclipped,andastheoscilloscopewasin‘peakdetect’mode,its amplitude can be assumed to be correctly captured at −1.7 mV.Summarising, the burning voltage jumped up by >3.2 mV and almostimmediatelyfellbackby1.7 mVtoanewslightlyhigherburningvoltagethanbeforethetwojumps.Maximum stability is achieved by stabilising the valve at the manufacturer’spreferredoperating current, but if this current changes, even if it returns to itsoriginalvalue,thevalvetakestimetorecoveritsoriginalstability.Althoughagasreferencemayoperateat150 V,itneedsextraenergytostriketheglowdischarge.Therearethreepossiblesourceofthisextraenergy:• Provide a sufficiently high (current limited) striking voltage. (Mullard150C4intotaldarknessneeds225 V.)•Allowthephotonsintheambientlighttoprovidetheextraenergy.(Mullard150C4strikingvoltagedropsto185 V.)

• Add a radioactive gas such as 85Kr that emits beta particles (electrons)havinganaverageenergyof200 keV.

Thesignificanceofthesethreesourcesisthatifthelasttwoarenotavailable,agas referencemay require ahigher strikingvoltage thanexpected.Krypton85has a half-life of only 10.756 years, so after 40 years itwill have decayed to7.6% of its original activity, significantly diminishing its striking assistance.Moral:Don’t relyonamanufacturer’s specified strikingvoltage if there’s anyreasontothinktheyusedradioactiveassistancetolowerit.TheGECQS121590Vstabiliser’sdatasheetstatesthatan(unspecified)radioactivematerialisusedtomaintainthesamemaximumstrikingvoltage(115 V)irrespectiveoflightordarkness, but theMullard 90C1 has similar specificationswith nomention ofradioactivity.Despite these theoretical caveats, the author’s soleQS1215 onlyneeded a striking voltage of 107.13 V in total darkness – well withinspecification.

OptimisedValveVoltageRegulators

OscilloscopedesignpresentsmanychallengesbecauseabandwidthofDCtoatleast 20 MHz is required. Valve oscilloscopes required stable, quiet HTsupplies,sotheirvoltageregulatorswerecarefullyoptimisedandheatervoltageswere stabilised againstmains voltage variation by control circuits involving asaturableinductorinserieswiththemainswindingoftheheatertransformer[17].Any voltage regulator can be improved by increasing the gain of its erroramplifier.A single triode has the lowest gain, but a pentode (or cascode) hashigher gain. If even greater gain is required, a pair of stages can be cascaded(morethantwostageswouldbeimpracticalbecausephaseshiftswouldalmostcertainlyturntheregulatorintoapoweroscillator).BecausetheerroramplifieramplifiesDC,driftmustbeminimised,sothefirststageofahigh-gainregulatormustbeadifferentialpair,andadualtriodeisconvenient.Thesecondstageismuchmore flexible, and could be another triode differential pair, or a single-endedstageusingeitheratriodeorapentode.

UsingaPentode’sg2asanInputforHumCancellation

Ifapentodeisusedasthesecondstage,g2canbeconsideredtobeaninvertinginput.IfthecorrectproportionofrawHTripplecouldbeinjectedatthispoint,itwouldcancelattheanode,resultinginaregulatorwithnohumatitsoutput,butthetacticisnotwithoutitsproblems:

•Forthepentodetooperatecorrectly,g2mustbeatthecorrectDCpotential.Thisisusuallyderivedfromapotentialdivideracrossthe(clean)outputofthesupply.Alarge-valueresistorcanthenbeconnectedfromtherawHT,anditsvalue adjusted until ripple is cancelled. The exact value of this resistor isawkwardtocalculatebecausewedonotusuallyknowthevalueof ,soitsvalue isusuallydeterminedbyexperiment.Valuescouldbeanywhere intherangefrom150 kΩto1.5 MΩ.•Although valvemanufacturers specifiedmost parameters quite tightly,wenow relyonanunspecifiedparameter, and there isnoguarantee thatvalvesmade by differentmanufacturers thatmeet all the specified parameterswillmatchourunspecifiedparameter.Asanexampleof thisproblem, the1970sfour-tube EMI2001 colour camera set beam current by controlling g 2, sowheneveranewtubewasordered(£1500ashotin1986),itwasnecessarytospecifythatthetubewastobeusedinanEMI2001colourcamera.Similarly,Tektronix stockedselected tubes (valves),notbecause theywerebetter thananyothers,butbecausetheywereguaranteedtoworkcorrectlyintheircircuit.•Variationsbetweenvalvesmeanthatthecancellationisnotperfect,butanyremainingrippleiseasilymoppedupbytheloopgainoftheerroramplifier.

IncreasingOutputCurrentCheaply

ThemajorityofcircuitrywithinoscilloscopesandaudioisClassA,soitdrawsaverynearly constant current.Oneof the functionsof a regulator is to regulateoutput voltage against changes in load current, but if the current is almostunchanging,muchoftheregulatingabilityisbeingwasted.Asanexample,theregulatormightfacea loadwithaquiescentcurrentof100 mAbut thatcouldrise to 150 mA, or drop to 50 mA under certain circumstances. We coulddesign the regulator tobe able topass150 mA,but thiswouldneed abiggerseriespassvalve.Instead,wecouldbypasstheseriespassvalvewitharesistorthat allowed50 mA to flowdirectly into the load.The series pass valvenowonlyhastopass100 mAunderfullload.Whentheloadrequiresonly50 mA,thisisprovidedentirelybythebypassresistor,andtheregulatorisindangerofdropping out of regulation, so this condition sets the limit for the maximumcurrentthatmaybebypassedbyaresistor.Adding the bypass resistor slightly increases ripple because it injects rawHTintothecleancircuit,butbecausetheoutputresistanceoftheregulatorislikelyto be <1 Ω, potential divider action greatly reduces the added ripple. As anexample, the following circuit incorporates both of these modifications (see

Figure 5.47 ). The regulator showcases some other tricks that improveperformance.

Figure5.47Optimisedvalvevoltageregulator.

As previously mentioned, gas references produce noise, but because we havechosentouseadifferentialpair,thegasreferencenowdrivesahigh-impedanceinput,sowecanaddafiltertoreducenoise.Thecapacitorpreviouslyacrossthereferencehasbeenremovedbecauseofthedangerofitcausingoscillationwhenexcited by voltage jumps (this was previously damped by rk of the valve).Additionally, the current through the gas reference has been stabilised at themanufacturer’spreferredoperatingcurrent,sojumpsshouldbeminimal.TheECC83differentialpairhasitsanodesat209 V,andalthoughitwouldjustbepossible todirectly couple this voltage to thegridof theEF91pentode, itscathodewouldbeat≈213 V,whichwouldnotonlycauseproblemswithVhk,butwould reducegain because of the necessarily highvalue ofRk.To reducethis problem,Vk has been reduced to a similar voltage to the cathodes of theECC83, allowing them to share a heater supply. We could simply insert acathoderesistortoground,butapotentialdivideracrosstheregulatedoutputcanset therequiredvoltageandgiveamuch lowerThéveninoutput resistance(15kΩversus800 kΩ).Thesignificanceofthisresistanceisthatitreducesthegainofthestage,sowewantassmallaresistanceaspossibletomaintainmaximumopen-loopgainintheregulator.TocoupleananodeoftheECC83totheEF91,apotentialdividerisneededtodropthevoltagefrom209 Vto90 V,thuswesacrifice≈7 dBofDCopen-loopgain.However, the sacrifice isworthwhilebecausegain is recovered faster bydroppingVk (and reducing local feedback) on the EF91 than it is lost by thepotential divider. Ultimately, the choice of Vk is usually determined by Vhk

considerations.Nevertheless,wecouldrecoverthegainatACbybypassingtheupperresistorwithacapacitor,althoughwewouldneedtocheckthatthecircuitwasstillstable.TheECC83differentialpairhasaconstantcurrentsinktail.Ifweweremakingsymmetricalsplit rail supplies,wecouldsimply takea large tail resistor to thenegativesupply,butasinglesupplyneedstheconstantcurrentsink.Finally, because of the greatly increased open-loop gain, the regulator has amuch lower output DC resistance than before (<10 mΩ), so it needs acommensurately large bypass capacitor to maintain low output impedance athigherfrequencies.Theauthor’srecentcapacitormeasurementsshowthatonlyplasticcapacitorshaveasufficientlylowESRtoshunt10 mΩ,but120 μF400Vplasticcapacitorsarebulkyandexpensive.Ascanbeseen,muchcanbedonetoimprovethebasicvalvevoltageregulator,butthepenaltyisconsiderablecostandcomplexity.

RegulatorSound

Single-ended amplifiers (whether pre-amplifiers or power amplifiers) suppliedfromaregulatorforcetheerroramplifiertotrackthemusicalwaveform.Thisisbecause the amplifier draws a current proportional to the music, and theregulator’s error amplifier strives tomaintain a constant voltage in the faceofthischangingcurrent.Athighfrequencies,theoutputshuntcapacitorisashort-circuit andmaintains a lowoutput impedance, but at low frequencies it is theerror amplifier that must do the work and cope with the (musical) currentwaveform. The quality of the regulator is therefore inevitably audible.Nevertheless, regulator defects are still an order of magnitude below passivesupplydefects.

PowerSupplyOutputResistanceandStereoCrosstalk

InChapter2,wedesignedsimplestagesandmadetheexplicitassumptionthatourpowersupplyhadzerooutputresistanceatallfrequenciesfromDCtolight.Feedbackregulatorshavelow,butnotzero,outputresistance,sothisparameterisoftenspecified.Asexamplesoftypical300 Vregulatorsatlowfrequencies,awell-implementedsimplevalveregulatorcanachieve≈2 Ω,anoptimisedvalveregulator≈10 mΩandatypicalMaidaregulator≈80 mΩ.The question is, how important is power supply output resistance? Or, morespecifically,howhighcanitbebeforeitbecomesaproblem?Allgainstagesusetheir load resistance RL to convert a change of signal current into a signal

voltage.IfthepowersupplyhasACoutputresistancersupply,thenthisresistanceisinserieswithRLandslightlyincreasesthegainofthestage:

Ifwefirstassumethatrsupplyisconstantwithfrequency,thenthere’snoproblemfor a single stage. However, if we share this supply between a pair of stereochannels,thesignalcurrentofonechannel’sstagecrosstalksintotheother,viaapairofpotentialdividers(seeFigure5.48).

Figure5.48Thetwopotentialdividersthatdeterminestereocrosstalkwhenacommonsupplyisused.

Rigorouscalculationofthiscascadeofpotentialdividersisunnecessarybecauseweknowrsupplymustbequitesmall,sowesimplydetermineindividualpotentialdividerattenuations, and thenmultiply them together.Asanexample, a stereopairofcommoncathodeE88CCstagesmighthaveRL=33 kΩ,ra=6.6 kΩandrsupply=2 Ω:

Crosstalk at−100 dB is certainly adequately low,but ifwe increase rsupply to200 Ω, crosstalk deteriorates to−60 dB,which although perfectly acceptableforanRIAAstage(cartridgecrosstalkrarelyexceeds−35 dB,eveninthemid-band)wouldundoubtedlybecriticisedelsewheredespite the fact thata26 dBdifferenceinlevelissufficienttoslewtheapparentpositionofthesourcefirmlytooneloudspeaker.However, we should note that because the factor RL appears in bothdenominators, the most effective way of reducing stereo crosstalk is bymaximisingRL, ratherthanminimisingrsupply.Notealsothatrsupply is likelytobe inductive due to falling regulator error amplifier gain with frequency,implyingcrosstalkthatdeteriorateswithfrequency.

PowerSupplyOutputResistanceandAmplifierStability

Whenwecalculatedstereocrosstalk,thesecondpotentialdividerdescribedhowwellthestagecouldrejectasignalfromthepowersupply,soitwasthePowerSupplyRejectionRatio(PSRR)termwefirstsawinChapter2,whereasthefirstpotential divider described how well the power supply could attenuate aninjectedsignal.Wheneverindividualstagesareinterconnectedtoformasystem,each stage requires power,whichmust ultimately be derived from a commonsource (even if that common supply is the AC mains entering the building).Thus,thestereocrosstalkconceptcanbeextendedtoincludecouplingbetweentwoentirelydifferentstagesviathepowersupply.The significance of common power supply coupling between two entirelydifferentstagesisthatonemightbetheinputtotheother,soiftheoutputofthesecond is coupled to the first via the common power supply there might besufficient loopgain andphase shift to allowoscillation. If the commonpowersupply had zero output resistance, there could be no coupling, but this is notpossible.Moreover, the common power supply is unlikely to have a constantresistance and ismore likely to have a complex impedance that changeswithfrequency.TraditionalelectronicsusedanRCladdernetworkasameansofprogressivelyattenuating power supply ripple from the (less sensitive) output stage to the(mostsensitive)inputstage.Thesmoothingcapacitorsareanopencircuitatverylowfrequencies,so theynolongereffectivelyattenuatepowersupplycouplingfrom the output stage back to the input stage, and if there is enough low-frequencygainintheamplifier,thesystemcanbecomeablockingoscillator[18]. This low-frequency (≈1 Hz) phenomenon was known classically asmotorboating,butmarginalstabilityprobablywentunnoticedmuchofthetime,becauseloudspeakersofthetimehadverystiffsuspensionsandtheirconeswererarelyvisible.Thefaultwasinthepowersupply,yetthetraditional‘cure’wastoreducethevalueofoneoftheamplifier’scouplingcapacitors.RatherthanhavinganRCladdernetwork,wecouldconnectall thestagestoasingleregulator.Providedthattheregulatorhaszerooutputresistance,therecanbe no coupling from one stage to another via the common power supply. Inpractice,afeedbackregulatoralwayshasacomplexoutputimpedancethatriseswith frequency (hence the2.7 mΩ+2.2 μH inductanceof the317) inorder tomaintain stability of its error amplifier. Thus, a feedback regulator has lowenough output impedance at low frequencies to prevent motorboating, but itsrising impedanceathigh frequenciesmightallow thecircuit itpowers toburstintohighfrequencyoscillationinstead.

Aguaranteedwayofbreaking the loop is toadda regulatorperstagebecausethisaddsthePSRRofeachregulator(typically60 dB)tothePSRRofthestage(anywherebetween0 dBand60 dB).Solid-state electronics could cheerfullyadda±15 Vregulatortoeachstageatminimalcost,butHTregulatorsaremoredifficult;aclutchofMaidaregulatorswouldbeasignificantinvestment,andtheideaofmultiplevalveregulatorsismindboggling(althoughthatdidn’tstopGlenCroftin1984).Thus,weneedsomethingcheap,simpleandrobust.

TheStatisticalRegulator

This circuit acquired its name because it applies simple statistical rules in anovelway, resulting in a simple regulator producing extremely low noise andhavingveryhighripplerejection.As we saw earlier, all regulators are based on the potential divider; seriesregulatorscontroltheupperarmandshuntregulatorsthelowerarm.It’sagoodengineeringmaximthatifalargeimprovementisneeded,it’seasiertoobtainitinanumberofsmallbitesthanonelargeone.Wehavetoworkhardtoachieve80 dBofattenuationinasingleregulator,butobtainingtwoattenuationsof40dB is easy.Thus,we could cascade regulators in the sameway thatScroggieshowed that cascaded filters achieved high attenuationmore efficiently than asinglebruteforcefilter,butthismultipliesthedrop-outvoltagebythenumberofregulators.Whatwouldbebetterwouldbetomakearegulatorthatcontrolsbotharms of the potential divider simultaneously.The individual arms need not beespeciallygoodbecausetheircombinationwouldmakeaverygoodregulator.It is probably possible tomake an adjustable high voltage regulator having afeedbackloopcontrollingseriesandshuntelementssimultaneouslythatdoesn’texplodeatswitch-on.Whetheritwouldbestablewhenconnectedtoarealloadis another matter. Fortunately, we won’t need our regulator to be adjustablebecausewewillknowtheexactvoltageandcurrent required.Thus,wedonotneed a potentially unstable control loop – we could optimise the two armsindependentlyandrunthemopen-loop.The ideal upper arm would have infinite slope resistance, whereas the ideallowerarmwouldhavezerosloperesistance.WesawinChapter2thatwecouldmake a very good constant current sink using two DN2540N5s and threeresistors, so thiswouldmake an excellent (and simple) upper arm.The lowerarmneedstobeaconstantvoltageandatitsverysimplestcouldbeastringofgasreferencesorZenerdiodes(seeFigure5.49).

Figure5.49Thisregulatorcontrolsbothupperandlowerarmsofthepotentialdivider.

Supposealoadneeded195 Vat15 mA.Toallowforsignalvariationinloadcurrentandtoensurethatthevoltagereferencesoperatecorrectly,thelowerarmshould pass a minimum of 10 mA. Thus, the constant current sink must bedesignedtopass25 mA.CurvetracermeasurementsofaDN2540N5at25 mAand100 V suggestedgm≈148 mA/Vand rds≈41 k, resulting inμ≈6,000.Forthatparticulardevice,Vgsfor25 mA≈1.45 V,soa56 Ωprogrammingresistorwouldbeneeded.Thecascodeconstantcurrent sinkmultiplies thevalueof itsprogramming resistor by the product of both μ, but the lower DN2540N5 isforced to operate at a very lowvoltage, badly compromising bothgm and rds,drastically reducingμ.CarefulACmeasurement suggestedrslope≈30 MΩwithanuncertaintyof±12%foraDN2540N5cascodeconstantcurrentsourcesetto25 mA.Suppose that the lower arm was a series chain of Zener diodes. We saw inChapter 3 that a composite device made of multiple 5.6 V Zeners wasparticularly quiet. To achieve 195 V (actually 196 V), we would need 35diodes,andatotalsloperesistanceof≈400 Ωat10 mAislikely.We can now use the potential divider equation to determine the attenuationcausedbytheconstantcurrentsinkandZenerstring:

97 dB is a very impressive attenuation, although it will vary considerablybetweendifferentsamplesofDN2540N5sand improvesubstantiallyascurrentincreases (Zener slope resistance falls with current whilst JFET gm rises).

Nevertheless,suchasatisfyinglylargenumbermeansweneednotdetermineitaccurately, we can just assume that it will be ‘good enough’ and turn ourattenuationtopracticalities.Thirty-five5.6 VZenerdiodes is a lot, and theknee-jerk reaction is to rejectsuch a solution. However, a little more thought suggests that it is entirelypractical,ifalittleunconventional.Theprimarydisadvantageisnotcost(Zenersarecheap)butthetediumofsolderingallthosediodesinseries(andeveryonethe rightway round).Zigzagging the diodes backwards and forwards across atag strip is ideal because despite the fact that the total wire length of all 35Zenerson theauthor’s tag strip≈680 mm,andhasacalculated≈1 μHseriesinductance,itstimeconstantof5 nsisinsignificant(seeFigure5.50).

Figure5.50AcompositeZeneriseasilyconstructedontagstrip.

Short-circuiting theoutputof the regulatorputs the entire inputvoltage acrosstheDN2540N5cascode.Surprisingly,theauthor’sprototyperegulatorsurvivedthis inadvertent abuse, but it is essential that the upper DN2540N5 has anadequateheatsinktocopewiththeshort-circuitdissipation.Shunt regulators also run the risk of self-immolation if their load is removedbecause this forces the shunt element to dissipate the design current plus loadcurrent.Both theBZX55andtheBZX79seriesareratedat500 mW,sofora5.6 Vdiodethatmeansamaximumcurrentof89 mA.

BypassingtheCompositeZener

AlthoughthecompositeZenerproducedverylownoisemeasuredovera22 Hzto22 kHzbandwidth, itproduced20 dBmorewhen this filterwas removed,which was a larger increase than initially expected, and the culprit is mainsinterference via the 12 pF output capacitanceCOSS of the DN2540N5. If weassume a slope resistance of 30 MΩ for the cascode constant current source(CCS)and400 Ωsloperesistanceforthe195 VcompositeZener,wecandraw

adiagram(seeFigure5.51).

Figure5.51DN2540COSSshort-circuitsthestatisticalregulator’sCCS.

Lookingat thediagram,weobserve thatCOSS short-circuits the30 MΩsloperesistance, and if we calculate their time constant (360 μs) this implies thatmainsnoiserejectionfallsat6 dB/octavefrom442 Hzupwards.Thesolutionisto convert the circuit into anoscilloscopeprobeby addinga0.9 μFcapacitoracrossthelowerresistancetoformanother360 μstimeconstant.Ourpotentialdividernowhasequaltimeconstantstopandbottom,implyingconstant97 dBattenuationwithfrequency.Inpractice,the12 pFCOSSestimateislikelytobeunreliable, but the calculation gives us a useful lower bound to the requiredvalue of bypass capacitor, and 4.7 μF would ensure that attenuation did notdeteriorateasfrequencyrose.Sincetheentirecircuitisreasonablysimple,itwaspossible tomake amodel includingZener andcapacitor series inductance andresistance, and drive it from COSS in parallel with 30 MΩ to simulate thecascodeCCS(seeFigure5.52).

Figure5.52Modelledcomparisonofstatisticalregulatorbypasscapacitors.

Asexpected, the0.9 μFcapacitor allowsconstant attenuationwith frequency,and the1 μHseries inductance(due towire length)of thecompositeZener isirrelevant.AswiththeLCfilter,thevalueofbypasscapacitancedeterminesthedepth of the attenuation plateau, its ESR nulls depth at the capacitor’s self-resonant frequency, and its series inductancedeterminesbehaviour above self-resonance.Themodel compares a typical 0.9 μFplastic capacitorhaving≈15mmtailsateachendwitha10 μFpolypropylenecapacitorhavingafour-wireKelvin connection that renders tail inductance irrelevant. We now have acompletesetofcomponentvaluesforoursupply(seeFigure5.53).

Figure5.53Thecompletestatisticalregulator.

Ascanbeseen,thestatisticalregulatorisverysimple,yetmeasurementsshowthat it is extremely good. Even better, it occupies little space so it can bepositionedattheoptimumpoint–adjacenttotheload.Sinceitisbestsuitedtopre-amplifiers,itisbesttositetherawsupply(transformer,rectifier,smoothing)remotely.

OptimisingtheStatisticalRegulator

ItisanengineeringruleofthumbthatZenersshouldoperateatacurrentof10mAormore(seeFigure5.54).

Figure5.54TypicalBZX555.6 VZenersloperesistanceagainstappliedcurrent.

ThegraphwasproducedbymeasuringZenervoltageagainstappliedcurrentforthecomposite195 VZener,fittinganequationoftheformV=a·ln(I)+b·Itothecurve,differentiatingthatequationtoproduceasloperesistanceequationand

dividing its coefficients by the number of individual Zeners. The graph isthereforeanaverageof35BZX555.6 VZenersfromonebatch,andalthoughexact coefficientsmay vary from one batch to another, the general trendwillremain.Thesloperesistanceoftheauthor’sbatchofBZX555.6 VZenerscouldbefoundfrom:

Thus,sloperesistancefallsfrom20 Ωat5 mAto11 Ωat10 mAand6 Ωat20 mA.The1.2 Ωconstantisprobablytheresistanceofthefinewiresneededtoconnecttothesilicondie.TheDN2540N5isapowerJFET,anditsgmatlowcurrents(<10 mA)isquitepoor,significantlyreducingthesloperesistanceofthecascodeCCS,soitshouldpassaminimumcurrentof20 mA.WesawinChapter3thatthenoisegeneratedbyaDCreferencewasinverselyproportional to the square root of applied current. Thus, although 10 mA ofZener current is sufficient to obtain a usefully low Zener slope resistance,doubling to 20 mA reduces Zener noise voltage by 3 dB. Since the currentrating of the composite Zener is a constant 89 mA (500 mW/5.6 V)irrespectiveoftotalvoltage,20 mAisperfectlytenable,leaving69 mAforloadcurrent.Itwouldbewastefultosink20 mAofZenercurrentjusttoprovide1mAofloadcurrent,sothisimpliesthatthestatisticalregulatorisbestsuitedtoloadcurrentsofbetween20 mAand70 mA.

ReferencesforElevatedHeaterSupplies–theTHINGY

AnelevatedLTsupplyisrequiredforanycircuithavingacathodesignificantlyabove 0 V because leakage currents fromheater to cathodeRhk(hot) otherwisedevelopanoisevoltageacrosstheACresistanceseenlookingintothecathode.Therearetwowaysofreducingtheleakagecurrentandthereforenoisevoltage:•Don’tusevalveswithpoorRhk(hot).Avalvetesterorpurpose-madejigcanbe used to select good examples. Because themost common cause of poorRhk(hot)isfluffordustcontaminationduringconstruction,itcanoftenbeburntoffbyincreasingheatervoltsby2/3andmonitoringRhk(hot)withoutdrawinganyanodecurrent.Theresistancewillbegintofall,andthemomentitstopschanging,switchtheheateroff,andallowtheheatertocool.Withluck,whentested again, Rhk(hot) will be significantly improved. Note that raising theheatervoltageeasilydamagesanoxide-coatedcathode,but if thevalvewas

unacceptableanyway,youhavenothingtolose.•If theDCvoltageacross the leakyinsulationwaszero, the leakagecurrentwouldbezero,andsowouldthenoise.

Inthisexample,ithasbeenassumedthattherearetwoheatersupplies:oneforvalveswithcathodesat≈0 Vandtheotherforvalveswithcathodesat≈130 V,so if wewere to follow the RCA recommendation, wewould require heaterselevatedby+40 Vand+170 V.Although thesevoltageswill not supply anycurrent,theyneedareasonablylowACsourceresistanceandadequatefiltering(seeFigure5.55).

Figure5.55TheTHINGY,superimposingsmoothDConheatersupplies.

Thecircuit isconnectedacross theoutputof theHTsupply,and it isapairofemitterfollowerswhoseoutputvoltageissetbyatappedpotentialdivider.Thecircuitisutterlynon-criticalofcomponentvaluesandiseasytodesign/modify.Since we are dealing with reasonably high voltages, we will neglectVbe andconsidertheoutputvoltagestobethesameasthevoltagesatthetappingsofthepotential divider. If we neglect base current and arbitrarily set the currentpassingdownthepotentialdividerto1 mA,theneachresistordrops1 Vper1kΩofresistance.Thus,ifwewant40 Vattheloweroutput,then39 kΩwillbe

nearenoughforthelowestresistor.If theupperoutputistobeat170 V,thenthe drop across the middle resistor is 170 V−40 V=130 V, and a 130 kΩresistorwilldonicely.IftheHTvoltageis390 V,thentheupperresistormustdrop390 V−170 V=220 V,soa220 kΩresistorisrequired.Althoughthecircuitonlyappliesapotentialtotheexternalcircuit,anddoesnotsource any current, each transistor must pass some collector current, but thiscurrentisnotcritical,andanywherebetween1 mAand2 mAisfine.IfwesetIc=2 mA, then theemitter resistorof the lowest transistorneeds tobe40 V/2mA=20 kΩ.We could connect the collector of this transistor directly to the emitter of theuppertransistor,butaddingacollectorloadresistorimprovesthecircuit’snoiserejectionandreducespowerdissipationinthetransistor.Theresistorvalueisnotin the least critical, but if we setVce=15 V for the lower transistor, then itscollectormustbeat40 V+15 V=55 V.Theemitteroftheuppertransistorisat170 V, so the voltage across the collector load resistor must be 170 V−55V=115 V.Sincetheresistorpasses2 mA,itsresistancemustbe115 V/2 mA,and56 kΩisquitecloseenough.TheadvantageofincludingthecollectorloadresistoristhatitreducesVce(whichreducesdissipation)andimprovesfiltering.The upper transistor also needs a collector load resistor. If we again assumeVce=15 V,thecollectoroftheuppertransistormustbeat170 V+15 V=185 V.TheHTis390 V,sotheuppercollectorloadresistordrops390 V−185 V=205V.Itpasses2 mA,soitsresistanceis205 V/2 mA,anda100 kΩresistorwilldo nicely. 205 V across a 100 kΩ resistor dissipates 0.42 W, so a 2 Wcomponentisrequired.Filtering is achieved by placing the filter capacitor not from base to ground,whichwouldrequireahighvoltagecomponent,butfrombasetocollector.Forthelowesttransistor,gaintothecollectorAv=−RC/RE=56 kΩ/20 kΩ=−2.8,andtheMiller effect therefore multiplies this capacitor by a factor of 3.8, so theeffective value is 3.8 μF. Input resistance at the base of the transistors isapproximatelytheThéveninoutputresistanceoftheresistorchain,andthefiltercut-off frequency is therefore 1.5 Hz. The lower emitter follower sees twocascaded1.5 Hzfilters,sonoiseisfurtherrejected.Thevalueofcapacitanceisnottheleastcritical.Thereisnoreasontostopatjusttwooutputs;extraoutputvoltagescaneasilybederived by cascadingmore sections. Each section adds extra filtering, so youmightchoosetoaddasectionjusttoimprovenoiserejection.Outputresistanceislessthan2 kΩ,althoughsupplementingeachtransistorwithanother,toformaDarlingtonpair,wouldlowerthisoutputresistance.

The authorwas stumped for some time in attempting to name this circuit, buteventuallyrealisedthatitisaTransistorisedHeaterInsulationNoiseGroundingYoke(THINGY),whichiswhatpeoplehavebeencallingitanyway.Note that all of the circuitry within an elevated LT supply is at least at theelevatedvoltageandthatitthereforerepresentsashockhazardiftouched.Eventhough thecircuitryonlycontainscomponents ratedat a lowvoltage, elevatedsuppliesshouldbetreatedwithasmuchcautionasHTsupplies.

Common-ModeInterferenceAllofthepreviousdiscussion(rectification,smoothing/filtering,regulation)hasbeen concernedwith producing a source ofDC power between two terminalswithaslittlenoiseorinterferenceaspossible,andalthoughnotexplicitlystated,this was differential-mode noise and interference. In this section, we willinvestigatecommon-modeinterferencewherethedifferenceinvoltagebetweenthesupply’sterminalsmaywellbezerobutbothterminalsarebouncingupanddowninunisonwithrespecttoearth.Common-mode interference often passes unnoticed. The problem becomesapparent when not only is common-mode interference present, but there is amechanismforconvertingitintodifferential-mode.

HeatersandHistory

Golden age pre-amplifiers had AC heaters and suffered hum by modernstandards.Sometimesthiswasduetoleakyheater/cathodeinsulation,butmostlyit was due to capacitance between heater wiring and signal wiring. The firstsolutionwas to centre tap theheater supply so that theheaterwireshadequaland opposite voltages, then to tightly twist the heater wiring. In this way,althoughtherewascapacitancefromeachheaterwiretoagivensensitivepoint,providedthetwistwastightenoughthetwocapacitanceswereequal(balanced),so the interfering currents cancelled. Because there’s a practical limit to howtight the twist can be, the two capacitances cannot be perfectly equal, butprovided that capacitances were minimised by pushing heater wiring into thecornersofthechassisandonlybringingituptothevalveatthelastmoment,theimbalancecapacitancethatcausedhumwasminimised.ThenextstepwastoreplaceACheatersupplieswithDC,andthisproducedanimmediate measurable improvement in 50-Hz or 60-Hz hum that was oftenessential inmicrophoneamplifiers.Remembering that thecouplingmechanismto the signal electronics is capacitive, high frequencies will be coupled moreeasily, and rectification produces a spray of high-order harmonics of mainsfrequency.DCheatersuppliesneedcarefulfilteringiftheyarenottosubstitutearattlingbuzzfortheoriginalhum;asimplerectifierandlargereservoircapacitorarenotsufficient.Filtering low-voltage,high-currentsupplieswasexpensive in the1950s,so theproblem was eased by a low current heater variant of the input valve (UF86needs100 mAat12.6 VasopposedtothefunctionallyidenticalEF86needing6.3 Vat200 mA).A tape recorderofsufficientquality to requirea low-hum

microphoneamplifierprobablyhadapush–pullloudspeakeramplifierthatdrew≈100 mAfromitsHTsupply,soacommontrickwastopowertheUF86fromthe HT supply return. The rarer, more expensive solution was to provide adedicatedheatersupplywithCRCfiltering.Any three-terminal IC regulator added after a rectifier and reservoir capacitorproduces a close enough approximation to DC that differential-modeinterferencefromheaterwiringiseliminated.

HowCommon-ModeHeaterInterferenceEnterstheAudioSignal

Common-modeheaterinterferenceisaproblemforsmall-signalvalvesbecausethe interference current is coupled from the heater directly to the enclosingcathodeviaChk(andRhkifitispoor).Theinterferencecurrentdevelopsanoisevoltage across the cathode impedance rk//Zk,whichappears as a signal at thecathode,issummedwiththewantedsignalandamplifiedbythevalve.Therearetwodistinctscenarios:• Inasingle-endedstage, thecathodewillbe (shouldbe)coupled togroundviaalowACimpedanceZk.ThislowimpedancemightbethesloperesistanceofanLEDoralargecapacitor.Butneithercomponentcanbondthecathodeemissive surface directly to earth, so the non-zero length of thewiring hasinductance which reduces coupling at RF, as does diode slope resistance,capacitorESRandwiringresistance.•Inadifferentialpair,thecathodeunavoidablyhasquiteahighresistancetoground (via the anode load resistorsdividedby theμ of thevalve–not thecathoderesistance)andcannotformausefulCRfilterinconjunctionwithChk.Weareforcedtorelyonthe(usuallyquitepoor)RFbalanceofthedifferentialpairtorejectRF,soadifferentialpairislikelytobemoresensitivetoheater-borneinterferencethanasingle-endedstage.

MainsTransformersandInterWindingCapacitance

Sincewecannot remove thepathwithin thevalveforcouplingcommon-modeinterference from the heater supply to the audio signal, we must preventcommon-modeinterferencefromreachingtheheatersupply.Atypicalmainstransformerhas1 nFofcapacitancebetweenadjacentwindings,so rather than a spike being stepped up or down by the winding ratio, it iscoupledunattenuatedviathiscapacitance.Thus,a1 Vvoltagespikethatisaninsignificant proportionof the300 VHTcanbe coupled to a6.3 Vwinding

whereitisverysignificant.HTrectifierdiodesinevitablygeneratespikeswhentheyswitch,andtheauthorhasobservedHTswitchingspikesonthe6.3 VACLT supply of aLeakStereo 20 chassis due to interwinding capacitance in thesharedmainstransformer.Sensitive heater supplies require a separate transformer from high-voltagerectification(HTsupplies,HTrectifierheatersandbiassupplies).

ReducingTransformerInterWindingCapacitance

Thecapacitanceofaparallelplatecapacitorisdirectlyproportionaltotheareaofthe plates and inversely proportional to the distance separating them, so ifwecould reduce the area between the primary and secondary and increase theirseparation, we would reduce the interwinding capacitance. (The effect ofattemptingtoadjustthedielectricconstantwouldbeminimal.)As an example, the Maplin 100 VA EI transformer kit is of split bobbinconstructionwiththeprimarywoundinonehalfofthebobbinandtheotherhalfleft empty for the user to wind the secondary. The area of the interwindingcapacitoronasplitbobbintransformerissimplytheareaofthedividerbetweenprimaryand secondary less a little at the cornersbecause thecopperwindingstendtocurveastheybendroundeachcorner(seeFigure5.56).

Figure5.56Interwindingcapacitanceinasplitbobbintransformer.

The capacitive area of the divider is ≈1,800 mm 2.Conversely, if the dividerwas to be removed and the bobbin filledwith layer-woundwindings, the areabetween the primary and secondary would be ≈7,200 mm 2, increasing thecapacitancebyafactorof7,200/1,800=4.Turning to the thickness between the plates, a typical polyester transformerinsulationtapemightbe0.055 mmthick,butalthoughasinglethicknesswouldtheoretically be rated at 3 kVbreakdownvoltage, a transformermanufacturerwouldbeawarethatpracticalitiescouldrequirefourlayersofthistapebetweenthe primary and secondary layers to guarantee adequate dielectric strength toadequatelyinsulatemainsvoltages,givingatotalinterwindingthicknessof0.22mm.Conversely,thedividerinthesplitbobbintransformeris1.07 mmthick,

soitreducescapacitancebyafactorof1.07/0.22=4.9.Takentogether, thereducedplateareaandincreasedseparationoftheexamplesplit bobbin transformer reduce interwinding capacitance by a factor of4×4.9≈19.5,implyinganinterferencereductionof≈26 dB.Beforemains-borneinterferencecanreachtheinterwindingcapacitance,itmustpass through the transformer’s leakage inductance, so these two componentsformaresonantnetwork.Ifweassume(forthepurposesofcomparison)thattheresultingcurrentdevelopsavoltageacrossa1 Ωearthbondresistancebetweenthe heater winding and the chassis, we canmodel the threemain transformerconstructions. The author measured the leakage inductance and primary tosecondaryinterwindingcapacitanceofthreecommercial100 VAtransformers,and then modelled how well common-mode interference transferred to theresistance(seeFigure5.57).

Figure5.57Modelledmainsinterferencetransmissionforthethreedominantmainstransformerconstructions.

Surprisingly, the large differences in leakage inductance are immaterial, andinterference at audio frequencies is determined purely by interwindingcapacitance,withthesplitbobbinexamplepassing27 dBlessinterferencethanthelayerwoundortoroid.

Post-TransformerFiltering

Wehave seen that segregatingHT and heater transformers and choosing splitbobbinconstruction(mandatoryinAustralia)reducecommon-modeinterferencebutfurtherfilteringmaybenecessary.Evenifa6.3 Vheaterwindingalreadyhasacentretap,wecanaddaverycheapLRfiltersimplybyconnectinga47 Ωresistorfromeachendofthewindingtochassis–thefilterusestheleakageinductanceofthetransformer.We canmake an explicit common-mode filter by adding series inductance toeachlegoftheheatersupplyandcapacitancefromeachlegtothechassis.Sincewe are trying to filter common-mode noise, rather than differential-mode, wewind a bifilar choke on a small ferrite core and do not worry about coresaturationbecausethecurrentsinthetwocoilscreateequalandoppositefields,which cancel, so the core does not see any net magnetisation. Commerciallymadecommon-modechokesarereadilyavailable.

PracticalIssuesAlthough we now have enough theory to determine component values andratings ineachofapower supply’s individualblocks, thereare somepracticalconsiderationsthatshouldbeaddressedbeforewedesignacompletesupply.

TransformerRegulation

Transformer manufacturers quote secondary voltage at rated current and alsoregulationasapercentage:

Atypical50 VAtransformermighthavearegulationof13%,soa6 V50 VAtransformercouldbeexpectedtoproduce1.13×6 V=6.78 Voff-load,andthisisthevoltagePSUD2needs.Perhaps more significantly, if we need 6.3 V, we can achieve it by under-runninga6 Vtransformer.Westartbyrearrangingthepreviousequation:

Wenowsaythatratherthanusingtheentirecurrentrating,wewilluseafractionofit:

Thus,forour50-VA6-Vexample,thefull-loadcurrentwouldbe8.33 A,butifweonlyneeded4 A,ourcurrentfractionwouldbe4 A/8.33 A=0.48,so:

Thus,wecanachieve6.3 Vfromastandard6 Vtransformerandhave80 mVin hand for voltage drop across the heater wiring. This trick of using anoversizedstandardtransformercanbeaveryusefulwayofavoidingtheexpenseofacustom-woundtransformer.

HTCapacitorsandVoltageRatings

Thecapacitorsfor300 VHTsuppliesareeasilyobtainedbecausetheswitchedmode supplies in computers need 385 V capacitors to cope with the 340 Vresulting from rectifying 240 Vmains. But if we need a higher HT voltage,perhaps 430 V for a pair of EL34s, then a 450 V rated capacitor would be

overstressedifmainsvoltageroseby6%(asit islegallyallowedtodo).Therearetwochoices:weeitheruseahighervoltagecapacitor,whichwillusuallybepaperorplasticfilmandgenerallyonlyavailableinquitelowvalues,orconnect‘n’equal-valueelectrolyticcapacitorsinseriestoobtainacompositecapacitorhavingatotalvoltageratingmultipliedby‘n’buttotalcapacitancedividedby‘n’.Because thecapacitorsareconnected in series, thecurrentpassing through thecapacitorsmustbeequal,soeachcapacitorreceivesanidenticalcharge(Q=It).Iftheircapacitancesareequal,thenthevoltageacrosseachoneofthemmustbeequal(Q=CV).Unfortunately, even if the capacitances are equal, the leakage currents in eachindividual electrolytic capacitor areunlikely tobe equal, so thevoltage acrosseach capacitor will not be equal. To equalise the voltages, and prevent onecapacitorfromexceedingitsratedvoltage,eachcapacitorshouldbebypassedbya resistor so that the resultingpotential divider chain forces thevoltages tobeequal(seeFigure5.58).

Figure5.58Bleederresistorsequalisecapacitorpotentials.

Thedividerchainshouldpassatleast10timestheexpectedleakagecurrentofthe capacitors to ensure correct operation. Typically, a 220 kΩ 2 W resistorsuffices.A technically better method is to use separate HT windings andrectifier/smoothingcircuits,andplacetheresultingfloatingDCoutputsinseriesto obtain the required HT voltage. This ensures that each capacitor cannot

exceeditsratedvoltage,but themains transformer isnowmorecomplex(readexpensive)(seeFigure5.59).

Figure5.59AchievingHT>340 VDCwithelectrolyticcapacitors.

CanPotentialsandUndischargedHTCapacitors

Bothof thepreviousschemes forproducingacompositeHTcapacitorofhighvoltage rating resulted in one capacitor with its negative terminal stood awayfrom ground potential. This is significant because the can of an electrolyticcapacitorisconnectedeithertothenegativeterminaloratapotentialverycloseto it.Cans at an elevated voltagemust not only be insulated from the chassis(flanged plastic capacitor clamps that prevent the can touching the chassis arethereforebest),butthecapacitormustalsobeproperlyinsulatedfromtheuser.HT supplies represent a formidable shock hazard, and it is essential thatprovision ismade for fullydischarging the reservoir and smoothingcapacitorswhen the equipment is switched off. TheHT supply therefore needs a purelyresistivedischargepathto0 Vatsomepoint,andthesimplestwayofprovidingthisistoconnecta220 kΩ2 Wresistoracrossthereservoirelectrolytic,whichnotonlydischargesthecapacitor,butalso(providedthatthereisareturnpath)dischargessubsequentHTcapacitors.

TheSwitch-OnSurge

TheSwitch-OnSurge

Ifwedonot use a valve rectifier, theHT switches on instantly, and suddenlyapplying 400 V to an electrolytic capacitor stresses both dielectric andelectrolyte, sowe should look to see if there is someway of prolonging life.(Given that computers typically last only five years before being consigned tolandfill,physical longevityof theirpowersupplies isscarcelyanissue,sotheydon’tworrymuchaboutswitch-ontransients.)When we apply rectified AC to the reservoir capacitor, we may be unluckyenough to switch at the instant that the cycle is at its peak voltage. Theinstantaneoustransitionfrom0 Vto325 V(dV/dt ≈∞)appliedtothecapacitorcausesatheoreticallyinfinitecurrenttoflowbecause:

If,however,wecouldalwaysswitchat thezero-voltagepoint, thenalthoughdV/d t for a sinewave is at amaximumat this point, it is not infinite, and theinrush current is reduced. Devices capable of performing this switching areknown, predictably, as zero-voltage-switching relays and the Crystal PalaceamplifierinChapter6usesonetosoftentheinrushtoitsmainHTsupply.However, theauthor isbeginning toharboursuspicions that theserelaysmightcause switching spikes as the mains crosses 0 V and switching is handedbetweenthetwoback-to-backthyristorsthatmakeuptheinternaltriac,andhe’scertainlyseensomeoddeffectsonlogiclinesasazero-voltage-switchingrelayswitched an inductive load, so in low-noise applications perhaps it’s time toreverttohardvacuumrectifiersandsimplyswitchmainstotheHTtransformer(that also has the rectifier heater winding) using a conventional switch orelectromechanicalrelay.

MainsFusing

AlthoughUKmainsplugshaveafuseintheline,it’stheretoprotectthelead,nottheequipment.Thefirstcomponentthelineshouldmeetwhenitentersapieceofequipmentisan appropriately sized fuse that protects against fire in the event of an over-currentfaultwithinthatequipment.Ifweuseonepieceofequipmenttoswitchand distributemains to other equipment, wemust fuse its internal electronicsseparately from the mains distribution. 230 V appliances in North Americarequiredouble-polefusing(afuseineachline)becausethe230 Visactuallyatwo-phasesystemof115 V–0–115 V(centretaptoearth),soalthoughasingle

fusewouldprotectagainstanover-currentfaultfromlinetoline,eachlinemustbeprotectedagainstlinetoearthfaults.Fusesaremanufacturedtobe‘fast’(F)or‘timed’(T).‘Timed’usedtobecalled‘anti-surge’, and these fuses are intended to survive a short inrush currentconsiderably higher than their sustained current rating. Almost all electronicequipment draws an inrush current at switch-on as reservoir capacitors arechargedortoroidaltransformerskick,sowealwaysneed‘timed’fuses,buthowdowedeterminetheirrating?Fusemanufacturers’ data sheetshaveplentyofgraphs that refer to I2t ratings.Whatthey’repointingoutisthatifafusewirehasacertainmass,itmustrequireadefinedquantityofheatenergytoraiseitstemperaturetomeltingpointsothatitruptures.Recallthatpower=I2Randthatenergy=Pt,andI2tratingssuddenlymakesense.Atthispoint,thehopefulauthorreachedforhisHalleffectcurrentprobe,usedhisdigitaloscilloscopein‘singlesequence’modetocaptureamainsinrushcurrentat switch-on, set theoscilloscope’s ‘math’ function toCh1×Ch1(to give I2), positioned cursors at the beginning and end of the pulse, gated a‘mean’measurementon‘math’bythecursors,andthenmanuallymultipliedthatmeanvaluebythetimebetweenthecursorstoarriveatanaccuratelymeasuredvalueofI2t.Unfortunately,furtherreadingoffusedatasheetrevealswhatwealreadyknewsubliminally.Fusesaren’tterriblyaccurate,andastheirI2tratingfallsclosertothe measured value, we’re more and more likely to suffer nuisance blowing.Understandably,fusemanufacturersexpressthesituationmoreformallyintermsofprobabilities,but theiradviceamounts to:Guess/measureanI2t rating, tryafuseof that ratingand if itblows toooftenwithout therebeinga fault, try thenextcurrentratingup.

MainsSwitching

Mainsswitchingissimilar tomainsfusingbutmayhaveacomplicationaddedbytheincomingmainsconnector.Forasinglephasesystem,asingleswitchinthelineconductorissafestprovidedthat connector polarity is unambiguous (IEC mains connector), but if theunpolarised two pin figure-of-eight small appliance connector is used, doublepoleswitching(oneswitchinlineandoneinneutral)isnecessarytoensurethatnomatterwhichwayroundtheconnectorisinserted,linepassesnofurtherthanthe switchwhen in its ‘off’position.Multiplephase systems (NorthAmerican230 V, German 380 V) are unlikely to be encountered in audio but would

requireswitchingofeachphase.Itmightbe thought thatasinglephasesystemshouldbedoublepoleswitchedirrespective ofmains connector, but consider a piece of equipment having anearthedmetalchassis,poweredviaanIECconnector,doublepoleswitched,andimagine that the switch in the neutral fails open circuit. The equipment losespower and superficially appears safe for investigation to determine the fault.However,lineisstillpresentonthemainstransformersandthereisaveryrealdanger of the investigator suffering a shock from line to the earthed metalchassis.TheeasiestwaytoensuresafetyofmainsfusingandswitchingistouseanIECinlethavinganintegralfuseandswitch.Arelayallowsremotemainsswitching.Thus,alowvoltageswitchonacontrolunitcouldenergisea remote relay toswitchmains.Unfortunately, that impliesthatweneedpermanentlyappliedstandbypowerinordertobeabletoswitchtherelay.The authorwas previously perfectly happy to leaveRIAA-stage heaterspermanently heated in standbymode, thus also providing power for the relay,butrecentelectricitypriceriseshavechangedthat.Nevertheless,youmightfeelthattheconvenienceofarelayoutweighsthecost.There’sanastylittleproblemtobeawareofinsomerelays.Atitssimplest,anelectromechanical relay is just a coil of wire round a soft magnetic core thatattracts a hinged softmagneticmaterial known as an armature to provide theswitching action. A simpler (cheaper) relay can be made by passing theswitching current through the armature, so when we switch our mains, weconnect the relay’s (electrically conductive) core to 240 V. The core’ssurrounding coil is wound on an insulating plastic former, so we have justconnected a significant capacitance from one side of our heater supply to themains–negatingallourdesigneffortsatreducingcommon-modenoise.Specifya relaywithstandvoltageof10 kV,and theproblemisunlikely tooccur.Therelays to be suspicious of have a low profile rather than being square whenviewed from the side. If in doubt, reach for a hacksaw and sacrifice one toscience to determine its exact construction before building that type in andhavingtodiagnosetheproblemlater.

APracticalDesignHaving investigated individual blocks,we are now in a position to be able todesign a complete HT and heater power supply. An RIAA stage imposes themostdemandingpowersupplyrequirements,sowewilldesigntwovariantsofapowersupplyfor thisuse;wecanthenadd/discard/modifyblocksasnecessaryforotherapplications.ThefirstvariantisforthebalancedhybridRIAAstageofChapter7thatrequiresanHTof195 Vat48 mAandasingleheatersupplyof6.3 Vat1.2 A.Wewillneed:•HTregulation•HTrectificationandsmoothing•Heaterrectificationandsmoothing•Heaterregulation•Mainsfiltering.

Wecannowdrawablockdiagram(seeFigure5.60).

Figure5.60Preliminaryblockdiagramofpowersupply.

HTRegulation

Therearethreepossibilities:•Valveregulator

•Maida(317)regulator•Statisticalregulator.

Valve regulators tend to be big. Techno-pretty, but big. An optimised valveregulator isbigger,prettier (evenmoreglowingglass)andneeds lotsofheatersupplies forall thatglass.Withcare,anoptimisedvalve regulatorcanachievenoise≈1 mVpk–pk.TheMaidaregulatorissmall,doesn’tneedheatersupplies,butiselectricallyfragile,andproducesnoisecomparablewithavalveregulatorbut without the DC drift. The statistical regulator is slightly larger than theMaidaregulator,butfarquieterandmorerobustthantheauthorexpected.ThebalancedhybridRIAAstageusesadifferentialcascodeinputstagehavinglimitedPSRR, so the lownoiseof the statistical regulatormakes it thenaturalchoice(seeFigure5.61).

Figure5.61Thestatisticalregulatorconfiguredfor195 Vat46 mA.

ThecascodeDN2540N5CCSmustbeprogrammedtopasstheloadcurrentplusthecompositeZenercurrent.ThecompositeZenercouldoperateat10 mA,butsloperesistanceandnoisearesignificantlylowerat20 mA,sotheCCSneedstobe programmed for 68 mA. Field Effect Transistor (FET) device variationmeansthattherequiredsourceprogrammingresistancevarieshugely,soa50 Ωvariable resistor is required – the 18 Ω resistor prevents accidental setting ofexcessive current. Although the programmed 68 mA current passes throughbothDN2540N5s,onlytheupperonehasanappreciablevoltageacrossit,soitwillrequireaheatsinktodissipate4–5 W,butwewon’tknowtheexactpowertobedissipateduntilwehavedesignedourrectificationandsmoothing.Weknowthatwemustuse5.6 VZeners,so195 V/5.6 Vmeansthatweneed35 of them in our composite Zener. Under normal conditions, the compositeZenerpasses20 mA,butintheeventofacatastrophicfaultcausingtheentire

load to be disconnected, the constant current source will drive its entireprogrammingcurrentof68 mAdownthecompositeZener.SinceeachZenerisratedat500 mW,itcanpassamaximumcurrentof0.5 W/5.6 V=89 mA,soa68 mAfaultcurrentistolerable.WesawearlierthatthecompositeZenerrequiresabypasscapacitortosetatimeconstant of at least 360 μs in conjunction with its slope resistance, so if weassume rslope=6 Ω per Zener at 20 mA, then the composite Zener’s sloperesistancewillbe210 Ω,and360 μswouldbeachievedby1.7 μF,butbecauseofthelikelyvariabilityofthat360 μstimeconstant,itwouldbesafertouse10μF.Thecapacitorhas195 Vacrossit,soa250 Vcomponentwouldbefine,buttheauthorhadabatchof10 μF400 VKelvincapacitors,sothisiswhatheused.

HTRectificationandSmoothing(aPSUD2Exercise)

Although the statistical regulator has excellent low frequency ripple rejection,rejectionofinterference>100 kHzisdeterminedprimarilybytheinductanceofitsbypasscapacitorwhichwillberesonantat<1 MHz.Thus,itmakessensetochooseapost-rectificationfilteringschemethatmaintainsitsfilteringtoashigha frequency as possible, and an LC filter using a capacitor having a Kelvinconnection is ideal. Having tested a prototype and proven the principle, theauthor had previously bought a batch of ten 100 μF 400 V metallisedpolypropyleneKelvinconnectioncapacitors,sothisiswhatheused.Thestatisticalregulatorrequiresanabsoluteminimumof10 VacrossitsCCSbeforeitwilloperate,but>20 VtoensurethatCOSSintheupperdevicefallstoitsasymptoticvalueof12 pF.Thus,weneed195 V+20 V=215 Vleavingthefilter,buttoallowcorrectoperationinthefaceofmainsvoltagevariation,itiswisetoincreasethisby≈10%,bringingitto240 V.AssumingaPSRRof40 dB(duetothedifferentialpair)attheinputstageofthebalancedhybridRIAAstage,an80 dBsignaltohumratiorequiresrippleonthe195 VHTtobe<2.7 mVpk–pk.Thestatisticalregulatorwillcertainlyhave>90dBrippleattenuation,sothiscorrespondstotolerating85 Vpk–pkrippleleavingtheLCfilter,implyingthatfilterdesignisnotcritical.Inpractice,85 Vpk–pkofripplereachingtheregulatorwouldrequireraisingitspeakinputDCvoltageby85 Vfrom240 Vto325 Vtoavoiddrop-out,soitwouldbebettertorequirethat theLC filter limit ripple to<10 V pk–pk.Thus,ourLC filtermustdeliver250 Vwith<10 Vpk–pkrippleatacurrentof68 mA,sowenowneedtoswitchonthecomputerandinvokePSUD2.

Sinceweneed<100 mA,ahardvacuumrectifier isnotonlya tenabledesignchoice,but also themost sensible, and68 mAsuggests theverycheapEZ80.Wedefinitelywant full-wave rectification,but abridge rectifierwithvalves isawkward, sowe should simulateusingPSUD2’s ‘full-wave’option, and ifwedon’thaveacentre-tappedmainstransformeroftherequiredvoltage,wesimplymakeahybridbridgerectifierusingtheEZ80andapairofSTTA512Fs.Pleasingly,youwilldiscover thathavingalreadychosen the100 μFcapacitorand EZ80 rectifier, it is very hard to design a 250 V 68 mA power supplyincorporating an LC filter that produces as much as 10 V pk–pk ripple. Inpractice,themaindesignlimitationturnsouttobepreventingthechoke’speakcurrentfromexceedingitsrating,somakesureyoumonitorI[L1]aswellastheoutputvoltage.Rememberalso that the transformervoltagePSUD2requires isnotthemanufacturer’sratedfullloadvoltagebuttheopencircuitvoltage.Theauthorhada260–0–260 V100 mA,6.3 V2 AAdmiraltypatternmainstransformer and a matching Admiralty pattern 20 H 120 mA choke, so theproblemwastopersuadethecombinationtoproducetherequiredDCvoltage.Theopencircuitvoltageofthetransformerfromthe0 Vtoeach260 Vtapwasmeasuredtobe282 VRMS.Quiteapartfromtheobvioussafetyconsiderations,thismeasurementneedstobemadequitecarefully–it’simportanttoknowthatthetransformer’sprimaryisactuallyreceivingitsexpectedvoltage.Supposethatthe transformer’sprimarywasstated tobe240 Vbutmains thatdaywas245V;thiswouldmeanthatthesecondaryvoltagewouldbefalsely2%high.Ifyouhavetwometers,usethemandcorrectformainsvoltagevariation.TheDCresistancefrom0 Vtoeach260 Vpinwasmeasured.Onewas99 Ωandtheother89 Ω,andthisdisparity iscommonin layer-woundtransformersbecauseitischeapertolayer-windacentre-tappedtransformerwithonehalfofthewindingontopoftheother,sotheaveragediameteroftheouterwindingisalittle larger than thatof the innerwinding,resulting inaslightlyhighercopperresistance. Unless balanced by adding an external resistance to the innerwinding, a ripple component at mains frequency appears at the output of therectifier, which is not particularly well attenuated by an LC filter. Thus, weshouldadda10 Ωresistorinserieswiththe89 Ωwindingtomakeboth99 Ω.PSUD2 requires transformer output resistance including reflected primaryresistance.Primaryresistancewas24 Ω,andsincetheopencircuitvoltagewas282 VRMSwhen the inputwas240 VRMS, the turns ratio is282/240=1.175.Impedances are transformed by the square of the turns ratio, so the reflectedprimaryresistanceis24×1.1752=33 Ω,andweaddthistothe99 Ωsecondaryresistancetogive132 Ω,andputthisvalueintoPSUD2.

The DC resistance of the choke was 367 Ω, and the ESR of the 100 μFpolypropylene capacitor is 6 mΩ, so these two valueswere also entered intoPSUD2.Theloadwassetto‘constantcurrent’and‘steppedload’startingat10mA, and then68 mAafter 1 s.The simulationwas set to run for 2,000 msafteradelayof0 s.Inthe‘Options’menu,‘Allowwarnings’,‘Autosimulate’,‘Dual axis’ and ‘Soft start’ were all ticked. Finally, V[C1] was ticked in theresultcolumn(seeFigure5.62).

Figure5.62PSUD2simulationshowsinsufficientvoltageandahintoflowfrequencyundershoot.

Asyouwillfindifyourunthesimulation,notonlycouldachokeinputsupplynot achieve the required 250 V at 68 mA, but there was a very slightundershoot when the stepped current load changed from 10 mA to 68 mA(temporarily reduce choke resistance from 362 Ω to 62 Ω to see this effectmore clearly). A capacitor input supply would certainly produce too muchvoltage(√2×282=399 V),soweneedanintermediatesupply.We highlight the entireLC filter, right click and ‘insert’ a ‘C’ filter. PSUD2automaticallysetsanynewcapacitor tobe thesameas theexistingone,soweeditC1to5 μF;a5 μFfilmcapacitorislikelytohaveanESRof≈10 mΩ,sowecaneditthisvalueifwewish(itdoesn’tactuallymakeanydifference).WenowchangetheresulttoV[C2]andfindthattheovershoothasdisappeared,butthatwehaveahighervoltage(310 V)thanwewantonC2.WeeditthevalueofC1 until we obtain 250 V, requiring 1.8 μF. Unfortunately, 2.2 μF is thenearestE6standardvalueandthisproduces260 V,whichisnotidealbecauseitincreasesdissipationoftheCCS’supperDN2540N5from3.6 Wto4.3 W,butthisisstillacceptable.Now thatwehave the requiredoutputvoltage,wecan check internalvoltagesandcurrents:

•ILpeaksat83 mA0.5 safterswitch-onbutoperatesat76 mApkduringnormaloperationwiththe68 mADCload.• V[C1] peaks at 383 V, so a 400 V component will not do − 630 V isneeded,implyingpolypropylenedielectric.• I[C1]peaks at+184 mAduringnormaloperation, and this is noproblemevenforametallisedcapacitor.•ItisquickertocheckthefaultvalueofV[C2]manuallythanusePSUD2,buttryitanywaytoproveittoyourself.V[C2]wouldriseto282×√2=399 Vwithnoloadcurrent,whichiswhya400 Vcomponentwasneeded.(Ifthemainsvoltagewas simultaneously high, the 400 V ratingwould be exceeded, butaudio is not life-critical, so it is conventional to assume only one fault at atime.)•I[D1]peaksat253 mA,but increasingtheloadcurrentbyonly8–76 mAcausesPSUD2toflashupanover-currentwarning,so theEZ80ismarginalandanEZ81mightbebetter, although itwould cause theoutputvoltage toriseto272 V.

Finally,weshouldchangePSUD2’ssimulationtimeto50 msanditsreportingdelayto5 stoinvestigatetherippleV[C2].Subtractingtheminimumvoltageonthegraphfromthemaximum,wefindwehave205 mVpk–pkofripple−34 dBbetterthanour10 Vpk–pklimit.Thestatisticalregulatorpasses20 mAthroughitscompositeZener,implyingasloperesistanceof200 Ωandtherefore103 dBrippleattenuation.Intheory,theentireHTsupplyhasthepotentialtoproduceits195 Vwithonly500 nVRMSripple.Inpractice,whatthismeansisthatripplewillonlybemeasurableifconstructionisflawed.Nowthattheprincipleshavebeendemonstrated,youcanuseacombinationofthe formulae given earlier in this chapter plus PSUD2 to design your ownrectificationandfilteringthatgivestherequiredperformanceusingcomponentsavailabletoyou.

HeaterRectificationandSmoothing(aManualExercise)

When designing the HT supply, we started with the regulator and thenprogressedtorectificationandsmoothing.However,fortheheatersupplies,weknowthatwemustuseasplitbobbintransformerinordertobenefitfromtheirgreatly reduced inter-winding capacitance, but such transformers tend to havestandardsecondaryvoltagessuchas6 VRMSor9 VRMSanditiseasiertotest

standardtransformervoltagesforsuitabilitythandemandanexactvoltage.Weultimatelyneed6.3 VDCat1.2 A,andthiscanbecateredforbythe1.5 A317. As before, regulator design begins with regulator drop-out voltage, anddespitewhatthedatasheetsclaim,atypical317needs>3 Vacrossittoregulatecleanly.Wethereforeneedaminimumvoltageof9.3 Vbeforetheregulator.Assumingacapacitorinputfilter,6 VRMS×√2=8.5 Vpk,whichisinsufficient,sowe need a 9 V RMS secondary,which provides 12.7 V pk.Wewill use abridge rectifier,whichalwayshas twodiodes inseries, so itwilldrop≈1.4 Vacrosstherectifier,whichbringsthevoltagedownto11.3 V.If a rectified sine wave of 11.3 V pk leaves the rectifier, then this is themaximum voltage towhich a reservoir capacitor of infinite capacitance couldcharge.Acapacitoroffinitecapacitancewillchargetothisvoltageonthepeaks,butitsminimumvoltagemustbe:

The absoluteminimum voltage thatwe can allow is 9.3 V, so themaximumripplevoltagewecantolerateis2 Vpk–pk.Usingourearlierequationthatrelatedripplevoltagetocurrent:

Theequationrequires6,000 μF,sowecoulduse6,800 μF,butthiswouldnotallowforanytoleranceoncapacitorvalue,ormainsvoltagevariation,so10,000μFwouldbeasaferchoice,resultingin1.5 Vofripple.You could analyse this circuit in PSUD2, but you will find that entering thetransformerresistancerequiresyoutobeabletomeasureasecondaryresistanceoftheorderof40 mΩ,whichcanonlybedonereliablyusingafour-wireKelvinconnection(notavailableonmostDMMs).Further,evenifyouareabletomakesuchmeasurements, youwill find that a ripple current of 9 A is predicted –much higher than the typical measurement of 6 A. Sometimes, manualcalculationbeatscomputersimulation.Ifthebridgerectifierdrops1.4 V,andpassesanaveragecurrentof1.2 A,thenitmustdissipate≈1.7 W(thisisacrudeapproximationbecauseIaverage≠IRMS,butwedon’tknow theaveraged ripplecurrent IRMSoveronecycle).This isasignificantamountofheattobelostfromthetypicalW021.5 Abridgerectifierpackage,sotheyinvariablybecomeveryhotandeventuallyfail.Itisthermallybettereither touse individualdiodessuchas the3-A1N54**series,ora4 Abridgerectifierpackage.An even better solution can be to use Schottky diodes, perhaps the 31DQ**

series,forthebridgerectifier.Thesehaveaslightlylowerforwardvoltagedrop,reducing diode dissipation, but themain justification for their use is that theyswitchoff cleanly,without the currentovershoot exhibitedby junctiondiodes.Asmentionedearlier,theovershootisanimpulsethatexcitesresonancesinthetransformer/rectifier/reservoircapacitorsystem.Theoutputvoltagefromtherectifierisonly11.3 Vpk,soVRRMforeachdiodeneedonlybe12 V;50 Viscommonlythelowestavailableratingavailableandallowsformainsspikes,sothiswillbefine.Each diode in the bridge should be bypassed with a film capacitor; 100 nF63VDCisagoodchoice,butalmostanythingwilldo,providedthatthevoltagerating>VRRMforeachdiode.

HeaterRegulation

Weshouldfirstconsiderhowmuchpowerthe317mustdissipatewhenthe1.2Aloadcurrentisdrawn.Assuming1.5 Vpk–pkrippleonthereservoircapacitor,theaveragevoltageappliedtotheregulatoris10.6 V,sothevoltageacrosstheregulator is 4.3 V, and the regulator therefore dissipates ≈5 W. 5 W is aperfectly reasonable dissipation for the (20-W) TO-220 package of a 317T todissipateprovided it is thermallybonded toanaluminiumchassis,so theolderand much more expensive 317K TO-3 metal ‘power transistor’ package isunnecessary.The1N4002protectstheregulatorfromreversevoltage.The next step is to determine the value of resistors needed in the potentialdivider. Experience shows that the reference voltage tolerance on the 317 isactually very good, and that it is unnecessary to include a variable resistor totweaktheoutputvoltage.Youmighthaveadifferentviewonthis,butanupperresistorof180 Ωandalowerresistorof750 Ωset6.5 Vthatallowsforthe0.2V voltage drop down the typical 3 m loop length of 0.6 mm-diameter solidcore twistedpair separating the regulator in the remotepowersupply from thevalvepins.TheThéveninresistanceofthe180 Ωand750 Ωcombinationis145 Ω,soa10μF speed-up capacitor should be used to bypass theADJ pin to ground. Themanufacturers’ application notes recommend that the output of the 317 bebypassed togroundwitha1 μF tantalumbeadcapacitorviaa2.7 Ωresistor,but tantalumbeadcapacitorsgenerallyhavesufficientlyhighESRtomake theexplicitresistorunnecessary.Ifyoudecidetodiscardthe2.7 Ωresistor,eithercheck the capacitor data sheet, or (best) measure the capacitor with an ESRmeter.Weneedacommon-modechoke,andwecouldput itbetween the transformer

secondaryandtherectifier,but thisreliesoncriticalbalancingof theopposingmagneticfieldsduetothe6 Apkripplecurrenttoavoidsaturation,soitisbettertoput itbetween thereservoircapacitorand theregulatorwhere itonlypasses1.2 ADC.Thefollowing10 nFcapacitorsshouldhaveleadsasshortaspossibleto chassis. If you can match the 10 nF capacitors, so much the better foravoidingconvertingcommon-modenoiseintodifferential-mode.Wecannowdrawaheatersupplycircuitdiagram(seeFigure5.63).

Figure5.633176.3 V1.2 Aheatersupply.

MainsFiltering

Theauthorhasneverbeenentirelyconvincedoftheutilityofmainsfilters,buttheyareabitlikeacarseatbelt–youwearitnotbecauseyouexpecttoneediteverydaybutbecausethedaymightcomewhenyoudo.Although the power consumed by electronic equipmentmay not be especiallyhigh, theripplecurrent(aswefoundearlier)canbemuchhigher thantheloadcurrent.MostcommercialRFIfiltersareratedat16 Aorless,whichmaynotbeenough for audio. If we want an RFI filter, we probably need to make itourselves,windingourownbifilarchokeonaferritetoroid(seeFigure5.64).

Figure5.64Mainsfilter.

A130 Jmetaloxidevaristorisconnectedacrossthemainstolimitmainsspikes.Manufacturers’datasheetsforthesedevicesdisingenuouslyshowthata100 Vspikeridingonthepeakof themainswaveformisclippedveryeffectivelybutdon’tshowthata340 Vspikesittingonthe0 Vcrossingpointwouldpassbyunmolested.Still,thedaymightcomewhenoneisneeded.Theseriescommon-modechokeisterminatedateachendbyapairofClassX2capacitors. X2 capacitors are the only type of capacitors that may be legallyconnectedbetweenmainslineandneutral(thereasonisthattheyarespecificallydesignedtofailsafely).ManyRFIfiltersalsoincludea4.7 nFClassYcapacitorfromlivetoearth,andanotherfromneutraltoearth,buttheirutilityisdebatableforaudioequipmentastheycanmaketheearthnoisy.If theHTmains transformerhasanelectrostaticscreen, itshouldbeconnecteddirectly to chassis. The heater transformer won’t have an electrostatic screenbecauseitisofsplitbobbinconstruction.Wecandrawafullpowersupplycircuitdiagram(seeFigure5.65).

Figure5.65CompletepowersupplyforbalancedhybridRIAAstage.

AdaptingthePowerSupplytotheEC8010RIAAStageThebalancedhybridRIAAstagerequiredanHTof195 Vat46 mA,but theEC8010RIAAstagerequires390 Vat67 mA,andapairofreferences(40 V,270 V)atzerocurrent.Ratherthanasingleheatersupplyof6.3 Vat1.2 A,theEC8010RIAAstageneedsfour300 mAat12.6 Vsuppliestiedto≈40 Vthatcanallcomefromonetransformersecondaryandafurthertwo300 mAat12.6Vsuppliestiedto≈270 Vrequiringanothertransformersecondary.Theheaterstrings were configured in this way to enable use of a standard transformerhavingtwosecondariesofthesamevoltage.Wewillneed:•HTregulation•Referencevoltages•HTrectificationandsmoothing•Heaterregulation•Heaterrectificationandsmoothing.

HTRegulation

Wewillagainusethestatisticalregulatorbecauseofitslownoise.390 Vmightseemanalarmingvoltagetosetfrom5.6 VZeners,butit’ssimplytwo195 VcompositeZenersinseries(70×5.6 VZeners).Theincreasedcurrentdemandispotentially more of a problem as 67 mA of load current plus 20 mA Zenerquiescentcurrentrequires87 mAfromtheCCS,andiftheloadshouldfail,theCCSwouldsinkall87 mAintothecompositeZener.Theauthorwasnervousthat87 mAwasfar tooclose to the89 mAmaximumrating,sohesimulatedtheinsideofanRIAAstagebycoveringasingleZenerwithasheetofcardboardtopreventpropercooling,andthentestedit(seeFigure5.66).

Figure5.66StressingaBZX555.6-VZener:voltageandappliedcurrentagainsttime.

Measurementswereloggedat1 sintervalsusingapairofAgilent34410A6½digitDMMs.TheexponentialcurvefollowingthetransientontheZenervoltage(upper trace) is due to the wires and silicon within the Zener heating andincreasing their resistance as a result of the increased applied current (lowertrace). The Zenerwas run for a short time at the statistical regulator’s designcurrentof20 mA,thenincreasedto68 mAtosimulateafaultinthebalancedhybridRIAAstage, and then87 mA to simulatea fault in theEC8010RIAAstage. The Zener survived 5 min at 87 mA, so it was clearly time for someabuse.Currentwas increased in10 mAstepsand left for roughly150 seachtime.Afterhalfanhourof this, theauthor’spatiencewasrunningthin,andhefinally applied 300 mA, which did provoke a reaction (smoke from thecardboardandaspikeonthegraph),sohebackedthecurrentofftotheoriginal20 mA.Astonishingly,despitediscolouredlead-outs,oncetheZenerhadcooleditsvoltageat20 mAwaswithin0.1%oftheoriginalvoltage.There seems to be no justification for fearing damage to the composite Zenerfromafaultcausingitscurrenttoriseto87 mA.

ReferenceVoltages

The40 Vand270 Vreferencescouldbe tappedoff thestatistical regulator’scompositeZener, but having devised an astonishingly low-noise regulator, theauthorisn’tabouttoruinitbyinjectingmainsinterferenceviatheinter-windingcapacitance of amains transformer, even if that capacitancewould be divided

downbyatransistor’shfe.The safest solution is touse aTHINGYconfigured for40 Vand270 Vandfeed it fromtherawsupplybefore theregulatorso thatanymains interferencethatdoesmanagetocrawlbackthroughtheTHINGYcanbeattenuated100 dBbythestatisticalregulator.

HTRectificationandSmoothing(aPSUD2Exercise)

Werequire390 V,andweneedat least20 Vacrossthestatisticalregulator’sCCS,soifweallow10%formainsvariation,weneed451 V,say460 V.Thisvoltageisbeyondwhatasingleelectrolyticcapacitorcouldtolerate,andputtingapair inserieswoulddouble typical series inductance from18 nH to36 nH,add20 mmofwireat0.75 nH/mm,andwewouldhave≈50 nH,guaranteeingpoorRFfiltering.OnceagainitmakessensetouseanLCfilterusingaplasticcapacitorhavingaKelvinconnection.Thecapacitorneedstoberatedat600 V,so100 μFwouldbelargerthanthatcanbewound,but47 μFisfeasible.A valve rectifier allows HT to be applied gently, and the critical parametergoverning rectifier choice is now voltage rather than current rating. ThetraditionalchoicewouldhavebeenaGZ34,butthesearenowfartooexpensiveandapairof6CK3/6CL3damperdiodesisfarcheaper.Ifwedon’twanttouseacentre-tappedtransformer,ahybridbridgerectifiercanbemadebyaddingapairofSTTA512Fstothe6CK3/6CL3.Foran80 dBsignal-to-humratio,theEC8010RIAAstagerequiresrippleonthe390 VHTtobe<1.7 mVpk–pk(slightlylesstolerantthanthebalancedhybridRIAA stage). The statistical regulator is certain to have >90 dB rippleattenuation, so this corresponds to it tolerating 53 V pk–pk ripple post-rectification.Asbefore,thismeanswedon’thavetoworrygreatlyaboutrippleand can concentrate on obtaining the required voltage using availablecomponentsandensuringLowFrequencystability.WhenyouexperimentwithPSUD2,youwillquicklydiscoverthatitisdifficulttoachieveLowFrequencystabilityinanLCfilterhavinga47 μFcapacitor.Theinductanceof thechokecanbehalvedfrom20 Hto10 H(reducingtheL/Cratio)toeasetheproblem,butLowFrequencystabilitycanonlybeachievedbyaddingacapacitorbeforethechoke.Evenso,withtypicaltransformerandchokeresistances, only a capacitor of around 3–4 μF before the choke completelyeliminates Low Frequency ringing. It seems we have designed anotherintermediatemodesupply.Giventhat lowfrequencystabilityspecifiedthefiltercomponentsquitetightly,

the required 460 V DC output voltage can only be achieved by adjusting thetransformersecondaryvoltageto400 VRMS(off-load)(seeFigure5.67).

Figure5.67PSUD2simulationachievesrequiredvoltagewithoutlowfrequencyringing.

HavingachievedtherequiredDCvoltage,wefindthattherippleis680 mVpk–pk,sotherewillbenoprobleminachievingour80 dBsignal-to-humratio.ThisisthepointwhereweconsideritamildnuisancethatPSUD2workswithoff-load voltages because transformers are specified by their on-load voltage.Therearetwowaysaroundthisproblem:eitherusethebaratthebottomofthescreen to reveal the on-load RMS voltage leaving the transformer, ormake aguessastotypical transformerregulation.Althoughthefirstmethodseemsthebest,itcontainsthehiddenassumptionthatyouguessedsecondaryandreflectedprimary resistance correctly. The author prefers to make the sweepingassumptionthat50–100 VAtransformershave≈10%regulation,sothatanoff-loadvoltageof 400 VRMS corresponds to anon-loadvoltageof 372 VRMS.This canbe used as a rough checkon the accuracyof your initial guess as totransformersecondaryandreflectedprimaryresistance–ifyouhaveguesseditreasonably well, the PSUD2 voltage will be about 3% lower than the 10%regulation guesstimate. (This discrepancy occurs because PSUD2 can’tmodelcorelosses.)

HeaterRegulation

The heaters in the EC8010 RIAA stage are run constant current rather thanconstant voltage and all six strings need 300 mA at an expected maximumvoltageof12.6 V.The317Tcanbe configured toproduce a constant currentveryeasilybyplacingasingleresistorbetweenOUTandADJthatdrops1.25 V

atthechosencurrent(seeFigure5.68).

Figure5.68317asaconstantcurrentregulator.

A4.17 Ωcurrentsenseresistorisneeded,andthiscanbeachievedbya4.7 Ωresistorinparallelwith36 Ω.Therequiredpowerrating(0.33 W)ofthe4.7 Ωresistorcombinedwith1%precisionusedtobeaproblem,butTO-220package4.7 Ω1%20 Wresistorsarenowreadilyavailable.EachregulatorcanbemadeverysimplybyfittingtheTO-220resistoradjacenttothe317Tontheheatsinkandhard-wiringthemandthe36 Ωresistor(noPCBneeded).Whentheheatersarecold,theirresistanceislow,soalmosttheentirereservoircapacitor’s voltage appears across each 317T, almost doubling its thermaldissipation,butafter20 sdissipationdropstonormal(seeFigure5.69).

Figure5.69Coldresistanceofvalvescauseslargevoltagedropacrossthe317atswitch-on.

HeaterRectificationandSmoothing(aManualExercise)

The317Tneeds>3 Vacrossittoregulatecleanlyand1.25 Visdroppedacrossthe current sense resistor, soweneed4.25 Vmore than the expected12.6 Vacrosseachheaterstring,implying17 Vminimumrequiredacrossthereservoircapacitor.

Looking from the other direction, 2×18 V transformers are common, so theywould produce 25.5 V pk or 22.9 V if themains drops by 10%. The bridgerectifierwilldrop1.4 V,leaving21.5 V,allowing4.5 Vofripple.Eachserieschainrequires300 mA,sothefourchainsrequireatotalof1.2 A,andtheothertwo chains require a total 600 mA. The 1.2 A supply requires a 3,300 μFcapacitor for3.6 V pk–pk ripple,whereas1,500 μFwould suffice for600mAsupply.Althoughitmightbeeasiertouse3,300 μFforboth,itwouldhalvetheripplevoltageonthe600 mAsupply,raisingtheDCvoltageandunnecessarilyincreasingthedissipationoftheassociated317T.The total DC current is 1.8 A from our raw 25.5 V pk, so this is 46 W,requiringa50 VAtransformerhavingasplitbobbinorfoilelectrostaticscreentominimisecommon-modeinterference.Now thatweknow thevoltageon the reservoir capacitor,wecanestimate thethermaldissipationofeach317T.IfwetreattheDConthereservoirasbeingitspeakvoltageminushalftheripple,then:

Eachheaterchaindrops12.6 V,and1.25 Visdroppedacrossthecurrentsenseresistor,leaving9.85 Vacrossthe317T,andP=IV=9.85 V×0.3 A≈3 W.Itisconvenienttomountallsix317Tsonacommonheatsink(viainsulatingkits),soitmustdissipate18 W,andfora20 °Ctemperaturerise,thatimpliesathermalresistanceof<1.1 °C/W.Wenowhaveafullpowersupplycircuitdiagram(seeFigure5.70).

Figure5.70CompletepowersupplyforEC8010RIAAstage.

Apowersupplyisadevicethatconvertsonevoltagetoanothermoreconvenientvoltagewhilstdeliveringpower.

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Chapter6.ThePowerAmplifier

Thedeterminingfactoristheoutputstage.Thesolutionadoptedheredictatesthetopologyoftheremainderoftheamplifier,sowewillbeginbyinvestigatingtheoutputstage.

TheOutputStageTypical audio valves are high-impedance devices and can swing hundreds ofvolts,butdeliveronlytensofmilliamperesofcurrent.Bycontrast,aloudspeakerof typically 4–8 Ω nominal impedance requires tens of volts and amperes ofcurrent.Theobvioussolutiontothisproblemistoemployanoutputtransformertomatchtheloudspeakerloadtotheoutputvalveorvalves.This iswhere theproblemsstart.Aswashintedearlier, transformersareratherlessthanperfect,andtheultimatequalityofavalveamplifieris limitedbythequality of its output transformer. Despite this, the transformer coupled outputstage isagoodengineeringsolution,and isused inmostvalveamplifiers (seelaterforOutputTransformer-Lessdesigns).Valves designed specifically for audio use generally have optimisedconfigurations that are detailed in the manufacturer's data sheets. Designingoutputstagesforaudiovalvesfromfirstprinciplesisreinventingthewheel,butanoverviewof thepracticalities ismostuseful; therefore,wewill indulge inabriefanalysisofacurrentlyfashionabletopology.

TheSingle-EndedClassAOutputStage

A typical transformer coupled output stage is the familiar common cathodetriodeamplifierusingcathodebias(seeFigure6.1).

Figure6.1Single-endedtransformercoupledstage.

Whenweinvestigatedvoltagestages,weusedaloadlinetochoosethevalueofanodeload,andgenerallyoptimisedforlinearity,ratherthanvoltageswing;thistime, we need tomaximise power. For this example wewill use an E182CC

double triode, which might be useful as a headphone amplifier. We wouldnormally set the operating point at the intersection between maximumcontinuousanodevoltage(Va=300 V)andmaximumanodedissipation(Pa=4.5 W).ButasthereisagridcurveintersectingatVa=295 V,theoperatingpoint has been moved for convenience. For maximum output power, theoptimumloadforatriodeis2×ra.Inourexamplerais3.57 kΩ,soRL=2×ra=7.14 kΩ,andweplotthisloadline(seeFigure6.2).

Figure6.2ACloadlinefortransformercoupledstage.

Vgk=−1 VisourpositivelimitfromthebiaspointofVgk=−13 V,thereforethe negative limit will be V gk =−25 V for a symmetric input voltage. Thisresultsinapeaktopeakoutputvoltageswingof430 Vto85 V=345 V,or122VRMS,whichequals2.1 Wdissipatedintheload.Undertheseconditions,4.5Wisdissipatedinthevalve,givinganefficiencyof32%.Weshouldnowobservesomeimportantpointsabouttheoperationofthisstage:• The loadline strays into the regionwhereP a≥4.5 W. Since the stage isdrivenonlywithAC(itmustbe,aswecouldnototherwisetransformercoupletotheload),thisisnotaproblem.Thisisbecausealthoughononehalf-cyclethe anode dissipation is ≥4.5 W, on the other half-cycle it is less, and thethermalinertiaoftheanodewillaveragethedissipationoutat≤4.5 W.

• We set the operating point of the valve at 300 V. If the transformer isperfect,thentherewillbenoDCvoltagedroppedacrosstheprimarywinding,andsotheHTvoltagemustbe300 V.YetwehaveallowedVatoriseto430V,whichisconsiderablyaboveHT.Thisispossiblebecausethetransformerstoresenergyinthemagneticfluxofitscore.Intheory,aperfectvalvecouldswing V a from 0 V to 2×HT, which is a very useful feature in a poweramplifier.•Wecarefullysetouranodeloadat7.14 kΩ,butindoingsoweassumedthatthe loudspeaker was a resistor. Loudspeakers are not resistive, and thetransformer isnotperfect, so theactual loadseenby thevalvewillnotbeapreciseresistance,butacomplexandvariableimpedance.ThevalvethereforeseesanACloadlinethatisanellipsewithitsmajoraxisroughly aligned with the theoretical resistive loadline. The gradient of themajor axis is the resistive component, and the width of the minor axisindicatestherelativesizeofthereactivecomponent.Thismeansthatmostofthecalculationswecanmakeforanoutputstageareinformedguessesatbest,andthereislittlepointworryingaboutprecisevalues.

•Becausewewishtomaximisethepowerintheload,wehavetomaximisethe anode voltage swing, resulting in poor linearity. We could improvelinearity by increasing the value of the anode load and plotting anotherloadline,butthiswillreduceavailableoutputpower.

Althoughthelinearityofsingle-endedstagesisnotgood,thedistortionproducedismostlysecondharmonic,which,asweobservedearlier,isrelativelybenigntotheear.Wecanestimatethepercentageofsecondharmonicdistortionfromthefollowingformula:

Inourexample,Vmax=430 V,Vmin=85 VandVquiescent=295 V,resultingin11% second harmonic distortion at full output. Clearly,>10% distortion is notHi-Fi, but the attraction of single-ended amplifiers is that their distortion isalways directly proportional to level, and so at one-tenth output power, thedistortionwouldbe≈1%,andsoon.Since,mostofthetime,musicrequiresverylittlepower,itisoftenargued(oddlyenough,bysingle-endedenthusiasts)thatitisthequalityofthefirstwattthatisimportant,nottheremainderthatarerarelyused.Thedistortioncouldbereducedbynegativefeedback,butthistechniqueisalmost universally shunned by the supporters of single-ended amplifiers, so

single-endedamplifiersnotonlyproducehighdistortion,butalso tend tohaveanoutputresistanceofhalftheassumedloadresistance.

TheSignificanceofHighOutputResistance

Thevastmajorityofmodernloudspeakersusemovingcoildriversinsealedorreflex boxes. The theory of the interaction betweenmoving coil loudspeakersand their enclosures was introduced in a landmark series of papers by A.N.ThieleandR.SmallintheJournaloftheAudioEngineeringSocietyintheearly1970s.Aclosedboxisasecondorderhigh-passfilter,whereasareflexbox isfourth order, although it can be designed to look like third order. The crucialpointisthatThieleandSmallshowedthattheQofthehigh-passfiltercouldbeprecisely set by the series contribution of voice coil resistance, crossoverresistance, and amplifier output resistance, which is normally assumed to bezero. Typical single-ended amplifiers make a mockery of the zero outputresistance assumption and cause the loudspeaker to produce a peaked bassresponsethattheloudspeakerdesignerdidnotintend.Reflex loudspeakers developed prior to Thiele and Small relied on themechanical damping contributed by the suspension of the loudspeaker todetermine bass response and made few assumptions about amplifier outputresistance.Hornsrelyonthe transformedair loadfordamping,so theytooaretolerant of high amplifier output resistance. As a further bonus, both of thesetypes of loudspeakers are sensitive, so they are popular with aficionados ofsingle-endedamplifiers.Bass isproducedbymovinga largevolumeofair, and requiresa large, rigid,and consequently heavy, cone. Treble is produced by accelerating anddecelerating a small area many times a second, requiring low mass. Therequirements for bass and treble reproduction are contradictory, so mostloudspeaker designers prefer to use optimised drivers for specific frequencybands supplied from an electrical filter known as a crossover. Nevertheless,othersfeelthatthepracticeofmultiplenon-coincidentdriversandcrossoversisso fundamentally flawed that they attempt the design of full-range drivers. Inpractice,thetrebleresponsetendstobepeakyanddirectionalafter10 kHz,andthe low-frequency resonance limits bass to ≈100 Hz, but this is a sizeableproportion of the audio band. Fortuitously, themotion of a full-range driver’slow-mass cone is easily damped, and when mounted on an open baffle, themechanicaldampingofthesuspensionisfrequentlysufficient.Thus,asensitivefull-rangedrivermountedonanopenbafflecanbeanidealmatchforasingle-endedamplifier.

TransformerImperfections

Whenweplottedthesingle-endedloadline,wetreatedtheoutputtransformerasbeingperfect,butweshouldnowconsiderhowitsimperfectionswillaffectthestage.Unfortunately,wepassaconstantmagnetisingcurrent(Iquiescent)throughtheprimaryoftheoutputtransformer.Inorderforthecorenottosaturate,whichwould cause odd harmonic distortion, we need a large gapped core. Anothermethodofavoidingcoresaturationistoreducethenumberofprimarywindings,which not only reduces the magnetising effect (ampere-turns, In) of thequiescentcurrentbutalsoreducesprimaryinductance.Usually both methods have to be used, which results in a physically largetransformer of low primary inductance at the operating point. Because thetransformerissolarge, ithascorrespondinglylargestraycapacitances,sohighfrequencyperformanceisalsocompromised.Typically,thetransformersusedinthis way are large, expensive, and have significantly reduced bandwidthcomparedtoan(ungapped)push–pulltransformer.Itmight therefore be thought that the single-ended transformer-coupled powerstage is a completenon-starter, but, curiously, this isnot so. Ifwe lookat thehysteresiscurvefortransformeriron,thisoffersacluetothistopology'srecentresurgenceinpopularity(seeFigure6.3).

Figure6.3ExaggeratedB/Hcurveofiron.

Whenused as a transformer, the hysteresis curvemay be treated as a transfercharacteristicshowingtherelationshipbetweenV inandVout .IftherewerenoDC current flowing through the transformer, then an AC signal would swingsymmetricallyabout theorigin. Ifwelookat thesmall-signalperformance,weseethatthereisakinkinthecharacteristicaroundtheoriginwheretheslopeofthecurveisreduced.Sincethecore’spermeabilityisproportional totheslope,the transformer has reduced primary inductance (L p ) at low levels. At low

frequencies,reducedLpreducesgainandincreasesdistortionintheoutputstage.Thecauseofthekinkisthattheindividualmagneticdomainsthatmakeupthecorehavestictioninreversingthepolarityoftheirmagnetism.(Thesameeffectistrueinelectrostatics,inthatthereisstictioninreversingelectrostaticchargesin polar dielectrics such as polyester and polycarbonate.) A recently popularsolutionknownaspinstripingusesamixofsteelandmu-metal laminations tomake up the core. Mu-metal has a much higher initial permeability, so itmaintainshighLpatlowlevels,butsaturatesquitequickly,atwhichpointthesteeltakesover,sopinstripingcanimprovetheinitialpermeabilityofthecore.Unfortunately,mu-metalisfragileandsignificantlymoreexpensivethansteel.Alternatively,bypassing thevalve'squiescentcurrent through the transformer,we ameliorate the problem of low initial permeability making the transfercharacteristic more linear, and it is claimed that this is responsible for theexcellentmidrangedetail in thisbreedof amplifiers.However, amoreprosaicexplanation is thatvoice coil inductancecauses loudspeaker impedance to riseabove 250 Hz, and that when driven from a source resistance of half theloudspeaker’s nominal impedance this typically results in a lift of 3 dBby3kHz.Althoughthetransformerhasalowprimaryinductance,suggestingapoorbassresponse,awell-designedcoreislesslikelytosaturateatlowfrequencies,sinceithadtobeoversizeandgappedtoaccommodatethequiescentcurrent.Becauseof this,L p is nearly constant from full AC output power to zero AC output.Provided that the loudspeaker is carefully matched, a good subjective bassqualitycanbeachieved,becauseitdoesnotchangesignificantlywithlevel.Unfortunately,wecanmakenoexcusesforthehighfrequencyperformance.Thelarge,leakyoutputtransformerhassignificantlossesathighfrequency,althoughexcellentconstructionhelpsmatters.Single-endedamplifierstypicallyusetruetriodeswithdirectlyheatedcathodes,such as 2A3, 300B, 211 and 845, rather than beam tetrodes or pentodesconnectedas triodes.Unfortunately,directlyheatedcathodesareprone tohumwhenfedwithAC,orprematurefailurewhenfedwithDC,becauseVgkatoneendoftheheater/cathodeislowerthantheother,causinghigheremissionatthelowVgkend.Tosumup:single-endedtriodeamplifiershavegoodlow-levelperformancebutthey require careful loudspeaker matching to make the most of their bassperformanceand lowpower (usually<10 W),and theircostperaudiowatt ishighdue to theexpensiveoutput transformerandesotericvalves.But theyaresimpletomake.

ClassesofAmplifiersThe‘class’ofanamplifierreferstotheproportionofquiescentanodecurrenttosignalcurrent.Untilnow,wehaveonlylookedatClassAamplifiers,althoughthefactwasnotexplicitlystated.Ifwerelaxthatrestriction,wewillneedsomedefinitions.Efficiencyisdefinedas:

Althoughthevalvealsorequirespowerfortheheaters, it isusualtodefinethe‘powerin’asbeingfromtheHTsupply.Thefollowingcomparisonsallassumethat the loadiscoupledto theamplifierbyaperfectoutput transformerbecause thisenables theDCcomponentof thevalve’s current to pass through the (reflected) load without loss (no resistivelossesinaperfecttransformer).Further,theoutputtransformerstoresenergyinits primary inductance enabling the anode to swing linearly to twice the HTvoltage.

ClassA

Anode current is set such that even with maximum allowable input signal,current never falls to zero. In other words, the valve never switches off.(MaximumtheoreticalefficiencyofaClassAamplifieris50%forasinewaveoutput.)

ClassB

Thereiszeroquiescentanodecurrent,andcurrentonlyflowsduringthepositivehalf-cycle of the input waveform. The valve is therefore switched off for thenegative half-cycle of the input waveform, and considerable distortion of thesignaloccurs,sinceithasbeenhalf-waverectified.Additionalmeasuresneedtobe taken to deal with this problem. (Maximum theoretical efficiency for sinewaveoutputis78.5%forapush–pullClassBamplifier.)

ClassC

Anode current flows for less than half a cycle of the input waveform. Thismethodisusedonlyinradiofrequencyamplifierswhereresonanttechniquescanbeusedtorestore themissingportionof thesignal,andresults inevengreaterefficiencyanddistortionthanClassB.Radio frequency engineers refer to the conduction angle to specify the

proportionoftimeinwhichanodecurrentflows.Usingthisdescription,weseethatClassAamplifiershaveaconductionangleof360°,ClassBhas180°andClassC<180°.ThetransitionbetweenClassAandpureClassBisquitebroad,andsothereisanintermediateclassknownasClassAB(seeFigure6.4).

Figure6.4RelationshipbetweenanodecurrentandinputsignalforClassesA–C.

InFigure6.4 , the transfercharacteristicof theoutputdevice isassumed tobeperfect,sotheinputsinewaveissimplyreflectedthroughthediagonaltransfercharacteristic toproducetheoutput.InClassBoperation, thebiasvoltagecutsoff the valve, and it is only on positive half-cycles that the signal is able toswitchthevalveon.ItwillbenoticedthattheoutputwaveformoftheClassBstage isvery similar to thepower supplywaveforms inChapter5and, for thesamereason,half-waverectificationistakingplace.Notethatasbiasvoltageisincreasednegatively,theconductionanglefalls.Inaudio,wenormallyrefertocurrentsratherthanconductionangles,andthereare subdivisions of classes defined by the grid current of the valve. (RF

engineersareunabletodothissincetheyinvariablyoperatewithgridcurrenttomaximiseefficiencyattheexpenseoflinearity.)

Class*1

Grid current is not allowed to flow. Many of the larger (≥50 W) classicamplifierswerepush–pullClassAB1.

Class*2

Theinputsignalisallowedtodrivethegridpositivewithrespecttothecathode,causinggridcurrent toflow.This improvesefficiency,since theanodevoltagecannowmorecloselyapproachzero,whichisparticularlyrelevanttotriodes.Attheonsetofgridcurrent,theinputresistanceoftheoutputstagefallsdrastically(possibly approaching 1/ gm ), and the driver stage needs a very low outputresistanceifitistomaintainanundistortedsignalintothisextremelynon-linearload without distortion. Some modern single-ended amplifiers use high- μtransmitter triodes intended for Class B2 operation that pass very little anodecurrentatVgk=0,sotheybiasthegridpositivetoforcetherequiredquiescentcurrent,andthusoperateentirelyinClassA2.

ThePush–PullOutputStageandtheOutputTransformerWesawthat theClassBstage introducedconsiderabledistortionbyhalf-waverectifyingtheinputsignal.Clearly, thisisadisadvantageforaHi-Fiamplifier,sincewerequirelinearity.Suppose, however, thatwe had twoClassB valves, one fed directlywith theinput signal, and the other with an inverted signal. During time t 1 the uppervalve conducts, whilst the lower is cut-off, and during t 2 , the situation isreversed(seeFigure6.5).

Figure6.5SummationofClassBsignalsinoutputtransformer.

Sofarallthatwehaveachievedistoensurethatanyonevalveisswitchedon,irrespectiveof incomingsignalpolarity.However,by invertingoneoutputandsummingitwiththeotherintheoutputtransformer,wecanrecreatetheshapeofthe original input waveform. The inversion is performed by reversing theconnectionofonewinding,andismarkedonthediagramwith+and–symbols.Whetherachievedbyatransformerorbyadirectcoupledseriesamplifier,suchasaWhitecathodefollower,thisformofconnectionisknownaspush–pull,andistheonlywayofapproximatinglinearityinaClassBamplifier.Unsurprisingly, this dissection of the signal and its subsequent restitching isratherlessthanperfect,andpureClassBisrarelyusedbecauseofthedistortiongeneratedatthecrossoverregion,whereonedevicetakesoverfromtheother.Inpractice,somequiescentcurrentisallowedtoflowinanattempttosmooththetransition,resultinginClassABoperation.Thetheoreticaloptimumbiasvoltagefor a ClassAB amplifier is found by extending the linear part of the transfercharacteristicuntilitintersectstheVgk-axis.However,practicaldevicesdonot

operate linearly down to cut-off and then suddenly switch off, so individualdifferences between devices mean that the ideal point is ill-defined, andcrossoverdistortionisnoteliminated.Push–pull output stages can also be used for Class A amplifiers, givingadditionaladvantages.Because of the reversal of one winding, the magnetising flux caused by thequiescent anode currents cancels (provided that they are equal). Because thetransformercoreonlyhastohandlesignalcurrent,itdoesnotneedagapandcanbefarsmallerforagivenpower—thisisthemainreasonforusingapush–pulloutputstageinaClassAamplifier.Sincethecoreissmall, it is important that thequiescentanodecurrentofeachvalve is identical, otherwise DC magnetisation of the core will generate oddharmonicdistortion.ThiscanbedonebyhavinganadjustmentforDCbalanceinthebiascircuit,orbyusingpairsofvalveswithmatchedanodecurrents(seeFigure6.6).

Figure6.6DCbalanceadjustment.

RV2 sets total anode current,whilstRV1 adjustsDCbalance by biassing onegridmoreorlesspositivelythantheother.If the core should become permanently magnetised (perhaps by failure of avalve), it will need to be degaussed, or it will generate additional (andunnecessary) distortion. This can be done by applying a sufficiently largealternating magnetic field to the core to saturate it both positively andnegatively,and then reducing the field tozerooveraperiodofabout10 s. Inpractice,thelowremanenceoftypicaltransformercorematerialsmeansthatthisprocedureisunlikelytobenecessary.

Auseful consequenceof the reduced size of transformer is an improvedHighFrequencyresponseduetothereductionofstraycapacitances.Not only does quiescent anode current cancel in the transformer, but powersupply hum also cancels, since it is in-phase in each winding. Improvedtolerancetopowersupplyhumallowsacheaperpowersupply.Additionally,evenharmonicdistortion,causedbyunequalgainonpositiveandnegative half-cycles, is cancelled, whilst odd harmonic distortion is summed.Since triodes generate primarily even harmonic distortion, this is useful, butpentodesgenerate primarily oddharmonics, and therefore require considerable(>20 dB) negative feedback to reduce their distortion to acceptable levels.Cancellationofevenharmonicdistortionisonlyachievedifeachwindingisfedidenticalsignalvoltagebyitsvalve,sosomeamplifiershaveadjustmentsforACbalance,whereasothersspecifypairsofvalvesmatchedforgain(seeFigure6.7).

Figure6.7ACbalanceadjustment.

ModifyingtheConnectionoftheOutputTransformer

Wehavemainlyconsideredtriodes,andgivenpentodesscantregardbecauseoftheiroddharmonicdistortion.Butifweimaginetheoutputtransformerprimaryasasetofwindings thatcouldbe tappedatanypoint,wesee that forpentodeoperationg2wouldbeconnectedtothecentretap(0%),whereasforatriodeitwouldbeconnectedattheanode(100%)(seeFigure6.8).

Figure6.8Blumleinor‘ultra-linear’outputstage.

Whatwould happen ifwewere to tap at an intermediate point?This questionwasaskedin1951byDavidHaflerandHerbertI.Keroes[1]andanamplifiernamed ultra-linear became synonymous with an output stage that had beeninvented by Alan Blumlein [2] in 1937. Regarding tapping points, Mullard’sEL84andEL34datasheetsquiteclearlystatethat43%gaveminimumdistortionand20%maximumpower,althoughitwassuggested[3]in1958that20%gaveminimumdistortionforKT66.This formofdistributed loadingbecamealmostuniversalinthefinaldaysofvalvesupremacy,sinceitcombinedtheefficiencyand ease of driving the pentode with much of the improved linearity of thetriode.Itshouldbenotedthat:

Andasaconsequence,negativefeedbackatg2isnotaslinearaprocessasonemight wish. Nevertheless, almost all power amplifiers using pentodes in theoutputstageusethisschemebecauseitisfarsuperiortopurepentodes.Upuntilnowwehaveplacedthetransformerintheanodecircuit,butwecouldplace the same transformer in the cathode circuit to form a cathode followerresultinginanextremelylowoutputresistancefromthevalve.Asanexample,apair of EL34s, connected as triodes, would each have an anode resistance ofabout900 Ω,butusedas cathode followers thedriving resistancewouldbeatenthof this at 90 Ω.Reflected through the transformer, theoutput resistanceseen by the loudspeaker would be a fraction of an ohm even before globalnegative feedback.Unfortunately, thereare twocripplingdisadvantages to thistopology.Firstly,althoughtheoutputstageisexcellent,wehavetransferreditsproblemstothedriverstage.Eachoutputvalvenowswings≈150 VRMSonitscathode,andhasagain<1,requiring≈500 Vpk–pktodriveit!Thiscanbedone,butitisnot a trivial exercise to design the driver stage, since we must either usetransformer inter-stagecoupling,ora resistiveanode load requiringahighHT

voltage.Secondly, thehighvoltageon thecathodeof theoutputvalvesseverelystrainsthe heater/cathode insulation, and can cause premature heater failure.Connectingtheheatertothecathodetransfersthestresstotheheatertransformerbutrequiresindividualheaterwindingsforeachhalfoftheoutputstage(toavoidshorting k 1 to k 2 ), and forces each valve to drive the transformer’s inter-winding capacitance (≈1 nF). In the early days of television, the (expensive)display tube often failed because of leaky heater to cathode insulation, so aservice engineer’s fix that avoided the expense of a new tube was to tie theheatertothecathodeandsupplyitfromanewtransformerratherthanincludingitintheseriesheaterstring.Butbecausethe3 MHzbandwidthvideosignalwasapplied to thecathode, the transformerneededa lowinter-windingcapacitance(typically25 pF),sothesewerereadilyavailable.Asimilartransformerhavingmultiple lowcapacitancewindingswouldbe ideal for cathode followeroutputvalves.Alternatively,thereareafewvalves(usuallyintendedforuseastheseries-passelement in regulators) whose heater/cathode insulation can withstand 300 V,such as the6080/6AS7G.Because this valvehas such a low r a , its optimumload resistance is fairly low, and its output voltage at full power is also quitelow, reducing the strain on heater/cathode insulation. Unfortunately, μ is alsoverylow,sothegainoftheoutputstageissubstantiallylessthanunity,andthedriverstagehastobequitespecial(seeFigure6.9).

Figure6.9Amplifierwithcathodefolloweroutputstage.

Ascanbeseen,acomplexpowersupplywouldberequiredsimplytoproduce6W.Admittedly,thedrivercouldcopewithanumberof6080sinparallel,butthe

cure still seems worse than the complaint. The only reason that this designsurvivedtothedrawingstageisthattheoutputstageshouldbequitetolerantofpoor output transformers; conversely, a good output transformer would allowverygoodperformance.Theamplifierusestriodesthroughout,whosedistortionispredominantlysecondharmonic,butthisiscancelledbypush–pullaction,sothe amplifier relies on accurate balance rather than global feedback to reducedistortion,andhasabalancedinput.Another formofdistributed loadingplacespartof the load in thecathode,andpart in the anode; Peter Walker’s Quad II amplifier in the UK used thistechniquetogainusefulbenefitsfromlocalfeedbackanddistortioncancellationwithreasonablyrelaxeddrivingrequirements.McIntosh[4]intheUSAtookthetechnique to its logical conclusion by having equal anode and cathode loadsbifilar wound to minimise the output transformer leakage inductance thatexacerbated Class B crossover distortion. Sadly, the drive requirements arealmostassevereasfor thecathodefollower,andinsulationbetweenthebifilaranode and cathode windings is crucial, so the technique has not been widelyadopted(seeFigure6.10).

Figure6.10QuadIIoutputstage(akaMcIntoshconfiguration).

Eachoutputvalvecontrolsitscurrentthroughequalanodeandcathodeloadssoanychangeinanodeandcathodevoltageisequalandopposite.Cross-couplingg2ofeachvalve to theoppositevalve’sanodemeans that foragivenvalve,g2andcathodevoltagechangestrack,implyingpurepentodeoperation,andthisissignificantbecause:•Apentode can swing its anode closer to 0 V, allowing it to delivermorepowertotheloadthanatriode.

• A pentode’s g 2 prevents feedback from the anode to the control gridreducinggain.Weoftenconsiderthisfeedbacktobeuseful(it’swhatcausesthelowraofatriode),butifwewanttoapplyexternalfeedback,minimisingthis gain reductionbecomes important.Thus, achievingpentodegainbeforeapplyingtransformerfeedbackmaximisestheamountof(distortion-reducing)feedback.

Thecommercial techniqueofbootstrapping thedriverstage’sHT to reduce itsdistortionandincreasevoltageswingisaformofpositivefeedbackandmakesamplifier high-frequency stability crucially dependent on output transformerdesign.

OutputTransformer-Less(OTL)AmplifiersAlmostallthedifferentoutputstageconfigurationsweredevisedinanefforttoreducetheadverseeffectoftheoutputtransformer,soitisnotsurprisingtofindthat there have been some designs that dispense with the output transformer.TheseareoftenknownasFutterman[5]amplifiers(whopatentedthenotion),orOTLs.Driving low-impedance loads directly is not natural for a valve, so radicalapproaches areneeded.Highpeakcurrents are required, sovalveswith robustcathodes are needed, which invariably were not designed for audio, and theytherefore have extremely questionable linearity and consistency. Examples arethe 6080/6AS7G double triode series regulator valve, and television line scanoutputvalvessuchasthePL504andPL519pentodes.Efficiencyisgenerallyonthelowsideofappalling.OutputstagesinvariablyuseparalleledWhitecathodefollowers with plenty of global feedback to reduce the output resistance (seeFigure6.11).

Figure6.11OTLoutputstage(paralleledWhitecathodefollowers).

These amplifiers are quirky in the extreme, yet some designers think that theproblems of output transformers are so severe that they persist in makingsuccessfulOTLamplifiers.However, the one OTL application where no excuses need be made isheadphoneamplifiers.Notonlydoheadphonestendtohaveahigherimpedance

thanloudspeakers(32–300 Ωversus4–8 Ω)therebyrequiringlesscurrent,butthe close coupling to the ear increases their apparent efficiency and furtherreduces the current required. The combination of these two factors makes anOTLheadphoneamplifiernotonlypossiblebutalsodesirable,whichaccountsforthenumberofrecentdesigns.

TheEntireAmplifierHaving looked at the problems of the output stage, we can now consider thesupportcircuitry indetail.Wewillmainlyconsiderpush–pullamplifiers,sincetheymakeupthemajorityofdesigns,althoughtheirdesignprinciplesmaywellsbe perfectly applied to single-ended amplifiers. The output stage isinsufficiently sensitive to be driven directly from a pre-amplifier, so it needsadditional gain. If it is push–pull, it needs a phase splitter. Since linearity isunlikelytobeideal,wewillprobablyneedglobalnegativefeedback,whichwillfurtherreducegain,andthiswillneedtoberestored.Acompletecircuitmightthereforecompriseaninputstage,aphasesplitter,adriverstageandtheoutputstage(seeFigure6.12).

Figure6.12Blockdiagramofcompletepoweramplifier.

AlthoughaClassAoutputstageisaconstantresistiveload,aClassAB2outputstage heavily loads the driver stagewhen drawing grid current, and its driverstagewould need very lowoutput resistance and be able to source significantcurrenttodrivethisloadwithoutdistortion.Unlike the output stage, and possibly the driver stage, the remainder of thestages in a power amplifierwill be loaded by predictable resistive loads. It isthereforepossible,anddesirable,todesignthesestageswithgreatcareinorderthattheyshouldnotdegradetheperformanceoftheentireamplifier.

TheDriverStageUnlesstheamplifierisquitelowpower,itwillrequireadedicateddriverstage.Weneedgoodlinearity,goodoutputvoltageswingand,unlesswearepreparedtoaddacathodefollower,lowoutputresistance.The differential triode pair is the ideal choice. The output stage probablyrequiresabout25 VRMStoeachgrid,andhasaninputcapacitanceof40 pF,ormore.Anoutputresistanceof10 kΩcoupledtoaninputcapacitanceof40 pFgivesahighfrequencycut-offof400 kHz,whichisperfectlyacceptable.Sincer a≈R out , the high- μ valves, which tend to have a high r a , are probablyunsuitable.Inaproperlydesignedpoweramplifier, theoutputstageshouldbethelimitingfactor,soweoughttodesignthedriverstagetohaveatleast6 dBofoverloadmargin. This requirement probably rules out our favourite valve, the E88CC.Veryfewcommonlyavailablevalvessatisfyourrequirements(Table6.1).

Table6.1DualTriodesSuitableasDriversType ra(kΩ) Comments

SN7/N7 ≤10 LowestdistortionECC82 ≤10 13 dBworsedistortionthanSN7/N7E182CC ≤5 Goodonpaper,butcansoundstrident6BL7 ≤3 CripplinglyhighCag6BX7 ≤2 Capableofdriving845;robust

TheSN7/N7familyisbyfarthemostlinearofthepreviousselection,andiftheSN7GTAorSN7GTBversionsareused,Va(max)=450 V.Theoctal6BX7and6BL7weredesignedforuseas thefieldscanamplifier in televisions,butfieldscanamplifiersarerequiredtobenon-linear,soaudioperformanceisvariable.Inadistortiontestofthirty6BX7triodesections,theauthorfoundthatdistortionvariedbyafactorof4betweensamplesandthatveryfewenvelopescontainedapairoflowdistortiontriodes.Ifultimateperformanceisrequired,itisfarbettertouseapairofsinglevalvesandaccept thatmoremetalwork is required.Theoctal6AH4 isa single triodequite similar to the dual 6BX7, whereas the noval 6S4A is more akin to the6BL7.Having tested2246S4A, theauthorfound that thosemadebyGEweremostlikelytomeettheirspecification,butSylvaniawastheworst(Table6.2).

Table6.2SinglePentodesSuitableasDrivers(WhenTriodeConnected)Type ra(kΩ) Comments

EF184 ≤5 Cheapandreallyplentiful,μ=60N78 ≤3 Uncommon,butdirtcheapA2134,EL84 ≤2 NOSEL84extinct,butcurrentSlovakproductionfine

Even lowerdriving resistance canbeprovidedby an additionaldirect coupledcathodefollowerstage,whichalsohastheadvantageofbufferingthedifferentialpairfromgridcurrenteffects(seeFigure6.13).

Figure6.13Driverstageusingdifferentialpairdirectcoupledtocathodefollowers.

ThePhaseSplitterThedriver stage is alwaysprecededby thephase splitter, and traditionally thetwo stageshavebeen combined–althoughaswe shall see, this is not always agood idea.Designof thephase splitter iscrucial to the successofapush–pullamplifier,sowewilllookatthisindetail.The phase splitter converts a single-ended signal into two signals of equalamplitude, but onehas invertedpolarity.There are three fundamentalwaysofachievingthisgoal(seeFigure6.14):

Figure6.14Fundamentalbasisofallphasesplitters.

•Weuseacentre-tappedtransformerinthesamewaythatweuseanoutputtransformertoprovideinvertedandnon-invertedsignals.Allof thepreviousconsiderations about transformers apply with a vengeance because of thecomparativelyhighimpedancesinvolved,sothetechniqueisnotwidelyused,eventhoughbalanceisnear-perfectunderallconditions(seeFigure6.14a).•Wehavetwooutputs:oneistheoriginalsignal,andtheotherissimplytheinputpassedthroughaninverter(seeFigure6.14b).•Avalvecontrolstheflowofcurrentbetweentworesistors,oneofwhichisconnected to ground and the other to HT. Increased current causes theinstantaneousvoltagedroppedacrosseachresistortorise,soatanyinstantthevoltage relative to ground is falling at one output,whilst the other is rising(seeFigure6.14c).

Thethirdmethodisthebasisoftheconcertinaphasesplitter.Althoughwewillseeshortly that the floatingparaphase invertercanbeapureexpressionof thesecond technique, it is more usual for the second and third techniques to becombinedinsomeformofcathode-coupledamplifierordifferentialpair.

Triode phase splitters having low resistance outputs are very sensitive to theirloading and have different output resistances when both outputs are loadedcomparedtoonlyoneoutputbeingloaded.Phasesplitterswithahighrahaveanoutput resistance dominated by R L , so phase splitters using pentodes andcascodesareimmunetoloadingproblems.Loadingsensitivitymeansthattriodephasesplittersshouldonlybeloadedbyastage thatcanbeguaranteednever todrawgridcurrentbecause the interactionbetween phase splitter loading sensitivity and drastically reduced inputresistanceduetogridcurrentexacerbatesdistortioncausedbygridcurrent.

TheDifferentialPairandItsDerivatives

Most classic phase splitters were based on the differential pair, and muchingenuitywasdemonstratedinimprovingtheirsmall-signalperformance.Aperfectdifferentialpaircomprises twodeviceshavingequal loadresistancesconnected so as to allow a signal current to swing backwards and forwardsbetween the two load resistanceswithout any losswhatsoever. Loss of signalcurrentfromthecathodetogroundimpairsperformance,sothetailresistanceiscrucial,andshouldideallybeinfinite.

>RLSolution",5,0,2,1,105pt,105pt,0,0>TheRk>>RLSolution

Adifferentialpaircanbeoptimisedwithapentodeorcascodeconstantcurrentsink in its tail.AnEF184pentode can achieve a tail resistance>10 MΩ, andeven the larger pentodes, such as the EL83, can attain 1 MΩ unaided.Alternatively,we canuse a cascoded semiconductor constant current sink, butwewillalwaysbelimitedathighfrequenciesbyCkhfromthedifferentialpair'scathode,evenifthesinkisperfect(seeFigure6.15).

Figure6.15Differentialpairwithtriodeconstantcurrentsinkasphasesplitter.

ThebehaviourofthedifferentialpairwasdiscussedinChapter2.ProvidedthatRk≈∞,abalancedoutputmustbeachieved ifRL1=RL2 .Output resistancemustalsobeidenticalfrombothoutputs,androut=ra|RL,asbefore.However,ifonlyoneoutputisloaded,then:

Loading one output heavily (driving grid current) is equivalent to leaving theother output unloaded, so we find ourselves in the unfortunate situation ofdrivingaconditionthatrequireslowsourceresistancewithincreasedresistance,whichiswhygridcurrentdistortionisexacerbated.

TheRk≈RLCompensatedSolution

Weacceptthatwecannoteasilyachieveahightailresistance,anddonoteventry.Weusearesistor,typicallybetween22 kΩand82 kΩ,asatail,calculatewhattheerrorswillbe,andtrytocorrectthem.Theprincipleisoftenknownasthe cathode-coupled or Schmitt phase splitter [6] because he was the first toanalyse the errors and show how they could be corrected. Practicalimplementations modify the circuit slightly to accommodate external DCconditions, so theLeakTLseriesofamplifierspaid thepriceofbiassing theirinputstageoptimallybyneedinganotherlow-frequencytimeconstanttocouple

to the self-biased variant ( Figure 6.16a ),whereas theMullard 5-20 used theelegantDCcoupledClare[7]variant(Figure6.16b).

Figure6.16Schmittcathodecoupledphasesplitters:LeakvsClarevariants.

V2canbeconsideredtobeagroundedgridamplifier,fedfromthecathodeofV1.Itisthisuseofthefirstvalveasacathodefollowertofeedthesecondvalvethatresultsintheapparentlossofgainofthesecondvalve,sinceforacathodefollower,Av<1.Byinspection,weseethat2 vgkisrequiredtodrivethestage,sothegainofthecompoundstagetoeachoutputishalfwhatwewouldexpectfromanindividualvalve.Iftheoutputsareinbalance,thenv1=v2,so:

ThegainofV2isA2,so

The signal current flowing in the cathode resistor is the out-of-balance outputsignalcurrent:

ThesignalattheoutputofV2mustbe:

ExpandingandcollectingI2terms:

Substitutingi1R1=i2R2,andsimplifying:

Thisshowsthatunlessthegainorthetailresistanceofthestageisinfinite,theratiooftheanodeloadsshouldbeadjustedtomaintainbalance.NotethatA2istheindividual,unloaded,gainofV2,andnotthegainoftheentirestage.Asanexample,theLeakTL12+phasesplitter/driverwasinvestigated.ThisusesanECC81andgivesagainof42forV2(R2=100 kΩ,μ=53,ra=26.5 kΩ),R1shouldthereforebe91 kΩ,andthisisexactlywhatLeakused(seeFigure6.17).

Figure6.17CathodecoupledphasesplitterasusedinLeakTL12+.

Theoutputresistanceofeachhalfofthestageisslightlydifferentbecauseitisinparallelwithaslightlydifferentanodeload,butcuringthisinordertopreserveHigh Frequency balance upsets the voltage balance at low frequencies. Thenearest approximation that we could achieve is to include the grid-leakresistances as part of the anode loadswhen calculating thenecessary changes.Thefollowinggrid-leakresistorsare470 kΩ,soRL2=100 kΩ‖470 kΩ=82.46kΩ,andthegainofV2fallsto40.TherequiredtotalloadforV1(includingthe470 kΩgridleak)isthus75.7 kΩ,andRL2=90.2 kΩ.Low Frequency balance is determined by the time constant of the griddecouplingcapacitoranditsseriesresistor,sinceitcannotholdthegridofV2to

ACgroundatverylowfrequencies.Ratherthantinkerwithresistorvalueswhosecalculationiscriticallydependentonvalveparameters, theauthorwouldratheraddaconstantcurrentsinktothecathodetoforcethestageintobalance.

TheRk<<RLHighFeedbackSolution

We make no attempt at providing a large value of tail resistor, and rely onfeedbacktomaintainbalance.ThiscircuitwasdevisedbyCarpenter[8],butisalso known as the floating paraphaseor see-sawphase splitter.Typically, thedesign uses a high- μ valve, such as the ECC83, from whose data sheet thiscircuitwastaken(seeFigure6.18).

Figure6.18Carpenterfloatingparaphaseorsee-sawphasesplitter.

Ifweredrawthecircuit(makingitidenticaltoFigure6.6ofCarpenter’spatent),weseethatV2issimplyaunitygaininverter,whosegainisdefinedbyresistorsR1andR2(seeFigure6.19).

Figure6.19Carpenterfloatingparaphasephasesplitterredrawntorevealinvertor.

Sincetheopen-loopgainofV2isnotinfinite,thesevaluesmustbeadjustedtogive a gain of –1.Unfortunately, the calculation is further complicated by thefact that R 2 affects the loading, and open-loop gain, of the stage. V 2 alsorequires a build-out resistor to equalise its output resistance, which has beensignificantly reduced by negative feedback. Once these corrections have beenmade, the balance of this phase splitter is good, since the operation ofV 2 isstabilisedbynegativefeedback.ThecircuitisanalysedbyfirstdrawingaDCloadlinetocorrespondtothe220kΩ anode load. The Mullard operating point is at V a =163 V. The 1 MΩfeedback resistor is in parallel with this at AC, so we draw an AC loadlinethroughtheoperatingpointcorrespondingto180 kΩ.FromthiswefindthattheACgainofthevalveis67.Weneedtofindthevalueofβthatwillgivefinalgainof1,using:

Wefindthatβ=0.985.Theeasiestwaytoachievethisistoincreasethevalueofthefeedbackresistor:

Thisgivesavalueof1,015 kΩ,sowewouldadd15 kΩinseries.Sofar,wehaveonlydiscovereda1.5%error,whichistrivial,butifweconsidertheoutputresistanceswe find amuch larger error. The output resistance ofV 1 is r a in

parallel withR L , and is ≈53 kΩ, but the output resistance ofV 2 has beenreducedbyafactorof(1+βA0),from53 kΩto≈790 Ω.52.2 kΩofbuild-outresistanceisthereforerequired,buttheneareststandardvalueof51 kΩwouldbe fine.Theseoutputsare theneach loadedby680 kΩ,and ifcorrectionsarenotmade,theoutputfromV2is≈6%high.Inpractice, thesecorrectionswerenevermade,whichperhapsaccountsfor thepoor reported performance of the stage. It might be thought that the cathodecoupling would improve balance, but V 2 has such heavy feedback that ifinadvertentlysettonon-unitygain(wrongratioofgain-definingresistors)itcaneasily overcome any self-balancing action generated at the cathode. Thejustification for cathode coupling has little to do with improving balance andmuch more to do with eliminating a pair of undesirable cathode bypasscapacitors.

TheConcertinaPhaseSplitter

Thephasesplittersbasedonthedifferentialpairwereallabletoprovideoverallgain, but once R k <∞, output balance became partially dependent on thematchingofμbetweenthevalves.Feedback causes the concertina phase splitter to have slightly less than unitygain to each output, and its output balance is almost totally determined bypassive components, so valve characteristics hardly enter the picture.Conceptually, operation is very simple. Modulation of grid voltage causes asignal current to flow in thevalve, the anodeandcathode loads are equal andtheyhavethesamecurrentflowingthroughthem,sothesignalsgeneratedacrossthemareequal,implyingperfectbalance(seeFigure6.20).

Figure6.20Concertinaphasesplitter.

GainoftheConcertina

Thegainof theconcertinato itsanodemaybefoundusingthestandardtriodegainequation,butnotingthatallundecoupledresistancesdowntogroundviatheanoderesistancearemultipliedbyafactorof(μ+1),then:

Butfortheconcertina,Rk=RL,so:

Becauseof this lowvalueofgain to theanode,Millercapacitance isalso low,andthestagehaswidebandwidth.Sincethereisnogridcurrent,anodecurrentisidentical to cathode current and applying Ohm’s law to the equal anode andcathode load resistances shows that gain to the cathode is equal togain to theanode.

OutputResistancewithBothTerminalsEquallyLoaded(ClassA1

Loading)

Theconcertinaisaspecialcase(Rk=Ra)ofanunbypassedcommoncathodeamplifierwithoutputstakenfrombothanodeandcathode.Thegeneralfeedbackequationis:

Thedenominatorofthefeedbackequationisthefactorbywhichresistancesarechangedand isknownas the feedback factor .Sinceweknow thegainof theconcertinaandthegainofasimpletriodeamplifier,wecansubstitutethemintothefeedbackequationtosolveforthefeedbackfactor:

Cross-multiplyingtofindthefeedbackfactor:

The anode output resistance of a common cathode triode amplifier with nofeedbackis:

The feedbackworks to reduce anode output resistance, so this valuemust bedivided by the feedback factor (practically, wemultiply by the inverse of thefeedbackfactor):

The(RL+ra)termscancel,leaving:

Initially, it seemsmost surprising that series feedback (R k=R a , after all)shouldreduceoutputresistancefromtheanodesothatrout≈1/gm,butthiscanbeunderstoodbyconsideringanexternalcapacitiveloadoneachoutput.InthesamewaythatRk=Radefinesagainof1atlowfrequencies,soXC(k)=XC(a)definesagainof1athighfrequencies,andchangingthisratioofcapacitancescertainly would change the gain, or frequency response at high frequencies,sinceitwouldchangethefeedbackratioβ.BecauseZ k=Z a , the frequency response at each output is forced to be thesame,sotheoutputresistancesmustalsobeequal,androut(k)=rout(a).

ConcertinaOutputResistance,OnlyOneOutputLoaded(ClassB

Loading)

Looking into the cathode,we seeR kdown to ground, in parallelwith r k theanodepathtoground:

Substituting:

Simplifying,andnotingthatRa=Rk=RL:

Alternatively,

Inapracticalapplication,the(μ+2)termisusuallysignificantlylargerthanthera/RLterm,sotoareasonableapproximation:

Although the cathode output resistance can be calculated fully, theapproximation isusuallygoodenough,andgenerallygivesavalueofabout1kΩ.Lookingintotheanode,weseeRatoHT,whichisACground,inparallelwiththecathodepathtoground:

Substituting

Tidyingterms

Ifweinspectthisequationclosely,weseethatthetermsinvolvingμaretheonlysignificantterms,andthatifμisreasonablylarge,then(μ+1)≈(μ+2),sothatrout≈RL.Thus,theconcertinasuffersasimilarweaknesstophasesplittersbasedon the differential pair in that one output driving grid current is equivalent to

leaving theotherunloaded.However, if thecathodeoutputdrivesgridcurrent,its output resistance remains low, whereas if the anode output drives gridcurrent, its output resistance rises significantly. This imbalance implies thatconcertina distortion due to driving grid current will contain additional evenharmoniccomponentscomparedtophasesplittersbasedonthedifferentialpair.Itisusualtodirectcoupletotheanodeoftheinputstage,andletthatdeterminethe DC conditions of the concertina, resulting in the saving of a couplingcapacitor and a low-frequency time constant. Although the concertina isfrequentlycriticisedforitsunitygaintoindividualoutputs,thisisadifferentialgainof2,sothecombinationofinputstageandconcertinagivesdoublethegainofthesame2valvesusedasaphasesplitterbasedonthedifferentialpair.

PhaseSplittersandClassBOutputStageMillerCapacitance

If a phase splitter drives a Class B output stage, only one output valve isswitched on at any given time, suggesting that there could be no Millercapacitancefromtheswitched-offvalve,therebyunbalancingthephasesplitter.However,theoutputtransformeractsasanautotransformer,sothevalve’sanodestillswingsand itsCagstillhasa largevoltageacross it,causing thechargingcurrent that manifests itself as Miller capacitance despite that valve beingswitchedoff,soitisnotnecessarytobufferthephasesplitter.Obviously, theautotransformerargumentdoesnotapply toOTLs,butbecauseOTLs have a cathode follower output stage, its input capacitance would beexpected tobe low.However, because the cathode followerdrives such a lowimpedanceload,itsgainisverylow,soitcannotbootstrapCgk,resultinginahigher input capacitance thanwouldotherwisebeexpected.SinceOTLoutputstagesarealmostinevitablyClassAB,ononehalf-cycletheloadisdrivenbyacathode follower and on the other by an anode follower (common cathodeamplifier). The two different amplifiers have entirely different inputcapacitances(Cga≠Cgk),suggestingthatbufferingthephasesplittercouldbeworthwhile.

TheInputStageTheinputstageiswhereglobalnegativefeedbackisapplied,soitmustprovidean inverting and a non-inverting input, both with low noise. The triodedifferentialpairisanobviouscandidateforthisstage,butthecommoncathodetriode or pentode can also be used, inwhich case global negative feedback ishabituallyappliedtoitscathode(seeFigure6.21).

Figure6.21Applicationofglobalfeedbackattheinputstage.

Designoftheinputstageisfairlytrivial,butcanbeslightlycomplicatedbytheusualpracticeofdirectcoupling to thephasesplitter,which restrictschoiceofanodeoperatingconditions.

StabilityWhenwelookedatRCnetworksinChapter1,wesawthatasingleRCnetworktendedtowardsamaximumphaseshiftof90°.Tomakeanoscillator,weneed180°ofphaseshift,soasinglestageamplifierwithoneRCnetworkcausinganLowFrequencyorHighFrequencycut-offcannotoscillate. Ifwecascade twosuchstages,wecanapproach180°ofphaseshift,andifwefeedthisbackintotheinput,itwillring,butnotoscillate.Ifwehavethreesuchstages,itisaracingcertainty thatwecanmake thecascadeoscillatewhenweapply feedback,andthisisthebasisofthephaseshiftoscillator.Toachieveoscillation,weneedmorethanphaseshift.Justbecauseourfeedbacksignal’sphasehasbeenshiftedby180°willnotnecessarilygenerateoscillation.We also need sufficient loop gain . The basis of oscillation is that it is self-sustaining; thegainof theamplifiermustbe sufficientlyhigh toovercome thelosses in the feedback loop before oscillation can occur. Loop gain is thusdefinedasthegainoftheamplifiermultipliedbythelossofthefeedbackloop.Ifwehaveaphaseshiftof180°andloopgain≥1,thecircuitwilloscillate,andthisisknownastheBarkhausencriterion.Nowthatwehavethiscriterion,wecanseehowtoavoiddesigningoscillators.Wehavetwoweaponsatourdisposal:•We can reduce the number of stages, such that phase shift never reaches180°.Werarelyachievethisideal,becausetheoutputtransformerplusoutputstage plus driver stage harbours so many phase shifts, but the principle ofminimisingthenumberofstageswithinafeedbackloopisstillvalid.•Weattackthesecondconditionoftheoscillatorstatement,andreduceloopgainto≤1atthetroublesomefrequencies.Thisisthebasisofallthemethodsthat you will see for stabilising amplifiers, and it is a powerful weaponcapableofoppressinganything.Whethertheresultingamplifierisofanyusemaybemoredebatable.

SluggingtheDominantPole

Thisrathervibrantandmystifyingdescriptionisactuallyverysimple.Apoleinelectronicjargonissimplyanotherwayofsaying‘highfrequencycutoff’.WhatweaimtodoistomaketheamplifierlookasifitonlyhasoneHighFrequencycutoff,which,withamaximumphaseshiftof90°,isunconditionallystable.We look for the RC network with the lowest High Frequency cut-offfrequency, i.e. the dominant one, andwe slug itwith yetmore capacitance to

makeitevenlower.Supposethatasaworstcase,wecascadedfouridenticalamplifiers,eachwithanHighFrequencycut-offfrequencyof300 kHz,andagainof10.At300 kHz,eachamplifiercontributesaphaseshiftof45°,makingatotalshiftof180°.Thegainofeachamplifieris3 dBdownat300 kHz,sothegainofeachamplifieratthatfrequencyis ,sothegainofthetotalamplifiermustbe:

In a typical amplifier we might want to reduce this gain from 2,500 to 125,whichwouldbe26 dBofnegativefeedback,andwouldreducedistortiontoatwentiethofitsoriginalvalue.Inordertodothis,thefeedbackloopwouldhavealossof0.0076.Ifwenowcheckforstability,0.0076×2,500=19.Theamplifierhasaloopgain≥1andaphaseshiftof180°,soitwilloscillate.Weneedtoreducetheopen-loopgainat300 kHzbyafactorof19,or25.5 dB,toachievestability (thishas littleeffecton the frequency responseof the finalamplifier). Remembering that 6 dB/octave is equivalent to 20 dB/decade,reducingonecut-off from300 kHz to30 kHzwill giveus20 dB reduction,andhalvingfrom30 kHzto15 kHzwillgiveusanother6 dB,making26 dBintotal.Thisproceduremaybeformalisedbythefollowingstatement:The loop gain may be as large as the ratio of the two most dominant timeconstants.Toapplythisrule,wesimplychoosehowmuchfeedbackwewant,calculatetheloopgain,andadjust thedominant timeconstantuntil the ratiobetween itandtheadjacenttimeconstantisequaltotheloopgain.Theamplifier isnowstable,butonly just,and itwillring.Weshoulddistancethedominanttimeconstantstillfurthertoincreasestabilityandremoveringing,certainlybyafactorof2,andpreferablyalittlemore.Itshouldberealisedthatover-zealous stability compensation reduces feedback, and compromisesdistortionreduction.Most practical amplifiers, having exhausted the first two possible methods ofachieving stability described, resort to manoeuvring the amplitude responseindependently of phase response using step networks , usually one inside thefeedbacklooptomanoeuvretheopen-loopresponseandanotheronthefeedbacklooptomanoeuvretheclosed-loopresponse.Suchnetworksareadjustedontestwhilstobservingasquarewaveandtypicallyrequiresimultaneousadjustmentoffourcomponents(notashardasyoumightthink).Realistically, we ought to consider that methods of designing for stability, in

priorityorder,are:•Reducethenumberoftimeconstantsorstageswithintheloop.•Slugthedominantpole.•Fudgethephase/amplituderesponseusingstepnetworks.

Therearesomestabilityproblemsthatarepeculiartovalveamplifiers,andtheyhavewell-knownsymptomsandcures.

LowFrequencyInstability,orMotorboating

This is an oscillation at about 1 or 2 Hz, and is invariably caused byunintentional feedback via the power supply, due to the rising impedance offilter capacitors at low frequencies. In effect, the entire amplifier becomes arelaxationoscillator[9].Thetraditionalcurewastoinsertanlowfrequencystepnetwork,ortoreducethevalueofthecouplingcapacitors,inthesignalpath,soas to reduce the loop gain. This solutionmolests the second condition of theBarkhausencriterion,butonlytreatsthesymptoms.TherealsolutionistoattackthefirstconditionbyremovingthefiltercapacitorsandtheirassociatedRCtimeconstantsbyfittingHTregulators.Thisgenerallykillstheproblemstonedead.Itisthisimprovementinstabilitythatisthereasonfor the superior bass in designs using regulated supplies, since it removespreviously unidentified low frequency ringing. It should be noted that thisproblemdoes not necessarily need a global feedback loop tomake it felt, and‘zerofeedback’pre-amplifiersarenotimmune.Itisnotunusualtodiscoverthatnotonlyistheamplifiermotorboating,butthatitalsohasburstsofhighfrequencyoscillation,knownassquegging.Ifpossible,it is best to cure the high frequency problem first, since it indicatesmarginalstabilitywhentheamplifierisundermaximumstressandmaybeconcealedoncethelowfrequencyinstabilityhasbeencured.It is possible to build a power amplifier with only two low frequency timeconstants–oneintheoutputtransformerandoneinthedrivercircuitry–butitissotemptingtoallowmorethanoneinthedriver.Wesawearlierthatwecanhaveasmuchloopgainastheratioofthetwonearest timeconstants,soifwehave three time constants that are not widely separated, we must place themiddle time constant at the geometric mean of the outer two. Unfortunately,bandwidth considerations force the middle time constant to be the outputtransformerwhich,havinganironcore,hasinductancethatvarieswithlevel,soits timeconstant isvariable, implying that it is alwaysmoving towardsoneorotheroftheoutertwotimeconstants,reducingstability.

WecannowseethatthetemptationtoallowmorethanonetimeconstantinthedrivermustberesistedatallcostsifLowFrequencystabilityistobeachieved,so we must now consider whether τ driver should be larger or smaller than τtransformer:

• τ driver < τ transformer : This can be achieved by fitting a small couplingcapacitor,butthisforcesourglobalnegativefeedbacktocorrectfallingopen-loop low-frequency response rather than reducing low-frequency distortiongeneratedintheoutputtransformer.•τdriver>τtransformer:Weknowthattheoutputtransformerinductancefallsassaturationapproachesor,toputitanotherway,ithasitslargesttimeconstantatlowlevel–whichiswhereitiseasiesttotestforstability.Thus,therearetwoadvantagestomakingτdriver>τtransformer:

•Stabilityincreasesasoutputtransformerinductancefalls.

•Globalnegativefeedbacknowreducesoutputtransformerdistortionratherthancorrectingfallingopen-loopresponse.

Unfortunately,thereisadisadvantage.Wecannottolerateblockingatanypricebecauseif itoccursitwillbeprolonged.Thus, theτdriver>τ transformersolutionrequires that τ driverbe implemented before a stage that cannot be overloaded.Thisisnotaproblem,butitmustbeconsciouslyconsidered.

ParasiticOscillationandControlGrid-Stoppers

The solution is almost encompassed by the description. Parasitics are theunwanted stray capacitances and inductances that result from the practicalattempttobuildacomponentoramplifier.Miller capacitance in the valve combineswith series inductance in the controlgridcircuit to forma resonantcircuit, sovalveswithahighgm (lowrk )areparticularly prone to oscillation. (Inductance in the cathode circuit is not aproblembecause it causesnegative feedback that reduces loopgain.)Thebestcure is to damp the resonant circuit by fitting agrid-stopper resistor in serieswiththegridascloseaspossibletothegridpinofthevalvebase.Thephysicalpositioning of the resistor reduces the wire’s inductance (very roughly 0.75nH/mm), whilst a given value of resistance in the grid circuit is far moreeffective at increasing the loss of the resonant circuit without compromisingfrequencyresponsethanifitisplacedinthecathodecircuit.Rememberingthat:

Thus, Q is most dependent on series resistance, so adding 10 kΩ of seriesresistancetothegridcircuitisasure-firewayofoppressingparasiticoscillation.Forsmall-signalvalvesthatarepronetothisproblem(E88CC,5842,EC8010)athin film surface mount resistor actually touching the pin is ideal, whereasleaded carbon film resistors are more convenient for power valves. Typicalvaluesrangefrom100 Ωto10 kΩ,andareusuallyfoundbyexperimentsinceindividuallayoutiscritical.Ifyoucanguarantee>100 MHzbandwidthatyourprobetip,useanoscilloscopetodeterminethesmallestacceptablevaluebecauseexcessive resistance increases grid current distortion, but beware that touchingthe typical 8 pF capacitance of a probe to a marginally stable circuit cansometimes tip the balance between stability and oscillation, so probe at theanode.Ifyoucan’tprobe,playsafeandusealargegrid-stopperbecauseunseenRFoscillationalwaysincreasesdistortion.

ParasiticOscillationofUltra-LinearOutputStages,andg2Stoppers

Ultra-linearamplifierswithpooroutput transformersorparallelpairsofoutputvalves sometimes need a series RC network between anode and g 2 . This isbecause this section of the winding has resistance in series with leakageinductance–theadditionalnetworkattemptstoreturnthisimpedancetoapureresistance.For43%taps,theimpedancebetweentheanodeandg2tapis≈9%ofthetotalanodetoanodeimpedance,sothisisagoodstartingpointforthevalueof resistor, but both have to be determined empirically (adding them to bothhalves of the transformer simultaneously, whichmakes life difficult), and areoftenaround1 nFand1 kΩ.BearinmindthateachcapacitorhastowithstandVHTwhentheassociatedanodeswingstowards0 V.

ParasiticOscillationandAnodeStoppers

Now that NOS audio valves are in short supply, it is common to substitutecheaplyavailableRFvalves,but (beingdesigned forRF) thesecansometimesoscillate at high frequencyorVHF.A common amateur radio solutionwas toadd a series anode stopper inductormade froma 2 W100 Ωcarbon resistoroverwoundwithabout10turnsof≈0.7 mmenamelledcopperwiresolderedtoeachendoftheresistor–theinductorpreventsthevalveseeingthecapacitance

that made it oscillate and the carbon resistor damps the inductor’s VHighFrequency self-resonance. Exactly the same trick is used at the output oftransistorpoweramplifiers toprotect theamplifier fromexcessive loudspeakercable capacitance that could causeHigh Frequency instability and consequentdestruction,anditwastheabsenceofthiscomponentthatcausedthewholesaledestruction of some well-known amplifiers when low inductance highcapacitanceloudspeakercablebecamebrieflyfashionable.

HighFrequencyStabilityandthe0 VChassisBond

Althoughwe tend to think thatwe require a low resistance bond at the inputsocket between the amplifier’s 0 V and the chassis tominimise hum, it alsoneeds to be low inductance to maintain High Frequency stability. There isinevitablystraycapacitancebetweeneachandeverypartof thecircuitand thechassis.Thus,therewillsomewherebetwocapacitorsinseriesthatconnectanamplifier’s output back to the input in phase , potentially causing oscillation.Connectingthechassisto0 Vshortcircuitsthejunctionofthosetwocapacitorsto0 Vandbreaksthatpositivefeedbackloop.

StabilityMargin

Stability of valve amplifiers is often described by the amount of additionalglobal negative feedback that would be required to cause oscillation. This issimply the ratiobywhich thedominant time constantswere further distanced,overandabovethenecessaryminimumrequiredforstability.Thedesignersofthe Mullard 5-20 were proud to claim that 10 dB more feedback would berequired to cause instability, whereas the Williamson is questionable at LowFrequencyevenwithoutadditionalfeedback.Unlikeatransistoramplifier,itisunusualtobeabletoapplymorethan30 dBofglobalnegativefeedbacktoavalveamplifier,andeventhendesignneedstobeplannedvery carefully to ensure that the feedback reduces distortion ratherthanstability.

ClassicPowerAmplifiersNowthatwecanrecogniseandanalyseindividualstages,wecaninvestigatethedesignofsomeclassicamplifierssuchastheWilliamson,theMullard5-20andtheQuadII.

TheWilliamson

ThedesignofthisamplifierwaspublishedinWirelessWorld[10]in1947,andsetastandardofperformancethatwasyearsaheadofitstime.The input stage is the standard common cathode triodewith 20 dB of globalnegativefeedbackappliedfromtheloudspeakeroutputtothecathode.Thephasesplitter is a concertina circuit direct coupled from the input stage, and feeds adifferentialpairusingbothhalvesofa6SN7(seeFigure6.22).

Figure6.22Williamsonamplifier(bypermissionfromElectronicsWorld).

Theoutputstageisapush–pullpairofKT66beamtetrodesoperatedastriodesthat provide 15 W output in Class AB1, operating mostly in Class A. RV 1adjuststheDCbalanceoftheoutputvalvesinordertominimisedistortionduetothetransformercore,whilstRV2setsthequiescentcurrentto125 mAfortheentirestage.The linearity and headroom of each stage is excellent due to the carefulpositioningofoperatingpointsandchoiceofvalves,butbecausethisamplifierhasfourstagesenclosedby thefeedback loop,stabilityneeds tobe takenveryseriously.Theinputstageinitiallyhasanoutputresistanceof≈7.5 kΩ,butthisisraisedbythefeedbackto≈47 kΩ.Incombinationwith12 pFofinputcapacitancefromtheconcertina,thisgivesahighfrequencycut-offof≈280 kHz.However,this

hasbeenmodifiedbyadding the stepcompensationcomponentsR2 (4.7 kΩ)andC 1 (200 pF) to the anode circuit ofV 1 . This circuit puts a step in theamplitude responsewhich begins to fall at ≈130 kHz, but the phase responseremainsvirtuallyunchangeduntil280 kHz.The concertina drives a driver stagewith an input capacitance of 60 pF, andbecausetheoutputtransformerfortheWilliamsonwasverycarefullyspecified,it seems unlikely that losses in the output transformerwould cause the globalfeedbacklooptoforcethedriverstageoutofClassAoperation.Theconcertina,thus,facesabalancedload,andhasanoutputresistance≈350 Ω,resultinginf−3 dB=7.5 MHz,whichissufficientlyhightobeinsignificant.Thedriver stagehas anoutput resistanceof≈8.7 kΩ, togetherwith55 pFofinputcapacitancefromtheoutputstage,thecut-offis≈330 kHz,andtheoutputtransformerisspecifiedtohaveacut-offof60 kHz.Thenumber of high frequency cut-offswithin the feedback loophas not beenminimised,andthedominanthighfrequencycut-off(theoutputtransformer)isratherclosetothepairwhicharenextmostdominant.Thus,theonlyremainingway to achieve stability at high frequency was to adjust the phase responseindependentofamplituderesponsebymeansofastepnetwork.At low frequencies it is more useful to consider time constants than –3 dBpoints.Theinputstageisdirectcoupledtotheconcertina,sowecanignorethis.TheconcertinafeedsthedriverstagewithaCRof≈22 ms,asdoesthedrivertooutput stage, and the output transformer is set to 48 ms. Additionally, theauthor's experience has been that decoupling theHT between input stage andconcertina can sometimes induce motorboating. In view of this, it is notsurprisingthatLowFrequencystabilityisquestionable,aswasconcededintheoriginalWirelessWorld article. In 1952,Hafler andKeroes decided that theiroutput stagewouldbenefit fromaWilliamsondriver [11] , so theyquintupledthe concertina to driver stage coupling capacitors from 50 nF to 0.25 μF toseparatethelow-frequencytimeconstants.It should be remembered that in 1947, circuits were designed using longmultiplication or tables of logarithms, and if speed was needed – slide rules.Computer-aidedACanalysiswasnotanoption!Mostamplifiersweredesignedas carefully as possible, then adjusted on test for best response – and wide-bandwidth(>1 MHz)oscilloscopeswererecentlydevelopedluxuries.

TheMullard5-20

Thiswasa20-Wdesign introducedbyMullard [12] to sell theEL34pentode.There is considerable similarity between this design, theMullard 5-10 (10 W

usingEL84),andsomeLeakamplifiers(seeFigure6.23).

Figure6.23Mullard5-20(MullardLtd,originatorofthisdesignisnowincludedinPhilipsComponentsLtd).

TheinputstageisanEF86pentode,whichisresponsibleforthehighsensitivitybut poor noise performance of these amplifiers. Most of the cathode biasresistanceisbypassed,sinceitwouldotherwisereducethegainfromaround120to33,whichwouldbeawasteofopen-loopgain thatcouldbeused tocorrectdistortionproducedby theoutput stage.Unadorned, thepentodehasanoutputresistanceof100 kΩ,anddrives≈50 pFof input capacitance from thephasesplitter,whichwouldgiveacut-offof32 kHz,butthisismodifiedbytheusualstepnetworkacrossitsanodeload.A slightly unusual feature is that the g 2 decoupling capacitor is connectedbetweeng2andcathode,ratherthang2andground.Inmostcircuits,thecathodeis at (AC)ground, and so there isno reasonwhy theg 2decouplingcapacitorshouldnotgotoground.Inthiscircuit,thereisappreciablenegativefeedbacktothecathode,andsotheg2capacitormustbeconnectedtothecathodeinordertoholdg2–k(AC)voltsatzero,otherwisetherewouldbepositivefeedbacktog2.Thecathode-coupledphasesplitteriscombinedwiththedrivercircuitusinganECC83.When loaded by the output stage, forV 2 ,A v=54, but gain to oneoutputishalfthisat27.Theanode load resistorshavenotbeenmodified togiveperfectbalance.Withthe470 kΩgrid-leakresistorsof theoutputstage inparallelwith the180 kΩanode loads, the effective anode load is 130 kΩ. Using the formula derivedearlier,thismeansthatV2bshouldhaveanACanodeload3%higherthanV2a,andRLforV2bwouldthenbe187 kΩ.Mullarddidactuallystatethis[12],butprobablyassumed thatmost constructorswouldnothaveaccess to sufficientlycloseprecisionresistorstousetheinformation.Theoutputstagehasaninputcapacitanceof≈30 pF,andthedriverstagehasan

outputresistanceof53 kΩwhenloadedsymmetrically,givingacut-offat≈100kHz,whichisquitepoor.Loadedasymmetrically,theoutputresistancerisesto≈90 kΩ,whichlowersthecut-offto≈60 kHz.Lookingat thedriverstage,weshould investigatehowcapable it isofdrivingtheoutput stage.85 Vwillbewastedacross the82 kΩ tail resistor,butwith410 VofHT,thisstillleavesuswith325 V.Withthecomponentvaluesgiven,thisputstheoperatingpointat240 Vonthe180 kΩDCloadline.DrawingtheAC130 kΩloadlinethroughthispointshowsthatthestagewouldgenerate≈4%second harmonic distortion at full drive ( V out =18 V RMS ), if it were notoperated as a differential pair.Mullard claimed 0.4% distortion for the entiredrivercircuitry.Although distortion appears acceptable, the driver stage has only 10 dB ofoverload capability. When output stage gain begins to fall due to cathodefeedbackor insufficientprimary inductance in theoutput transformer,or inputcapacitanceloadsthedriver,theglobalfeedbackloopwilltrytocorrectthisbysupplying greater drive to the output stage, and the 10 dB margin will beeroded,increasingdistortion.The driver circuitry was designed to produce an amplifier of high sensitivityevenafter30 dBoffeedbackhadbeenapplied,andthishasforcedotherfactorstobecompromised.WhereastheWilliamsonsacrificedstabilityforlinearity,theMullard5-20achievesstabilityattheexpenseofnoiseandlinearity.TheoutputstageisapairofEL34sinBlumleindistributedloadconfiguration,with 43% taps for minimum distortion. Unlike the Williamson, there is noprovisionforadjustingorbalancingbias,andthismightseemtobearetrogradestep.Biasadjustmentimpliesconnectingthecathodestogetherandusingaproportionofgridbiastoprovidethebalanceadjustment.Becausethebiassingisfirmlysetby the potentiometers, there is no self-regulation of bias current, and as thevalves age, balance will need to be reset. In short, providing this adjustmentensuresthatithastobeusedregularly.Bycontrast, theMullard5-20has separatecathodebias resistors and reliesonautomatic bias to hold the anode currents at their correct, and therefore equal,currents.Inpractice,thisworkswell,althoughitdoesnotquiteachievethelowtransformercoredistortionofafreshlybalancedadjustablesystem.This system does have a disadvantage in that the individual cathode biasresistorsapplyseriesnegativefeedbacktotheoutputvalves,raisingtheiroutputresistance.Theoutputtransformercouldberedesignedtomaintainthematchtotheload,butthisisundesirableasitwouldrequireahigherprimaryimpedance,

whichmakesahighqualitydesignmoredifficulttoachieve.Becauseofthis,thecathode bias resistors must be bypassed by capacitors, and this is where theproblemsreallybegin.ThecapacitorisashortcircuittoAC,andsopreventsfeedback,butitsreactancerises at very low frequencies, so it is no longer a short circuit, and allowsfeedback. Because the output stage is matched to the load, the unwantedfeedbackcausesasharpriseindistortionandreductionofoutputpowerduetothemismatch.Theobvioussolutionis tofita largeenoughcapacitor toensurethattheLowFrequencycut-offforthiscombinationisbelowallfrequenciesofinterest,perhaps1 Hz.RememberingthattheresistancethatthecapacitorseesisRkinparallelwithrk,wecaneasilycalculatethevaluerequired.Forapentode,rk=1/gm ;a typicaloutputpentodehasgm=10 mA/Vat itsworkingpoint,sork≈100 Ω,whichisinparallelwithabiasresistorof≈300Ω,givingatotalresistanceof75 Ω.For1 Hz,wethereforeneed2,000 μFofcapacitance.2,000 μF 50 V capacitors were simply not available at the time, and theyweren’tfitted.Theyarereadilyavailablenow,butthere’samoresubtlereasonfor using a smaller value.When the output stage is driven intoClassB, eachcathode tries to move more positively than negatively. It can't turn off anyfurther,butitcancertainlyturnonharder.ThecathodecapacitorintegratesthesechangesintoagentlyrisingDCbiasvoltage,whichbiassesthevalvefurtherintoClass B, and the problem continues. The effect of this is that a momentaryoverload can cause distortion of following signals that would normally havebeenwithinthecapabilitiesoftheamplifier–thisisaformofblocking.Asthecathode bias capacitor becomes larger, the recovery time from overloadlengthens.Theoretically,weneveroverloadamplifiers,andthisisnotaproblem,butoccasionaloverloadisinevitable,anditseffectsshouldbeconsidered.Onewaytodealwiththisproblemistoreducethecathodebiasresistorto≤1 Ω,sothatitnolongercausesnoticeablefeedback,andmeasurethecurrentthroughitusinganoperationalamplifier.ThisthenfeedsanasymmetricclippersothatwhenthevalvestraysintoClassBandclipsonehalf-cycle,theclipperremovesanequalamountfromtheotherhalf-cyclebeforefeedingtheprocessedsignaltoanintegrator.TheintegratorcanhaveanRCtimeconstantofalmostanyvaluewechoose,and10 sisnotunusual.TheoutputoftheintegratorisasmoothedDC voltage proportional to anode current, which can be compared to a fixedreference,and thedifferencebetween the twolevelsdrivesanamplifierwhoseoutputsetsthenegativegridbiasfortheoutputvalve.If theanodecurrentofonevalve is setasa reference, then theothervalve,or

valves,cansharethisreference,whichthenforcesanodecurrentsintobalance.The increased complexity of this scheme is (partly) offset by its improvedperformance and reduction in HT voltage required, since the cathode biasschemewastesHT(seeFigure6.24).

Figure6.24Principleofoutputbiasservo.

Thiscircuitwasdesignedtosensea40 mAanodecurrentbydeveloping40 mVacrossthe1 Ωresistor;therestofthecircuitisbasedonthis40 mVsignal,soifadifferentcurrent is tobesensed, thesenseresistorshouldbechangedtosuit.The5534hasagainof100,andamplifiesthemeanDClevelto4 V,withACpeaks rising to 8 V. Any peak above 8 V is clipped by the diode/transistorclamp, since the other half-cyclewill already have been clipped by the valve.Theclippedsignalisintegratedbythe2.2 MΩresistorincombinationwiththe470 nFcapacitor,giving τ=1 s.The071compares this smoothedDCwithareferencederived from thepotential divider chain, anduses this to control thebias transistor. The clamp reference voltage set by the 2 kΩ variable resistorshould be adjusted to achieve constant anode current under all conditions ofoverload. Although this circuit was designed to provide –11 V bias, this caneasily be changed by returning the bias transistor's collector load to a morenegativesupplyasnecessary;nootherchangesarerequired.

TheQuadII

The Quad II is an unusual design, which at first sight does not look toopromising,butworksbecausethedesignissynergetic.

In this design, not only has the phase splitter been combined with the driverstage,butithasalsobeencombinedwiththeinputstage.Inordertoachievethenecessarygain,pentodeshavebeenused.Outputresistanceisthereforehigh,asisinputnoise.Tomakemattersworse,avariantofthesee-sawphasesplitterhasbeenused.Theoutputstagehaslocalfeedback,requiringincreaseddrivevoltage(seeFigure6.25).

Figure6.25QuadII(bypermissionfromQuadElectroacousticsLtd).

TheoutputstageisapairofKT66beamtetrodeswithanodeandcathodeloadssplitintheratio9.375:1.Thecathodeconnection,therefore,provideslittledrivetotheloudspeakerandmaybeconsideredtobeseriesfeedbackfromtheoutputtransformer.However, thecathodecurrent intheoutput transformeris thesumoftheanodeandg2currents,anditwasfoundthatthissummationreducedthirdharmonic distortion by a further 8 dB over that due to the negative feedback[13].The effect of this transformer-coupled feedback on output resistance is theopposite to what might be intuitively expected [14] . If we simply leave acathoderesistorunbypassed,thenthisgeneratesseriesfeedbackwhichincreasesra,yettransformer-coupledfeedbackreducesra.Thiscanbeunderstoodifweapplya shortcircuit asa load.Clearly, theoutput stage isunable todriveanyvoltageintothisload,butconverselythereisnofeedbacksignalappliedtothecathodes.Thegridsarethereforedrivenbythefullinputsignal,ratherthantheinput signal minus the feedback, so the output stage is driven harder as itattempts to maintain its voltage into a short circuit. This action is directlyequivalenttoreducingoutputresistance,andthenewvalueofoutputresistancecanbefoundusingthenormalfeedbackequation.Thetransformerprimariesareequivalentto3 kΩanodetoanode.Withtetrodes,

thislowvalueofanodeloadresultsinareductionofthirdharmonicdistortion,andanincreaseinsecondharmonic,whichisthencancelledbypush–pullactionin the output transformer (assuming that the output valves are perfectlymatched).The automatic bias is shared, so there is no provision for balancing anodecurrent, andwe can expect an increase in distortion at low frequencies due tosaturationofthe(rathersmall)transformercore.Curiously,thecathoderesistorwasonlyratedat3 W,yetitdissipates3.8 W.IfyourQuadIIdistorts,aburnt-outcathodebiasresistormaywellbethecause.Evenwithpentodes, there isnotagreatdealofgain from thedrivercircuitry,andinputsensitivityislow:1.4 Vforfulloutput.Thisisanexcellentchoiceofinputsensitivityforapoweramplifier,asnotonlydoesitguaranteeimpeccablenoiseperformance(evenfromapentode),butalsoitmeansthattheinputisfarlesssusceptibletohumandnoisefrominputcablesorheatercircuitry.TheQuadIIwasonlybeateninsignal-to-noiseperformancebytheWilliamson,whichwasquieterbecauseithadatriodeinputstage.Despite being a variant of the see-saw phase splitter, the phase splitter/inputstagedoesnot relyon feedback forbalance, and itsoperation isquite elegant.The output valvesmust each have a grid-leak resistor, so instead of applyingadditional loading to thedrivervalves,a tapping is taken fromoneof these toprovidetheinputforV2 .Providedthistappinghasanattenuationequaltothegain of V 2 , the output of the phase splitter must be balanced. Componentvariationmeans thiswillnotalwaysbe true,so thecathodesof the twovalvesaretiedtogethertoimprovebalance.Pentodestageshaveoutputresistance≈RL.SinceRLfortheQuadinput/phasesplitter/driveris180 kΩ,thiswouldappeartobeverypooratdrivingthe≈30pF input capacitance of the output stage, resulting in a cut-off of ≈30 kHz.However,apartfromtheoutputtransformer,thisistheonlyHighFrequencycut-off in thecircuit,andit isnotaproblembecauseit is thedominantpole.Eachoutputvalverequiresaswingof≈80 Vpk–pk,whichiseasilyprovided,becausepentodes can approach 0 V more closely than triodes, and also because LCfilteringwasusedon theHT line, rather thanRC filtering, thus increasing theavailableHT. The LC filteredHT supply also feeds g 2 of the output valves,whichhasthevaluableadvantageofreducinghum,sincetheanodecurrentofatetrodeorpentodeisfarmoredependentong2voltagethananodevoltage.Pentodesneedtohaveg2decoupledtoground.InsteadofeachEF86havingacapacitor to ground, a single capacitor is connected between g 2 of the two

valves.Thishasthreeadvantages:•Ifwehadtwoindividualcapacitors,theywouldeffectivelybeinseries,withacentretaptoground.Sinceeachvalveisconnectedtoanequalbutoppositesignal,thecentretapwouldbeatgroundpotentialevenifitweredisconnectedfromground.Therefore,we could cheerfullydisconnect the centre tap fromground, leaving two capacitors in series that can be replaced by a singlecapacitorofhalfthevalue.•Sincethisonecapacitorisconnectedbetweentwopointsofequalpotential,it doesn’t need the full voltage rating to ground. However, it is as well toconsidertheeffectoffaultconditionswhendeterminingthevoltagerating,sothisisnotagreatadvantage.•Connectingg2ofeachvalve togetheratAChelpsmaintainbalance in thesamewayascommoningthecathodes.

Although substituting one stage that combines the functions of input, phasesplitter anddriverdoesnot achieve the linearityofpurposedesigned stages, itachievesbetterlinearitythantheMullardcircuitbecauselessgainisdemandedfromit.With only a simple driver circuit and output stagewithin the global feedbackloop,theelegantQuadIIhasnostabilityproblems,butithasbyfarthesmallestoutput transformer of all three amplifiers. A small output transformer alwaysmeanscompromisedprimaryinductance,whichmeansthatmuchof theoutputstage’s available current is wasted driving the output transformer’s reactanceratherthantheexternalload.However,rememberthattheQuadIIwasdesignedto drive an electrostatic loudspeaker (open circuit at low frequencies), so thisweaknesswasnotapparentinitsintendeduse.

NewDesignsWehaveinvestigatedindividualstages,wehavelookedatfunctionalblocks,andwe have seen how classic designs were configured. Rather than merelyobserving,itisnowtimetoputthatknowledgetouse,anddesignanamplifier.In early editions of this book, itwas suggested that an old amplifier could becannibalisedforitstransformersandchassis.Sadly,thisapproachcannolongerbe justifiedbecauseclassicamplifiersarenow likely tobe fiftyyearsold,andtheamountofworkexpendedinre-usingcomponentsthatmightfailwithintenyears is prohibitive. It is now cheaper and easier to make an amplifier withcompletelynewcomponents.

Single-EndedMadnessTherearethreereasonswhyasingle-endeddesignhasbeenincluded:•Theauthorfeelsthatthesingle-endedgenreshouldbegivenafairtrialandhanging.Ornot,asthecasemaybe.•TheauthorwasgivenanNOS6528,andrealisedthatnotonlycoulditformthe basis of a stereo amplifier, but also he already had a suitable mainstransformer, chokes, rectifiers, and HT capacitors. (The fact that a pair ofcustom-designed output transformers would be needed was not allowed tointrudeuponthislogic.)• A single-ended amplifier is electrically simpler than push–pull, so it canmakeagoodfirstproject.

However, be warned. For a given output power, single-ended amplifiers aresignificantlybigger,heavier,andmoreexpensivethanpush–pull.

TheScrapboxChallengeSingle-EndedAmplifierUnfortunately for the transformermanufacturers,muchof the ironmongery forthis amplifier came from the author’s salvage stock – hence the amplifier’sname.Almostnoneofthecomponentsarecritical,althoughalternativeswillbeofferedasthedesignargumentprogresses.

ChoiceofOutputValve

Power amplifier design startswith required output power,which then leads tothe choice of output valve(s). Thankfully, loudspeakers are gently becomingmoresensitiveastheirdesignersappreciatetheadvantagesofacarefullychosenconematerial,soeven≤10 Wsufficesperfectlywellwithouthavingtoresorttoexpensivehigh-efficiencydesignssuchashorns.Havingdecidedon≤10 W,thenextchoiceiswhich300Btouse.Theworldprobablyhasenough300Bdesigns,sothe6528madeforaninterestingalternative.The6528(distributedbyTung-Sol/Chatham,Cetron,andRaytheon)isadoubletriode intended foruseas a series-passvalve in regulatedpower supplies.Theglass envelope andbase resembles aGECKT88, and it is internally akin to a6080,but thedetailedconstructionandconsequentspecificationsarepositivelyheroic(Table6.3).

Table6.3Comparisonof6080and6528DualTriodeSeries-PassRegulatorValves6080 6528

μ 2 9gm 7 mA/V 37 mA/Vra 280 Ω 245 ΩPa(max) 13 W 30 WIk(max) 125 mA 300 mAVa(max) 250 V 400 VIh 2.5 A 5 ACag 8.6 pF 23.8 pFCgk 5.5 pF 17.8 pF

Theprimaryattractionof the6528is itsastonishinglylowra ,whichsuggeststhat we could use a low-impedance output transformer – enabling bettertransformerdesign.Wenowneedtodecidewhattheprimaryimpedanceshouldbe,sowewillsoonplotloadlinesontheanodecharacteristics,butwemustfirstclarifytheclassofoutputstage.

ChoiceofOutputClass

Actually,thereisverylittleroomformanoeuvre.Asingle-endedamplifiercanonly be Class A. Class A2 implies grid current and requires power drivingcircuitrywithextremelylowoutputresistance,sothislow-poweramplifierwillbeClassA1,wherenogridcurrentispermitted,allowingasimplevoltagedriverstagetosuffice.

ChoosingtheDCOperatingPointbyConsideringOutputPower

andDistortion

Apowervalveconsumesexpensiveheaterpower,soitdoesnotmakesensetooperateitatanypointotherthanitsmaximumanodedissipation(30 W).Thismeans thatour loadlinemustbea tangent to theP a(max)curve.Wealsoknowthat formaximumoutput,weshouldnotcliponehalfof thewaveformbeforetheother,soourDCoperatingpointmustallowequalandoppositegridswings.Using theTung-Sol/Chathamcurves, sweeping a transparent ruler along thePa(max)curveresultedina2kΩloadlinewithanoperatingpointatVa=255 V,whichrequiredVgk≈−27 VandIa=120 mA(seeFigure6.26).

Figure6.26Operatingconditionsof6528outputvalve.

From the operating point, we can swing quite linearly to almost V gk =0 Vbeforedrawinggridcurrent,andtoaroughlyequalandoppositeswingofVgk=−50 V before cut-off begins to cramp the grid curves. Oncewe know howmanygridvoltscanbeswung,wecancheckthecorrespondinganodeswing.AtVgk=−0 V,Va=68 V,andatVgk=−50 V,Va=392 V,sothepeak-to-peakanode swing is324 V. Ifweassume thatwe swinganundistorted sinewave,

then324 Vpk–pk=115 VRMS.The loadline passes from 500 V ( I a =0) to 250 mA ( V a =0), whichcorrespondsto2 kΩ,andthisismuchhigherthantheconventionalchoiceof2ra.Ifweknowtheanodeloadandthevoltageswingacrossit,wecancalculatethepowerdevelopedintheloadtoseeiftheproposedloadlineisacceptable:

Wecanestimatethepercentageofsecondharmonicdistortionusing:

Atthechosenoperatingpoint,Vmax=392 V,Vmin=68 VandVquiescent=255V,resultingin7.7%secondharmonicdistortionatfulloutput.This performance is typical for the genre, and other loadlines predictedsignificantlylessaudiopowerorworsedistortion.(Thereisnopointinbeingtoocritical about the anode load, since real loudspeakers are nothing like pure,constantresistancesanyway.)

SpecifyingtheOutputTransformer

Wearenowabletospecifytheoutputtransformer:Type:Single-endedIDC=120 mA

Pmax≈6.6 W

Primaryimpedance=2 kΩ.

The transformer designer will immediately want to know the secondary loadimpedance,andbecauseloudspeakersarenotpure8 Ωresistances,itisusuallybetter to design for a 4-Ω load. Since a good output transformer hasmultiplesecondary sections, transformer manufacturers commonly offer four sectionsthat can be configured for 1 Ω, 4 Ω (preferred setting for practicalloudspeakers), 8 Ω and 16 Ω (ideal if you could find a genuine 16-Ωloudspeaker).Thenextimportantquestionisthelowestfrequencyforwhichmaximumpowerisrequired.Thisisanexpensivequestion.Asanexampleofclassiccommercialpractice, the Leak Stereo 20 and TL12+ amplifiers could only produce theirspecified power down to 50 Hz. The Sowter 9512 output transformer was

specified for 8 W at 25 Hz in the unlikely event that practical powermightexceedpredictedpower.

BiassingtheValve

Wecouldapply−25 Vdirectlytothegridofthevalvetosettherequired120mAofanodecurrent,butasmalldropingridbiasvoltagewouldcausePa(max)to be exceeded instantly. This is the reason why valve manufacturers do notrecommendgridbiaswithhighmutualconductancevalves–35 mA/Visveryhighbyvalvestandards.Wemustusecathodebias.Weneedtodrop27 Vacrossaresistor thatpasses120 mA,sobyOhm’slaw:

Iftheresistorhasavoltageacrossit,andcurrentpassingthroughit,thenitmustdissipatepower:

A 5 W power resistor is required as an absoluteminimum.We could use anMPC-5thickfilmresistor,whichisnon-inductive,butthesegetveryhotwhendissipating >2 W in still air, or we could screw a WH15 aluminium-cladwirewound resistor to the chassis,whichwouldbecool.Aftermuchhavering,theprototypechoicewasa200 ΩMPC-5positionedintheairflowbelowthevalve and connected in serieswith a 100 Ωwirewoundvariable resistor, thusallowingaprecisecurrenttobeset.

TheCathodeBypassCapacitor

The cathode resistor must be bypassed with a capacitor to avoid unwantedfeedback that would raise the valve’s r a , and require a new loadline. As insmall-signalcalculations,welooktoseetheACresistancestogroundfromthecathode.Lookingintothevalve,thecapacitorseesrk:

Butthisisinparallelwiththe225-ΩcathoderesistorRk,so:

Inasmall-signalstage,wewouldwant thebypass toworkdownto1 Hz,butthis is not necessarily the case in a power stage. By definition, power stages

swing large voltages and produce distortion. In a single-ended triode stageoperated below clipping, the distortion is primarily second harmonic, but thisincludesaDCcomponent that thebypasscapacitor integrates,shiftingthebiasawayfromtheintendedDCoperatingpoint.Oncethelargesignalhasgone,thebypass capacitor gently recovers to the designed bias. Recovery time isdeterminedbythetimeconstantofthecapacitorinconjunctionwithRk//rk.Ifwesetf−3 dB=1 Hz,thisimpliesatimeconstantτ=159 ms.Ittakes5τforaCR combination to recover fully from a disturbance, and 0.8 s might beconsidered tobe too long inmusical terms, sowemight set f−3 dB=10 Hz,whichmeansthattheoutputstagewouldrecoverfrombiasshiftinonly80 ms:

Theauthordidn’thaveany150 μFcapacitorsinstock,oreven220 μF,buthedid have some low ESR 1,000 μF 35 V, so he used these and accepted anoverload recovery time of 0.5 s. His reasoning was that overload should beuncommon, but that a small capacitor would increase anode resistance andincreasebassdistortionintheoutputtransformer,andthisdefectwouldbethereall the time. Far more designs are done this way than you might think – wecalculate carefully (possibly on the back of an envelope), then justify ourengineering compromise according to component availability at the time. It isquitepossiblethattheoptimumvalueofthiscapacitorcouldbestbesetbyear.

FindingtheRequiredHTVoltage

TheoutputtransformerdropssomeHTacrossitsprimarywindingresistance,soR DC(primary) needs to be known. The transformer manufacturer can usuallypredict this value, but it is useful to have ameasurement. For the transformerused,RDC(primary)=152 Ω,soOhm’s lawdictates that thevoltagedropdue to120 mAofanodecurrentis:

OurdesignrequiresVa=255 V,withcathodebiasof27 V,andwedrop18 Vintheoutputtransformer,soweneedanHTof300 Vatthetopoftheoutputtransformer. Finding this HT voltage is significant because it determines themaximum HT available to the driver stage (unless we are prepared to add asubsidiaryHTsupply).

HTSmoothing

Push–pull amplifiers cancel HT hum in their output transformer, but single-ended amplifiers cannot cancel, so their HT supplies must be much quieter.Worse,single-endedamplifiersdemandachangingcurrent(from0≤IDC≤2IDC) from their supply, so the low output resistance of a choke input supply isalmostobligatory.

HTRectification

The heroic specifications of the 6528were not achievedwithout anAchilles’heel. To avoid cathode stripping, the data sheet specifically warns that thecathoderequires30 stowarmupbeforeHTmaybeapplied.Thisseemstobeaperfectapplicationforavalverectifier.Weonlyneed120 mAplusalittleforthe driver, perhaps 10 mA, and the HT voltage is only 300 V, so an EZ81wouldbeideal.Inpractice,typicalvalverectifiersstartconducting≈11 safterpowerisapplied,soafurtherdelayisrequired,whichcanbeprovidedbya thermaldelayrelay.Thermal delay relays look just like valves, and consist of a heater actuating abimetallicstripinanevacuatedglassenvelope.Thebimetallicstripiscomposedoftwobondedmetalshavingdifferentthermalcoefficientsofexpansion,sothestripbendswhenheated,andformsthemovinghalfofaswitchcontact.Becausethe relay is almost evacuated, switch contact arcing is almost eliminated, andthermallossesareinsignificant,sotheheatrequiredtomakethestripactuatetheswitch contacts is determined substantially by its specific heat capacity andthermalmass.Ifnecessary,delaycanbeincreasedbyafactorofupto3:1overtherelay’srateddelaybyreducingitsheatervoltage.Ifthedelayrelaycontactsareplacedinthepathoftherectifier’sheatersupply,thenthedelayoftherelayisaddedtothedelayoftherectifier,andtheHTrisesgently over a periodof≈5 s at the appointed time.Alternatively,manydelayrelayscansafelyswitchACmains,buttheremustbenegligiblevoltagebetweentheheaterandthemovingcontact,implyingswitchingtheneutral,whichalwaysmakestheauthoruneasybecauseitleavesanapparentlydeadamplifierwithlivemainsonmany terminals.At the time, theauthordidn’thaveanydata for theAmperite6NO45Tdelayrelayhefoundinhisscrapbox,butfromthepartcodehe deduced that it required a 6.3 V supply, that the contacts were NormallyOpen(prettyobviouswhenyoucanseethecontactsthroughtheglass),andthatitwouldgivea45 sdelaytime.Thedevicewasanall-glassenvelopeonaB9Abuttonbase,soitwaseasytoseewhichpinwaswhich,andtestthededuction.Ontestat6.3 V,theheaterdrew300 mA,andtheswitchcontactsclosedafter41 s.

Whenpower is applied, themains transformer delivers heater andHTvoltagesimultaneouslytothevalverectifier,butitsheateriscold,sothecathodesuffersion bombardment. Although placing the delay relay in the rectifier’s heatercircuitensuresthattheHTtotheaudiocircuitryrisesgentlyfromzero,itdoesmeanthattherectifiersuffersanextra45 sofionbombardmenteachtimetheamplifier is switched on. This is an engineering compromise – the EZ81 is acheapsacrificetoappeasethefarmoreexpensive6528.

TheHTTransformer

Weneed300 VofHTatthetopoftheoutputtransformer,andhaveelectedtouse valve rectification combinedwith a choke input supply. The choke dropsvoltage across its R DC , so this must be determined. The author’s scrapbox(moreofaroom,really)yieldedapairof15 H,250 mAParmekochokesthatlookedhopeful andwhoseRDC=136 Ω, so 130 mApassing throughone ofthesechokeswoulddrop17 V,andthiswouldbeaddedtothe300 V,togive317 V.Therectifiermanufacturer’schokeregulationcurveswereusedtodeterminetherequired transformer voltage. Interpolation of Mullard EZ81 curves predicted≈375 VRMSforourrequired317 VDC.Nowadays,wewouldsimplydropthenumbersintoPSUD2.FurtherrummaginginthescrapboxuncoveredalargeC-coretransformerwithapair of 375–0–375 V at 250 mA windings and numerous 6.3 V heaterwindings,sothisseemedideal,allowingdualmonoconstructionononechassis.

HTChokeSuitability

Wefinallyhavesufficient information to testwhetherornot theposited15 H250 mA HT choke is satisfactory. Using equations from Chapter 5 andassuming50 Hzmains:

Thechokeisratedat250 mA,soitshouldeasilysupportthiscurrent.Theminimumloadcurrentrequiredis:

Theoutputstagedraws120 mA,sowearesafelyabovethislowerlimit.

We can estimate the hum due to HT once we know the proposed value ofsmoothing capacitor. The author had some 120 μF 400 V polypropylenecapacitorsinstock,so:

Theanodeloadandraformapotentialdivider,sotheripplevoltageseenattheanodeis:

Anoutputtransformerrespondstothevoltageacrossit,soitsees625 mV–104mV=521 mVofhum.Atfulloutput, theoutputstageswings115 VRMS ,so521 mV corresponds to a 47 dB signal/hum ratio, which is inadequate, so afurtherstageoffilteringisneeded.AsecondstageofLCfilteringhavinga lossat100 Hzofonly32 dBwouldimprovethesignal/humratiotoalmost80 dB.32 dBcorrespondstoavoltageratioof40, so theACpotential divider formedby the secondLC filterwouldneedXL/XC ≈ 40.Ifanother120 μFcapacitorwereavailable,thenevena1H130 mAchokewouldbeadequate.However,theauthordidn’thaveanothersuitablepairofchokes,andhadalreadyrealised that the amplifier was going to be large and heavy (even by valvestandards).Addingyetmoremasswasnotatallattractive.

TheHTRegulatorOption

LC filtersmight be good at reducing hum, but their output impedance is stillquite high (many tens of ohms). This is particularly significant for a single-ended amplifier because the output valve is unable to distinguish between thereflectedloadoftheloudspeakerthroughtheoutputtransformerandtheoutputresistanceofthesupply(seeFigure6.27).

Figure6.27Theeffectofnon-zerosupplyresistanceonapoweramplifier.

Theswingof theoutputvalve isdevelopedacrossboth thesecomponents,yetwecanonlycoupletheswingdevelopedacrosstheoutputtransformer.Welosepower, and our output resistance rises.AnHT regulator allows optimumbassperformancefromasingle-endedamplifier.Eachchanneloftheamplifierrequires300 Vat130 mA,andyoucouldsimplyuse theentireHTsupplyofFigure5.45withoutanymodifications.Butwedonot need a great deal of ripple rejection, so an adaptation of the simple two-transistorregulatorisapossiblealternative(seeFigure6.28).

Figure6.28TwotransistorHTregulator.

Thetwo-transistorregulatorhastheadvantagethatitdoesnotneedtodropmanyvolts, which reduces heat dissipation.Wewill assume that the regulatormustdrop≥10 V,andthatthiswilloccurwhenthemainshasdroppedby6%(asitisallowed to do). Thus, the nominal HT voltage required at the input to theregulatoris:

CheckingtheEZ81datasheet,thiswouldrequireamainstransformerwith412–

0–412 VHTwindings.High-voltagebipolarpowertransistorshaveratherlowhFE,theyareslow,andtheyareexpensive,soahigh-voltageMOSFETpowertransistorcanoftenbeabetterchoicefortheseries-passelement.Whennoiseisnotcritical,itmakessensetomaketheZenerreferencevoltageashighaspossiblebecausethisreducesdissipationintheerrortransistor,andalsoallows increased loop gain, which gives more feedback to reduce outputresistance. 220 V is therefore a good Zener choice for a regulator that mustprovide an output of 285 V. Although 220 V Zeners are available (and theauthorhadsomeinstock),threecascaded72 VZenersarebetter.Thereasonforthis is that theveryhigh-voltageZenersare rathernoisybecause theymustbeoperated at a low current to reduce device dissipation (P= IV ).Using threecascaded Zeners allowed a Zener current of 4 mA, which reduces noise. Toreducenoisefurther,theZenersarebypassedbya22 μF350 Vcapacitor.ThegateoftheMOSFETwillbeatVout+Vgs=300 V+4 V=304 V(despitehugedevicevariation,4 VisareasonableroughassumptionforVgsofapowerMOSFET).SincethecollectoroftheerrortransistorisconnectedtothegateoftheMOSFET,andtheemitteristiedtothe216 V(3×72 V)Zenerreference,VCE=304 V–216 V=88 V.Wewanttheerrortransistortopass4 mAintotheZenerreference,soIc=4 mA,andthepowerdissipatedinthetransistoris352mW.ThisisasignificantcalculationbecauseitconfirmsthatourchoicesofVCEandIcenableustouseasmall-signaltransistor.Whenworking, the error transistoronlyhasVCE=88 V,but at the instantofstart-up, the 22 μF Zener bypass capacitor clamps the emitter of the erroramplifierto0 V,soitmustbeabletosurviveVCE=330 V.Therequirementsfortheerrortransistorarenowclear,andthe400 V,625 mWMPSA44isideal.High-voltagetransistorshavelowhFE,andtheMPSA44isnoexception.Whentestedundertheexpectedoperatingconditions,hFE≈100.Ic=4 mA,soIb=Ic/hFE=40 μA.Even ifwepass1 mA through the samplingpotentialdividerchain, we cannot treat it as a pure potential divider because the 40 μA basecurrentdisturbstheresult.Wesetthesamplingdividerchaincurrentbyconsideringthepowerdissipationofthelowerresistorfirst.Ifweusea0.6 Wcomponent,andallowittodissipate0.2 W,itshouldremainsensiblycool.Theresistor isconnectedtothebaseoftheMPSA42,whichis0.7 Vhigherinvoltagethantheemitter,sotheresistorhas217 Vacrossit.UsingP=V2 /R , itsresistancemustbe2172 /0.2=235kΩ,sowewillusethenearestpreferredvalueof240 kΩ,whichwilldissipate

196 mW.Thecurrentthroughtheresistoris217 V/240 kΩ=904 μA.Becausetheerrortransistorsteals40 μAforitsbase,theupperpotentialdividerresistor passes 904 μA+40 μA=944 μA of current. The voltage across thisresistoris300 V–217 V=83 V,soitsresistancemustbe83 V/944 μA=87.9kΩ,andthestandardvalueof91 kwillbefine.There is no point in adding a speed-up capacitor across the upper resistorbecause the low attenuation of the divider chain (2.8 dB)means that it couldonlymarginallyimproveripplerejection,yettherequiredvaluewouldslowtheresponse of the regulator to Low Frequency transient current demands (seeChapter5).The least critical circuit value to be calculated is the error transistor collectorload resistance. We know that the input to the regulator is 330 V, and thecollectorvoltageis304 V,sothisresistorhas26 Vacrossit,passesIc=4 mA,anditsvaluemustbe26 V/4 mA=6.5 kΩ,sothestandardvalueof6k2willbejustfine.Back-of-an-envelope calculations suggested that the output resistance of thisregulatorwould be <5 mΩ, and that itwould reject hum by >50 dB. In thisinstance,thesefiguresaremorethanadequate,andofferbetterperformancethananotherchoke.

EstimatingAmplifierOutputResistance

CheckingACconditions,r acanbeapproximatedbydrawinga tangent to the−25 Vgridlineadjacenttotheoperatingpoint,andthisgivesavalueof≈400Ω.Thisissignificantbecausewecanuseittocalculatetheoutputresistanceofthe amplifier. The output transformer matches the assumed 8 Ω load of theloudspeaker to the 2 kΩ required by the valve, giving an impedance ratio of250:1. (The author matched to 8 Ω rather than 4 Ω because he knew theamplifier would be used with 12 Ω Rogers LS3/5a.) Conversely, sourceresistance is divided by this ratio, and we should include output transformerprimaryresistance(Sowter9512,Rp≈150 Ω),giving2.2 Ω,whichisinserieswith output transformer secondary resistance pluswiring resistance (0.95 Ω),leading toafinalestimatedoutput resistanceof≈3 Ω.Anoutput resistanceofhalfloadresistanceistypicalofsingle-endedamplifiersandistoohighformostloudspeakers to operate as their designer intended. Later,wewill see that notonly did adding cathode feedback halve distortion, it also lowered measuredoutput resistance to a quarter of load resistance, making it slightly moreacceptable.

WhataretheDriverStageRequirements?

WhataretheDriverStageRequirements?

In the output stage, the maximum undistorted grid swing from the operatingpoint is limited by the onset of grid current and a symmetrical swing in theoppositedirection.Gridcurrentoccursat0 V,andbysymmetrythemaximumoppositeswingmustbe2 Vgk,sotherequiredpeak-to-peakgridswingforanyClassAamplifierisalwaystwicethegrid–cathodebias.Inourcase,thismeansthatweneed54 Vpk–pkor19 VRMS.Weknowthatthe6528mustswing≈115 VRMSatitsanodeand≈19 VRMSatits grid, so it amplifies by a factor ofA v ≈6, allowing us to find theMillercapacitance,whichisCag ·(Av+1)=23.8 pF(6+1)≈167 pF.ThisisinparallelwithCgk(17.8 pF),sothetotalinputcapacitanceincludingstraysis≈200 pF.Wewillinvestigatedetailedargumentsfortherequiredhigh-frequencyresponseofanamplifierinChapter7,butifwemakethesweepingassumptionthatf−3dB>150 kHz,thisrequiresasourceresistanceof:

The6528hasaveryhighgm ,andwilloscillateatRFgivenhalfachance. Ittherefore needs a grid-stopper resistor to prevent oscillation, and themanufacturer’s recommendedminimumvalue of 1 kΩbites into our requiredsourceresistance,reducingitto4.3 kΩ.This isa lowoutputresistanceforavalvedriverstage,andseverelylimitsourdesignchoice. Inapracticalcommoncathodedriverstage,output resistance isroughly equal to the valve manufacturer’s claimed value of r a , so we arelookingforavalvewithaverylowra.Frame-gridvalvescanachievethisvalueofra,buttheytendtoproducemorethirdharmonicdistortionthanvalveswithhelicalgrids,soadriverstageusingconventionalvalveswith theoutput takenfromacathodewouldbepreferable.

DriverStageTopology

Therearevariousoptionsforthedriverstage:• A carefully designed common cathode stage (probably with active load)couldbeDCcoupled toa cathode follower.This couldgive stunningly lowdistortionandrs<4.3 kΩ.

•Aμ-followercouldgivelowdistortionandrs<4.3 kΩ.

•An SRPP could give r s<4.3 kΩ, and a higher voltage swing than aμ -followerbutwithhigherdistortion.

At thetimeofconstruction, theauthordidn’thaveanyDN2540N5sforsimpleactiveloads,sotheμ-followerwastheobviouschoice,buttestingshowedthat290 Vwasn’tquiteenoughHTtoenabletherequired18 VRMSswing.Further,weknowthattheoutputstageisacapacitiveload,forwhichtheSRPPisverywell suited, and it can swingmore signal than theμ -follower for a givenHTvoltage,sohighersecondharmonicdistortionduetothelowRL/raratioatthelowervalveisitsonlydrawback.

ChoiceofValvefortheDriverStage

Ideally,wewould likeadrivervalve thatproducesprimarily secondharmonicdistortionwith insignificant higher harmonics, because thatmight conceivablyallowsomedistortioncancellationwiththeoutputstage.Frame-gridvalvesarenow almost eliminated (although theE88CC is easily one of the best), so theobvious choice is the SN7/N7 family. The author makes no apologies forarriving at the same choice as dozens of other single-ended designs. If soundengineeringargumentsdictate that roundwheelsarebest, then that iswhatwewilluse.However,anSRPPhasitsuppercathodeat0.5VHT,soitrequiresanelevatedheater supply if heater/cathode insulation is not to be strained. In a stereoamplifier,oneSN7/N7couldbesharedbytheuppervalves,andanotherforthelower.Alternatively, the6J5GT ishalf of a6SN7, so apair of these couldbeusedinamonoblockamplifier.Theauthorchosetouse6J5GTsbecausehehadpreviously bought lots of them.Additionally, if individual valves are used, nounsightlymetalworkisneededtomodifythedesignlateron;perhapsahigh-μinput valve (6SQ7) as a common cathode stage with LED bias and constantcurrent sink loadDC coupled to a 6J5GT cathode follower if global negativefeedbackwasrequired.Ontest, the6J5GT/6J5GTSRPPstageeasilyswung21 VRMSat1 kHz,withsecond harmonic at −40 dB and third at −54 dB. However, loadingconsiderations meant that this measurement was taken purely by theoscilloscope/spectrumanalyser,sothereliablemeasurementdynamicrangewaslimitedtoonly≈55 dB,andhigherharmonicscouldnotbeseen.Nevertheless,thisdistortionwasfelt tobeacceptablecomparedtothepredicteddistortionoftheoutputstage.

DeterminingtheDriverStageOperatingPoint

DeterminingtheDriverStageOperatingPoint

Thetitle‘SRPP’(ShuntRegulatedPush–Pull) implies thatSRPPstagesshoulduse identicalupper and lowervalves. Inpractice, this seemsnot tobecritical,andtheauthorhasnotmeasuredanyadvantagewhentryingdifferentvalves,butitiscertainlyeasiertodesignwithidenticalvalves.Thevalvesareinseries(sotheypassthesamecurrent),andidentical,sotheanodeofthelowervalvemustbeathalftheHTvoltage.Therefore,wedesignbyconsideringthelowervalvetobeacommoncathodestagewithVa=0.5VHT.The6J5GT ideally likes I a≥8 mA for constant r a , or to consider it anotherway, I a ≥8 mA is likely to give lowest distortion.We will set I a =8 mA,requiringVgk≈3.4 V.Asacorollary,driving200 pFofshuntcapacitanceat20 kHzwith19 VRMSrequires≈0.48 mARMS,or≈1.3 mApk–pkofsignalcurrent.AnSRPPpassing8mA should be comfortably able to provide this signal currentwithout addingslewingdistortion.

SettingDriverStageBias

TheuppervalveofanSRPPmustberesistorbiassed,withoutabypasscapacitor,otherwisetherewouldbenosignaltodrivethevalve,butthelowervalvehasalittlemorefreedom.The conventional cathode bias choice for the lower valvewould be a 430 Ωresistor bypassed by an appropriately sized capacitor. However, when wedesignedtheoutputstage,weconsideredtheeffectsonbiasafterrecoveryfromdistortion.SinceeachhalfoftheSRPPoperateswithonlyhalfoftheavailableHT voltage (limiting signal swing), recovery after distortion or overload isimportant,soitwouldbebettertousefixedbiasinthelowervalve.FixedbiascouldbeprovidedbygridbiasorbyLEDcathodebias.Gridbiasisexpensive,but LED cathode bias can increase distortion if the anode load is not large.Fortunately, the author’smeasurements found that even in this stage, at thesesignal voltages, the additional distortion produced by LED bias wasinsignificant,anditallowsinstantaneousrecoveryfromoverload.

IstheOutputResistanceandGainoftheProposedDriverStage

Adequate?

TheoutputresistanceofanSRPPdriverstagewouldintuitivelybeexpectedto

besufficientlylow,butthiscanbecheckedusing:

Forthisdesign,usingmeasuredvaluesofμ=21andra=7.1 kΩ,theequationpredicts r out≈2.3 kΩ,which comfortably allows for a 1 kΩcathode stopperresistortoreducethelikelihoodofRFoscillationintheSRPP.ThegainoftheSRPPstageis≈14,andtheoutputstagerequires≈19 VRMS,sotheinputstagerequires≈1.4 VRMStodrivetheamplifiertofulloutput–whichis convenient because it allows ≈3 dB of gain from a standard 2 VRMSCDplayertoallowforpoorlyconformedrecordings.

ButWhatAboutGlobalFeedback?

It is de rigueur for single-ended valve amplifiers not to use global negativefeedback.Theargumentgenerallypresentedforrejectingglobalfeedbackisnotthat feedback has to be applied carefully tomaintain stability, but that single-ended amplifiers produce distortion that is primarily second harmonic,innocuous and proportional to level, and that adding feedbackwould translatedistortion harmonics up in frequency towhere they aremore noticeable. Thisargumentisbasedonthefollowingfacts:• Classical tests of distortion showed that second harmonic distortion wasinaudibleonsinewaveswhenitwas<5%.•Distortioninasingle-endedamplifierisproportionaltolevel.•Baxandallshowedthatfeedbackimpliedthatanamplifiergeneratingsecondharmonicdistortionwoulddistort thedistortion, leadingto theproductionofhigherharmonicsthatwerenotpresentbeforethefeedbackwasapplied.• Shorter showed that higher order distortion harmonics are moreobjectionableandthatareasonableweightingwasn2/4.

Wewillreturntothisvexedquestionlater,butforthemomentmerelynotethataddingdistortiontomusicraisesthenoisefloor.However,nobodyappearstoobjecttoaddingasmallamountoflocalfeedbackat theoutput stageby including thesecondaryof theoutput transformer in thecathodecircuit.

SummingUp

Nowthatdetaileddesigniscomplete,itisworthreviewingtheconsequencesofthedesignchoicestoseewhetherthewholedesignlooksworthwhile(seeFigure6.29).

Figure6.29Practical‘ScrapboxChallenge’poweramplifier.

•Predictedoutputpower≈6 Wwith≈8%distortion.•Inputsensitivityforfullpower≈1.4 VRMS.

The amplifierwas built to test the predictions andweighs 64 lb. Put anotherway, itweighs ≥10 lb per stereowatt. Compared to a push–pull design, it isheavy and expensive to achieve a limited objective, but precisely the sameallegationwouldbelevelledbyasemiconductordesigneratanyvalveamplifier.Valveamplifiersarethesteamenginesoftheelectronicworld–andtheyarousesimilarpassion.

TeethingProblems

Racing car engines achieve their outstanding performance by operating everypart just under its limit – so small errors are catastrophic. The 6528 can beconsideredtobearacingcarengine in that it is ratedat30 Wperanode,andconsumes 31.5 Wof heater power, so it has to lose 91.5 Wof heat from anenvelope the size of a KT88 ( P total =52 W). Initial testing thereforeconcentratedon ensuring that the6528wouldnot expirebefore the chequeredflag.The 6528valve basewasmounted on awire finger-guard intended for an 80mm fan, and an 80 mm lownoise (claimed12 dBA) fan blowsgently frombelowthevalvebase.Asaconsequence,even though thevalve isoperatingatmaximumP a , itsmeasuredenvelope temperature is justwithin limitsand thechassisisstonecold.Atthefirsttest,theACheatervoltageatthevalvebaseofthe6528measuredbyareliabletrueRMSmeterwas6.5 Vinsteadof6.3 V,sothemainstransformerprimarytappingwaschangedfrom240 Vto250 V,whichreducedtheheatervoltageto6.296 V–whichiscloseenough.(BecausetheACmainswaveformgenerallycontains≈5%distortionwithsignificantharmonicsupto1 kHz,ACheater voltage measurements should always be made by a true RMS meterhavinggoodaccuracyupto1 kHz.)Additionally, one of the 6J5GTs had to be rejected because of poorheater/cathodeinsulation(despitemeasuring>25 MΩ(hot)onanAVOVCM163valvetester).Eventhoughtheheatersaredecoupledtoground,thefaultcaused5 mVofhumandrectifierswitchingspikestobefedtotheoutputstage.

ListeningTests

Because of the importance of the trial, the ScrapboxChallenge amplifierwas

carefullyauditionedoveraconsiderabletimethroughtheauthor’spairofRogersLS3/5as.AlthoughtheLS3/5aisaverynicelittle loudspeaker, it isnot ideallysuited toweedy amplifiers.Unfortunately, they are the only passive crossoverloudspeakerswithanypretensionstoqualitythattheauthorowns.The amplifier started barely tolerable, but improved greatly over the first fourhoursoflistening,andthefactthatabottleofVeuveClicquotwassymbolicallyopenedsecondsafterthemusicbeganisquiteirrelevant.

Designer’sObservations

Theamplifier’swiringwascompletedoveraweekendfollowedbytwonationalholidays. Murphy’s law thus dictated that missing parts would only bediscoveredlateontheFridayevening.Theauthorintendedtousehisvariantofchoke snubbers for theHT supply, but the cupboardwas inexplicably bare of220 nFpolypropylenefilm/foil,sohewasinitiallyforcedtouseatraditional10nFfilm/foil+10 kΩsnubber(althoughthisdefectwascorrectedaweeklater).With hindsight, thiswas fortuitous, because the poorer snubbing revealed thatthecheapEZ81rectifierswitchesonandoffsurprisinglycleanlyandprovokedverylittleringing(seeFigure6.30).

Figure 6.30Voltage waveform at the output of the EZ81 rectifier with traditional snubber. (The lower, expanded trace showsrectifierbehaviourasitswitchesonandoff.)

Building the Scrapbox Challenge amplifier initially reinforced the author’sdeepening suspicion that the magnetic cores of chokes and transformers candeteriorate with age. The ripple predicted in 2002 after the first stage of HTfilteringwas56 mVRMS,butthemeasuredvaluewas7 dBhigherat124 mVRMS ,andthiswasthoughttobeduetothechokes(oneofwhichhadprevious

form–buzzinginanearlyEL84amplifier).Fortunately,workingthroughVA3uncovered an equation error (corrected in this edition), correcting the rippleprediction to 104 mVRMS , implying amere 1.5 dB discrepancy. Sadly, theoversizeC-coremainstransformerthrobbedevenbeforeHTcurrentwasdrawn,andrequireda5 Afuseinthemainsplugjust tosurvivetheinrushcurrentastheamplifierwasswitchedon.Moral:Forty-year-oldelectromagneticcomponentscouldbetheweakestlink.Ameasuredfailingmightnotbeduetoyourdesign.Listeningcloselyatswitch-on(beforethedelayrelayactivatedtheHTrectifiers)revealedthatsomehumwasbeinginduceddirectlyintotheoutputtransformersfrom themains transformer. If you decide to build this amplifier, itwould bebesttobuilditontwochassis,onefortheaudiocircuitryandoneforthepowersupply – allowing the noisy power supply to be distanced from the sensitiveamplifier.Ontest,theamplifierdelivered6 Wat1 kHzwith3.2%THD+N.Theamplifierwas testedwithandwithoutoutputstagecathodefeedbackat1 dBbelowfullpower(Table6.4).

Table6.4ScrapboxChallengeDistortion2nd 3rd 4th 5th 6th

Withoutcathodefeedback(dB) −25.2 −57.8 −55.6 −60.6 −58Withcathodefeedback(dB) −31.7 −64.3 −57.1 −74.3 –Improvement(dB) 6.5 6.5 1.5 13.7 –

Thefeedbackreducedamplifiergainby3 dB,yetthetableshowsasignificantlygreater improvement on all harmonics except the fourth – making it a veryworthwhiletrade.

Conclusions

With the rightprogramme(yes,acoustic jazz), thisamplifier isextremelyeasyontheear.Itisn’taccurate–theinevitablehighoutputresistance(2.1 Ωon8 Ωsetting) causes under-damped bass, it falls apart on choral music and LedZeppelin, and it is very heavy (10 lb/W).Nevertheless,when the authorwasfoolish enough to lend it to a friend having high-efficiency open baffleloudspeakers, itwas3yearsbeforehewasable to reclaim it.On theavailableevidence,thecasehasnotquitebeenproven,sothehanginghasbeenpostponed,even though the amplifier’s distortion figures are risible compared to acompetentlydesignedtransistoramplifier.Whatthisamplifierneedsforanacquittalissomeglobalnegativefeedback.Ifitwastobetheauthor’sprimaryamplifierforlisteningtomusic(ratherthanatest

mule),theSRPPwouldbereplacedbya6SQ7(μ=100)biassedbyaninsipidgreenLED (1.8 V at 300 μA) and loaded by aDN2540N5CCS active loaddirectcoupledtoa6J5GTcathodefollowersothattheextra18 dBofgaincouldbe spent on shunt applied global negative feedback to reduce distortion by afactorofseven.Taking the distortion at 6 W as 3.2%, dominated by second harmonic, thisfigure was entered into the Baxandall equations to estimate the amplitude ofhigherdistortionharmonicsgeneratedby14 dBofglobalnegative feedback (Table6.5).

Table6.5PredictedHarmonicGenerationResultingfrom14 dBGlobalNegativeFeedback2nd 3rd 4th 5th

Beforefeedback(%) 3.2 – – –After14 dBfeedback(dB) −45 −70 −95 −118

Notethatsecondharmonicfalls14 dBto–45 dB(0.6%)exactlyasexpected,butthatadditionalhigherharmonicshavebeengenerated.Theamplifieralreadyproduces fourth at −57.1 dB, and fifth at −74.3 dB, so the addition of newharmonics at ≈40 dB lower amplitude (≈1%) is entirely negligible.However,the feedback-generated third harmonic at −70 dB is comparable with theamplifier’s existing third harmonic at −64.3 dB, so 14 dB feedback can beexpected to degrade third harmonic. Without explicitly knowing the phaserelationshipbetweenthetwothirdharmonicsignals,wecanonlyapplyapowersummation, and doing so suggests that the third harmonic amplitude willincrease by 1 dB to −63.3 dB, or in the worst case scenario when the twosignalsareperfectlyinphaseby3.6 dBto60.7 dB.Shorter’sn2/4weightingsuggeststhatthesubjectiveeffectofthirdharmonicdistortionis3.25 dBworsethan its raw amplitude would suggest, so wemight be really ungenerous andconsiderthenewthirdharmonicdistortiontobeat−57 dB.However,thisstillmeansthatdistortionisdominatedbysecondharmonicat−45 dB.To summarise, there is no logical argument whatsoever for rejecting theapplication of a 14 dB global negative feedback, and ifmore open-loop gaincouldbefoundwithoutcompromisingHighFrequencyphaseresponse,yetmoredistortion-reducingglobalnegativefeedbackwouldbeevenbetter.

ObtainingmorethanSingleDigitOutputPowerBearing inmind thatwhilst increasingvolumeby3 dB isnoticeable, it isnotsignificant,merelydoublingoutputpowerisnotenough.Thetraditionalmethodofsignificantlyincreasingpowerwastouseapush–pullpairofMullardEL34orGEC KT88. Once push–pull has been chosen, pure Class A is no longerenforced,andClassABcanbeused;usingthesetechniques,wecanobtain50WfromapairofMullardEL34orGECKT66,and100 WfromapairofGECKT88[15].Afterthis,weresorttotransmittervalvesatamuchhighercostperwatt.Transmittervalveshaveanumberofdisadvantages:•Theyareinvariablydisproportionatelyexpensive.•Theytendtoneedhigherimpedanceanodeloads–makingthedesignofagoodoutputtransformermoredifficult.• They have savage drive requirements – often needing a power valve asdriver.•TheyusehighHTvoltages–sothesmoothingcapacitorsareexpensive,andtheHTsupplyisamajorsafetyhazard.•SmoothingathighHTvoltagestendstoenforcehighL/Cratios,makingitincreasinglydifficulttopreventsubsonicringinginthepowersupply.

However,therearewaysofavoidingtheseproblems.

Sex,LiesandOutputPower

Inthelate1960sandearly1970s,somequiteunpleasantaudioamplifiersweremade using transistors . Compared to the valve behemoths, these transistoramplifierswereverysmallandlight,buttheydidn'tactuallysoundanybetter(infact,mostsoundedagooddealworse),sosomethingwasneededtomakethemsell.Theonethingthatevenearlytransistoramplifierscoulddowastoprovideplentyofpowerintoaresistiveload,andthusthepowerratingwarstarted.Tomakeatrulypowerfulamplifier,alargepowersupplyisneeded,butthisisexpensive.Now (classical)music generallyonlyhas short durationpeaks, andnobodylistenedtoanythingelse(oratleast,nobodywhoseopinionsweretakenseriously at the time), so amplifiers were designed that could manage higheroutputpowers,butonlyforaveryshorttime.Thisallowedpowerratingstobeincreased further, and the ‘music power’ rating was born. We measure themaximumoutputpowerat10%distortion,ortheonsetofclipping(thepointat

whichasinewavebegins tohave itspeaksclippedoff),withburstsof1 kHzdriving one channel only into a resistive load. By this means, it is perfectlypossible to convert a 20 Wamplifierwith a poor power supply into a 50 Wmodel,andifwenowdoubletheoutputtoaccountfortwochannels,wehavea100 Wamplifier.At least four fallacies were used in the previous argument, but they were asnothing compared to the outrageous power claims made for many computerloudspeakersystems.Oneexamplehavingawooferboxthesizeofalargeloafof bread and a pair of small loaf satellites claimed a power rating of 800 WPMPO and all for £23! (PMPO=Peak Music Power Output, or in this case,PurelyMythicalPowerOutput.)

LoudspeakerEfficiencyandPowerCompression

We can make more efficient loudspeakers. This is the best solution, sinceinefficient loudspeakers invariably suffer from power compression, an effectwhereby the resistance of the voice coil rises due to temperature, and reducessensitivityuntilthecoilhascooleddown.Unfortunately, making an efficient loudspeaker that is uncoloured is difficult,andthelazywaytoreducecolourationistoaddacoatofvisco-elasticdampingmaterial to the moving diaphragm. Unfortunately, the damping materialinvariablyaddssignificantmass,reducingefficiency.Theworstexamplesofthisapproachoccurredduringthe1970swhentheplasticBextrenewaspreferredasacone material over paper because of its ease of moulding and comparativeconsistency, but damping the Bextrene quack to acceptable levels required aheavycoatingofaqueouspolyvinylacetate,resultinginstaggeringlyinefficientloudspeakers.However,themostcriminallyeffectivewayofdiscardingloudspeakerefficiencyistomakeloudspeakerssmall.Let’sbeclearaboutthis:‘small’inaloudspeakercontext means ‘smaller than a domestic washing machine.’ Anything smallersuffers not just because acceptable bass can only be obtained by deliberatelyaddingmass to the cone (drastically reducing efficiency) but also because thebox’s small baffle area typically requires an extra 2 dB of baffle stepcompensation that subtracts directly from efficiency. 2 dB might not soundmuchbutit’sthedifferencebetween10 Wand16 W,andthatcosts.

ActiveCrossoversandZobelNetworks

Wecandrivetheloudspeakersmoreeffectively.Ifeachdriveunitisdrivenbyadedicatedamplifierprecededbyanactivecrossover,manybenefitsresult[16].

Producing loudbassmeansmovinga largevolumeofair, soweeitherhavealargeareacone(whichrequiresalargebox),orweuseasmallconewithlargeexcursion,whichwastespowerbecausewiththenotableexceptionofATC(whouseunderhungvoicecoilswithalonggap),thisforcesthevoicecoiltobemanytimesthelengthofthegap.ClassDswitchingamplifiersnowoffer200 WfromanamplifiermodulesmallerthanapairofboxedEL34s,andalthoughtheyareimproving all the time, their fundamental mode of operationmeans that theirweaknessesmustshowupathighfrequencies,sowhilsttheyareidealforthoselowefficiencybassboxesonlyaveryfewareacceptablefullrange.Conversely,valvepoweratlowfrequenciesrequiresanoutputtransformerwithalargeexpensivecore,sovalvesexcelatmidrangeandtreble.Theenforcedlowmass of midrange and treble drivers and the recent availability of powerfulneodymiummagnetsmakeshighefficiencyeasilyattainable,ideallymatchingasmallvalveamplifier.Takingthetwoprecedingargumentstogether,itnowmakesagreatdealofsenseto design an active loudspeaker system using a 200 W switching amplifierdrivingaprofessional≥15″driverchosenforitsefficiencyandtameconebreak-up,anda20 Wvalveamplifierabove250 Hzdrivingahighefficiency4–6″driveraugmentedbyaribbontweeterabove5 kHzviaapassivecrossover.Almost all moving-coil loudspeakers have significant self-inductance, so theirdedicated amplifier sees a rising impedance which can compromise HighFrequency stability. Additionally, beam tetrodes and pentodes produce higheramplitudehigherharmonicsintheirdistortionspectrumasloadresistancerises–so correcting voice coil inductance to the optimum impedance loadwould beworthwhile.Fortunately,asimplemoving-coilloudspeakeriseasilycorrectedbyaddingaZobelnetworkdirectlyacrossitsterminals(seeFigure6.31).

Figure6.31Zobelnetworkforcancellingvoicecoilinductance.

Intheory,theZobelresistorisequaltotheDCresistanceoftheloudspeaker,and

thecapacitorvalueisfoundusing:

Inpractice,becausetheloudspeakercanbeconsideredtobeatransformerwithitsvoicecoil looselycoupledtotheshortedturnofthepolepieceswhichhavehysteresislosses,thesimplemodelofpureinductanceinserieswithresistanceissomewhat inaccurate, and the requiredZobel resistance is typically 1.2RDC .Given that the voice coil inductance may not be known, the best way todetermineZobelvaluesistomakeonewithresistanceinitiallysetto1.2RDC,adjust the capacitor value to give minimum change in meter reading asfrequency issweptacross theaudioband, thenfine-tune resistance (seeFigure6.32).

Figure6.32TestcircuitfordeterminingZobelvalues.

Fortunately, values are not critical and the author simply selects E24 resistorvalues fromhis stock rather than finely adjusting a precision variable resistor.Likewise, the required capacitor value can easily bemade up if a few valuesbetween0.47 μFand4.7 μFareavailable.Havingdoneso,theimprovementisquiteremarkable(seeFigure6.33).

Figure6.33ImpedanceagainstfrequencywithandwithoutZobelnetwork.

ParallelOutputValvesandTransformerDesign

Thisisacrackingsolution,andgivesmanyadvantages.Ifweusemultiplepairsof parallel output valves, we can keep theHT voltagewithin reasonably safebounds,perhapsevenat320 V,ifwearepreparedtousemanypairsofvalves.Witheachadditionalpairofvalves,thetransformerprimaryimpedancefalls,asdoes the turns ratio, making it easier to design a good quality component.Statistically,totalanodecurrentpersidebecomesbetterbalancedasweincreasethenumberofvalves,anddeliberateselectionwillimprovethisstillfurther.

DrivingHigherPowerOutputStagesWhethertheyarecomposedofparalleleddevicesornot,higherpoweredoutputstages always require more of the driver circuitry.When we investigated theWilliamsonamplifier,wefoundthatithadadedicateddriverstage,butthelargenumberofstagesmadestabilityaproblem.Clearly,abetterapproachisneeded.Asbefore,listingtherequirementshelpssolvetheproblem:•Weneedlowoutputresistancetodrivetheincreasedinputcapacitanceoftheoutputvalves,andacathodefollowermaybeneeded.• We need to provide a large output voltage with low distortion; thisinvariablydemandssomeformofdifferentialpair.•Widebandwidthandhighgainarealsodesirable,becausewewouldliketohaveonlyone setofcouplingcapacitors toensureLowFrequencystability,andthecascodemightbeideal,althoughacarefullydesignedcascadeofDC-coupleddifferentialpairscouldbeevenbetter.

Wewillfirst investigateacascodedifferentialpairwithdirectcoupledcathodefollowers, sometimes known as the Hedge [17] circuit, after its designer(although the original Hedge circuit did not include cathode followers) (seeFigure6.34).

Figure6.34Hedgecascodedifferentialpairplusdirectcoupledcathodefollowers.

Designof the individualpartsof thiscircuitwascovered inChapter2 , soweneed not go into great detail on this circuit other than to make a fewobservations.A single differential pair is not the ideal phase splitter, sowemust take extracareoverthistoobtainagoodresult.Theanodeloadresistorsshouldbeaged,matchedandgenerouslyratedtoavoiddrift.Theconstantcurrentsinkshouldbemadetohaveashighanoutputresistanceaspossible,andstraycapacitancetogroundfromthecathodeshouldbeminimisedtomaintainahighimpedanceathighfrequency.Matchingthevalveswouldbeusefulifpossible.Eachpairofvalvesrequiresaseparateheatersupply.Sad,buttrue.Thecathodefollowers need ≈200 V superimposed on their heaters, the upper pair of thecascode need ≈100 V, and the lower pair 0 V. Flirting with this rule willgenerateproblems related toheater cathode insulationbreakdown/leakage, andemission from the heater to the cathode will be summed with the intentionalcathodecurrent.Youhavebeenwarned!

Aswasmentionedbefore,theonlyreallysatisfactoryvalveforuseasthelowervalveinacascodeistheE88CC;anyothertypewastesHT.Thecathodevoltageon the lower valves is usually quite low, ≈2.5 V, and because phase splittersinevitablyhavehalftheinputsignalvoltageonthecathode,thetailofthesinkneedstobetakentoasubsidiarynegativesupply.Feedbackfromtheoutputcanbeappliedtoagrid,whichmakesthecalculationsoffeedbacknetworkmucheasier,orthestagecouldacceptabalancedinput.

TheCrystalPalaceAmplifierAswith the ScrapboxChallenge amplifier, the design of any power amplifierbeginsattheoutput.Onceallofthesoft-startandgeneralsafetyconsiderationshavebeentakenintoaccount,thecostofanamplifiersupplyisproportionaltothe square of its HT supply voltage. Thus, reducing the HT voltage releasesmoney that can be spent elsewhere to achieve a better overall set ofcompromises.PossiblecontendersfortheoutputstageareshowninTable6.6.

Table6.6ComparisonofPossibleOutputValves

NotethatthevaluesinthistableapplytoNOSvalves,andmaynotbeapplicabletorecentlymanufacturedvalves.aManufacturer’sclaimedvalue.bValuederivedfrommanufacturer’sdatasheet.cValuemeasuredbyauthor.

845 813 4×EL34 13E1Pa(max) 100 W 100 W 100 W 90 WPg2(max) – 22 W 32 W 10 WIk(max) 120 mA 180 mA 600 mA 800 mAVa(max) 1,250 V 2,250 V 800 V 800 VVg2(max) – 1,100 V 500 V 300 V

μ 5.3a 8.5a 10.5a 4.5a

gm 3.4 mA/Va 4 mA/Vb 46 mA/Va 35 mA/Vb

ra 1.6 kΩb 2.1 kΩb 230 Ωa 130 Ωa

Vh 10 V 10 V 6.3 V 26 VPh 32.5 W 50 W 37.8 W 33.8 WCag 12.1 pFa 17 pFc 44 pFc 40 pFc

CMiller 76 pF 162 pF 500 pF 220 pF

Of these valves, the 845 is a true triode, the 813 is a triode-strapped beamtetrode, the quartet of EL34s is a triode-strapped pentode, and the triode-strappedbeamtetrode13E1actuallycontainsaduetofparalleledvalves.EventhoughtheAEIdatasheetspecifiesPa(max)=95 Wfora triode-strapped13E1, all the options offer P a(max) ≈100 W, so they could all achieveapproximately the same output power.NOS 845 are extremely expensive, butmodernproduction isavailable.NOS813are readilyavailable,but require thesame expensive HT as the 845 (≈1,000 V). Sadly, the 13E1 is often moreexpensivethanaquartetofEL34.Nevertheless,whentheauthorsawa13E1,itwaslustatfirstsight.Youwillprobablybemorerational,andoptforaquartetofEL34.

13E1Conditions

Push–pull output stages can be analysed using composite curves [18] .Compositecurvesareobtainedbyplacingasecondsetofcurvesback tobackbelow the first. Fictitious lines are then drawn between opposite true anodecurves,andthesearedeemedtobethecompositeanodecurves(seeFigure6.35).

Figure6.35Compositeanodecurvesforpush–pullstage.

TheoperatingpointiswherethecompositelinefromVgk=−60 VofV1toVgk=−60 VofV2passesthroughIa=0atVa=250 V.Formaximumpoweroutput,RL=2ra,andthisloadlinecanbedrawnbymirroringthecompositeVgk=−60Vlineaboutaverticallinepassingthroughtheoperatingpoint.Inthisparticularinstance,RL=277 Ω,and thepredictedpoweroutput is42 W.Note that thisparticularoperatingpoint impliesClassABoperation, sinceV a=250 V,V gk=−60 VimpliesIa=49 mA.QuiteapartfromanyreservationswemighthaveaboutClassAB, the extremely steep loadlineproducedby thismethodgreatlyincreases odd harmonic distortion. Although composite curves are a usefultheoreticalconcept,anddemonstratethedifferencebetweenClassAandClassB

veryclearly,theyimplyidealvalvesandarequitefiddlytoproduceandadjust,evenonacomputer.We will find that it is much easier to analyse one half of the output stage,treatingitasasingle-endedstage.Oncewehavediscoveredtheoptimumsingle-endedloadline,wesimplyconvertthatintothepush–pullrequirement.Intheory,welosesomeaccuracybynotusingcompositecurves,butprecise loadlines inpower stages are futile because loudspeakers are not pure resistances, so thesavingindrawingeffortiswellworthwhile.Because this is an output stage, andwewant to extractmaximum power, wemustoperate thevalveatPa(max)=95 W.Ingeneral,whenshufflingloadlinesand operating points for a given valve, we will find that output power isproportional to anode voltage, whilst distortion is inversely proportional. Butcostriseswiththesquareofanodevoltage,sowewillsetVa=400 V.SincePa(max)=95 WandVa=400 V,wecanuseP=IV tocalculate thatIa=237.5mA,andplotthispoint(seeFigure6.36).

Figure6.36Settingthe13E1operatingpoints.

Thereisananodecurveneartoouroperatingpoint,sowecanfindra.Inthisinstance,wefindthatra=282 Ω.(Weshouldnotworrythatthisissignificantlypoorerthanthemanufacturer’sclaimedvalueof130 Ω–theytypicallymeasureatVgk=0,Ia=Ia(max)).Traditionally,wesetRL=2raformaximumpower,sothe author tried this loadline.After extrapolating the curves (plausiblymakingthemup),the564 Ωloadlineoffered14 Wfromthevalve.SincePa=95 W,

thisdidn’tseemtoopromising,butagentlerloadlineof625 Ωpredicted20 Wwithlowerdistortionatthesamedissipation,soapush–pullpairshouldprovide40 W.Inapush–pullClassBamplifier,eachoutputvalvemustseealoadof625 Ω,soeachhalfofthetransformeriswoundwiththecorrectnumberofturnstoreflectthis load. However, push–pull transformers invariably specify the load fromanode to anode.Since reflected impedances change by the square of the turnsratio,doublingthenumberofturnsquadruplestheimpedance.Thus,ouroutputtransformerwouldmeasure4×625 Ω=2.5 kΩfromanode toanode.However,inClassA,bothvalvescontribute to loadcurrentatall times,so thecurrent isdoubled,requiringahalvingofloadresistancefromanodetoanode,resultingina theoretical optimum load of 1.25 kΩ from anode to anode for the ClassApush–pull pair of 13E1s. Measurement showed that maximum power wasobtainedwhenthedummyloadwassetto5 Ω(whichcorrespondedto1,124 Ωanodetoanodeoncewiringresistancessuchastransformerwindingsweretakenintoaccount)(seeFigure6.37).

Figure6.37MeasuredCrystalPalaceoutputpoweragainstloadresistance.

Ascanbeseen,powerfallsrapidlybelowtheoptimumloadresistancebutmuchslowlyabove,andthis iswhyit isbetter tobepessimisticaboutexpectedloadresistance.Theauthor’sCrystalPalacewasconceivedandbuilttodriveJordanJX92Shavinganaverageimpedanceabove200 Hzof5.1 ΩoncecorrectedbyaZobelnetwork,soitisperfectlymatched,butyoumightnotwishtosailquitesoclosetothewind.

Eagle-eyedreaderswillnotethatVg2(max)=300 V,butthatthefinaldesignsetsVg2=400 V.StrappingpentodesandtetrodesastriodesandthenexceedingtheirVg2(max)ratinghasbeendonebefore,mostnotablybyLangford-Smith,usingapairoftriode-strapped807sat400 V(Vg2(max)=300 V)toreplaceKT66inaWilliamsonamplifier.Moresignificantly,Philips[19]gaveperformancedatafora triode-strapped QE 05/40 beam tetrode audio amplifier operating at 400 VdespitethefactthattheyquotedVg2(max)=250 Vforthesamevalveusedasabeamtetrodeinanaudioamplifier.Nevertheless, the author still has misgivings about the long-term effects ofexceedingVg2(max)ratings,sotheemphasisinthisdesignisondesigningdrivercircuitryofirreproachableperformancethatcoulddriveanyofthevalveslistedinthetable.

DriverRequirements

The stipulation ‘irreproachable performance’ is very vague, and needs to beconvertedintoengineeringrequirementsthatcanleadtoengineeringsolutions:(1)Minimalmeasureddistortion(2)Distortiontobecomposedofloworderharmonics(3)Push–pulloutputwithgoodbalance(4)Largeundistortedvoltageswing(5)Sufficientgaintoenableglobalnegativefeedbackifrequired(6)LowDCoutputresistancetoavoidproblemswithDCgridcurrent(7)LowACoutputresistancetodriveloadcapacitance(8)Toleranceofoutputstageconductionanglechangesfrom360°to0°(9)Instantaneousrecoveryevenaftergrossoverload.

FindingaTopologythatSatisfiestheDriverRequirements

(1)MinimalMeasuredDistortionThis requirement implies nearly horizontal loadlines. A horizontal loadlineimpliesanactiveload,butlargeresistiveloadsrequiringahigherHTvoltagearealsoapossibility.(2)DistortiontobeComposedofLowOrderHarmonics

This requirement implies triodes rather thanpentodes.Takingrequirements (1)and (2) into account simultaneously suggests that triodes from the SN7/N7familywouldbeideal.(3)Push–pullOutputwithGoodBalanceThisrequirementisbestsolvedbytwocascadeddifferentialpairswithconstantcurrent sink tails. Since triodes produce predominantly second harmonicdistortion,whichthedifferentialpaircancels, thissatisfiesrequirement(1),butreinforces thepreference for theSN7/N7familybecausevalvesproducing lowthird harmonic distortion are now needed due to odd harmonics summingconstructivelyinadifferentialpair.(4)LargeUndistortedVoltageSwingOneofthestrengthsofthedifferentialpairisitslinearitywhenswinginglargevoltages. Nevertheless, the more HT voltage available the better, so thisrequirement implies that the driver stage should have HT>400 V. Since theoutputstage is likely touse≈400 V, this implies that thedriverstageneedsadedicatedHTsupply.(5)SufficientGaintoEnableGlobalNegativeFeedbackifRequiredThisrequirementcanprobablybesatisfiedbytwocascadedSN7/N7differentialpairs. If necessary, the gain could be doubled by using a high- μ valve dualtriodesuchas6SL7,7F7,ECC83orECC808in the inputdifferentialpair,butthiswouldprobablyincreasedistortionbecausethehigh-μvalvestendtoneed400 VHT,whichmightnotbeavailable.(6)LowDCOutputResistancetoAvoidProblemswithDCGridCurrentMostofthelargerpowervalvespasssignificantgridcurrentevenwhenthegridis negative, which is why manufacturers’ data sheets recommend such lowmaximumvaluesfortheirgrid-leakresistors.Yetasmallgrid-leakresistorisanunnecessarilyharshloadfortheprecedingstage.SatisfyingthisrequirementdemandsthatthedriversbeDCcoupledtotheoutputvalve grids. Output stage HT is used most efficiently if the cathodes of theoutputvalvesareat0 VbecausethismeansthatVHT≈Va .Therefore,Vaofthedriverstagemustbenegativetobiastheoutputvalvescorrectly.TheanodesofthedriverdifferentialpaircanonlybeatanegativevoltageifthetailofthedifferentialpairisreturnedtoasubstantialnegativeHTsupply,perhaps–300 V.IfthedriverstageusestheoutputstagesupplyforitspositiveHT,itnowhasarail-to-railHTof700 V,whicheasilysatisfiesrequirements(4)and(1).(7)LowACOutputResistancetoDriveLoadCapacitance

(7)LowACOutputResistancetoDriveLoadCapacitanceAlthoughtheSN7/N7familyproduceslowdistortion,raisnotparticularlylow,andfailsthisrequirement.Valvessuchasthe6BX7and6BL7havelowerra ,but their distortion tends to be very variable, and their Miller capacitance ispunitive. Adding cathode followers to the outputs of the differential pairdivorces the responsibilities for low distortion and low output resistance,allowing the differential pair to be optimised for linearity and swing, and thecathodefollowersforcurrentdrivingability.(8)ToleranceofOutputStageConductionAngleChangesfrom360°to0°There is more to meeting this requirement than first appears. When weinvestigated phase splitters,we found that all phase splitterswere sensitive totheir loading, requiring Class A loads. The requirement for cathode followershasnowbeenreinforced,sincetheirbufferingactionallowsthetwo-stagephasesplittertooperateundisturbedbyarbitraryoutputstageconductionangles.TheauthorconsidersthatattemptingtodriveanoutputstagecleanlyintoClassAB2 isnotworth the candle, so the cathode followerswill bebiassedonly sothat theycandrive theoutput stageMillercapacitancecleanly,andnoexplicitattempt to drive grid current will be made. To maximise output swing, thecathodefollowersarelikelytobeoperatedwiththeircathodesathalftherail-to-railHTvoltage,soVa=350 V.Ifwedonotattempttodrivegridcurrent,Ia=7mA is adequate, resulting inP a =2.5 W, which is just within range of theSN7/N7family(seeAppendix).(9)InstantaneousRecoveryEvenAfterGrossOverloadThis requirement means that the amplifier must not suffer from blocking.Therefore, the coupling capacitorsmust bepositioned so that they couple to astage that cannot be overloaded. By definition, the output stage can beoverloaded,butwehavealreadyspecifiedthatitmustbeDCcoupled.Thereisnoadvantageinplacingthecouplingcapacitorsbetweentheseconddifferentialpairandcathodefollowers,becausetheanodesofthedifferentialpairneedtobeatroughlythesamevoltageasthegridsofthecathodefollowersinordertotakeadvantage of the rail-to-railHT voltage. The correct position for the couplingcapacitorsisbetweenthetwodifferentialpairs.Anearlyiterationofthedrivercircuitryachieved0.03%THD+Njustbelowthepointwhereoutputstagegridcurrentimposedcatastrophicloading.Theauthorissimultaneouslyembarrassedandproudtoreport thatmeasuringitsdistortionwhilst itcleanlyswungadifferentialvoltageof+47 dBu(177 VRMS) intoa100 kΩloadbrieflygaveafigureof0.11%THD+NbeforehisMJS401Daudio

testsetbrieflyflashed‘LEVELHIGH’anddied.Moral:Don’tgetcarriedawayandabuseyourtestequipment.Inamorecarefulgrid current test on the author’s ‘Plug and Pray’ test mule, identical drivercircuitryonlyexceeded0.2%distortionwhena2A3gridgoingupto+57 Vmetitsanodecomingdownto+57 Vandconductedhard,clippingthedriver.Summarising the outcomes of the requirements, we need a cascade ofdifferential pairs separated by coupling capacitors, using valves from theSN7/N7family,andpoweredbyasplit-railHTsupply.Theoutputofthedriverdifferential pair will be DC coupled to cathode followers, which will be DCcoupledtotheoutputstagegrids(seeFigure6.38).

Figure6.38Conceptualdiagramtoshowtopologyandpositionofcouplingcapacitors.

CircuitTopology:PowerSuppliesandTheirEffectonConstant

CurrentSinks

The SN7/N7 family of valves produces primarily second harmonic distortion,whichcanbecancelledinadifferentialpairifnosignalcurrentislostinthetail.Thus,weneedactive tails forbothdifferentialpairs,butbecause thegridsarecapacitorcoupled from theprevious stage, theirgridsare returned to the samesupply as the constant current sink, V k must be low, so these must besemiconductorconstantcurrentsinks.Theseconddifferentialpairislikelytohave≥500 VofHTvoltage,soVgk islikely to be ≈−10 V, which allows sufficient voltage for a cascode constant

current sink to operate without an additional supply, especially when weconsider that theinputsignal isalreadydifferential,sowedonotneedtocopewithaudioatthecathodes.Sadly,thefirststageislikelytohavequitealowHTvoltage,reducingVgk,andif the input signal is unbalanced, half its amplitudemust be on the cathodes,furtherreducingvoltageavailabletotheCCS.Thus,acascodeCCSwouldneeda subsidiary supply, but the 334Z IC constant current sink can cope without.Just.However, the 334Z has an absolutemaximum current rating of 10 mA,whereaswe candesign a cascodeCCS to pass any currentwe like.Thus, ourchoiceofvalveoperatingpointshasalreadybeenrestricted.

Va(max)andthePositiveHTSupply

Wehaveelectedtodirectcouplethecathodefollowerstothegridsoftheoutputvalves, so their cathodes will be at ≈−82 V, depending on individual outputvalves.IftheanodesofthecathodefollowersareconnectedtotheoutputstageHT,Vak=482 V,whichwecannotallow.(EvenfortheGTAorGTBversionsofthe*SN7,Va(max)=450 V.)However,thisproblemisnotasbadasitsounds,becausewe do not need the cathode follower to swing 482 V pk , sowe canlowerourpositivesupplyto160 V,whichreducesVakto≈250 V,allowinganyvalvefromtheSN7/N7familytobeused.Next,wemustconsidertheDCbiassingoftheoutputstage.Thehighgmofourchosenoutputstage(whether13E1,oraquartetofEL34s)meansthattheoutputstagecurrentisextremelysensitivetochangesinVgk,and30 mA/Visaveryhigh mutual conductance in valve terms, so we cannot permit the grid biasvoltage to drift. Because the driver circuitry is DC coupled from the outputvalves to the anodes of the second differential pair, a change in itsV a couldpotentially damage the output valves since (by definition) they operate at ≈Pa(max).ACconsiderationsdictatethatthedifferentialpairsrequireconstantcurrentsinktails.Oncethedriverdifferentialpairhasanodeloadsmadeof(constantvalue)resistors,Ohm’slawensuresthatunchangingVacanbeachievedbyregulatingthe160 VpositiveHTsupply.Ourdesignhasnowevolvedtothepointwhereitrequires an HT regulator to work safely. Drawn in full on a circuit diagram,regulatorsareintimidating,butonlyavalveregulatorismoreexpensivethanadecentHTcapacitorandseriesresistor.

SymmetryandtheNegativeHTSupply

SymmetryandtheNegativeHTSupply

Because cathode followers operate under 100% negative feedback, theycontribute very little distortion compared to the second differential pair, butbecause they drop ≈8 V across V gk , they modify the anode voltage of thesecond differential pair from −82 V to −90 V. Since we require maximumlinear swing from the second differential pair, the negative HT should besymmetricallyoppositeitsanodevoltage,requiringanegativeHTof−90 Vto260 V=−350 V.ThenegativeHTvoltageisnotatallcriticalanddoesnotevenneedtoberegulatedbecausevariationssimplychangeVakwithoutaffectingIa.AlthoughtheprecisevoltageofthenegativeHTisnotcritical,itisessentialthatthissupplyisreliable.Failurewoulddrivetheoutputvalvegridspositiveandtheresulting anode dissipation would quickly destroy them. Thus, not needing aregulator for the negative HT has the bonus of improving reliability.Nevertheless,theoutputstageincludesanHTfuseforprotectionintheeventofnegativeHTfailure.

TheSecondDifferentialPairandOutputStageCurrent

NowthatwehavesomefirmHTvoltages,wecanbegindetailedaudiodesign,workingbackfromthecathodefollowerstowardstheinputstage.The SN7/N7 family offers optimum linearity when I a ≥8 mA. The voltageacrossRLforthecathodefolloweris−82 V–(−350 V)=268 V,soOhm’slawdictatesthata33 kΩ6 Wwirewoundresistordissipating2.2 WwouldachieveIa=8.1 mA.Furthermore, the 13E1 presents 220 pF ofMiller capacitance whichmust bedrivencleanly.At20 kHz,thereactanceof220 pFis36 kΩ.Atfullpower,theoutput stage demands 58 V RMS , and maintaining this voltage across thereactanceofthe220 pFcapacitancedemands1.6 mARMSor2.3 mApk.Thecapacitive load forces anode current to swing vertically ±2.3 mA on theloadline,whichrequiresgm tobeconstant.Fortunately,atIa=8.2 mA,gm isreasonablyconstant.Va=160 V–(–82 V)=242 V,andwealreadyknewIa,sowecandetermineVgk at these conditions. Referring to the curves,V a=242 V and I a=8.1 mAroughly intersects the V gk =−8 V curve. Knowing this voltage is importantbecauseitmeansthatwenowknowthatthegridvoltageis−82 V≈8 V≈90 V.The grids areDC coupled from the anodes of the second differential pair, sotheirrequiredanodevoltageisalso−90 V.

Fortheseconddifferentialpair,thevoltageacrossRLis160 V–(–90 V)=250V.Eachtriodeintheseconddifferentialpaircanpass<8 mAbecausemostofits distortion will be cancelled by push–pull action (this is not true for thecathodefollowerswhentheoutputstageentersClassAB).50 kΩMPC-5anodeloadresistorsareconvenient,sothecurrentrequiredtosetVato−90 Vis250V/50 kΩ=5 mA,sothetotaltailcurrentistwicethisat10 mA.The tail current is highly significant. Increased tail current causes increasedvoltage drop across the anode load resistors of the second differential pair,causingtheirabsolutevoltagetobecomemorenegative.Thecathodefollowersfaithfully follow this negative change, and so the grids of the output valvesbecome more negative, reducing their anode current. Thus, making the tailcurrentadjustableallowsustosetoutputstagecurrent.The output valves may not be perfectly matched, so interposing a variableresistorbetweenthecathodesoftheseconddifferentialpairallowsustoadjustthebalanceof thestage,andthereforeoutputstagecurrentbalance(seeFigure6.39).

Figure6.39SettingtheDCconditionsfortheamplifier.

WhyNotHaveTighterStabilisation?

SincewesawearlierthattheoutputstagewassensitivetochangesinVgk,andthatthisissetbytailcurrent,itseemsintuitivelyobvioustostabilisetailcurrent

astightlyaspossible.However,weshouldconsidertheeffectofanincreaseinmains voltage inmore detail.Whenmains voltage rises, the negativeHT railbecomes slightly more negative, and more current flows through the resistorchain supplying the reference LED, so the voltage across its slope resistancerisesslightly.ButVbeforthetransistorisunchanged,sothevoltageacrossthecurrent programming resistor rises identically, and tail current increases.Increasedtailcurrentreducesoutputstagecurrent,buttheriseinmainsvoltagecaused the (unregulated) HT to the output stage to rise, which would haveincreased current, so the two effects tend to oppose one another, which isdesirable.Thus,wediscoverthattightlystabilisingthetailcurrentandnegativeHTwould be counter-productive because itwould also require stabilisation ofthehigh-currentHTsupplytotheoutputstage.Asmainsvoltagevaries,itchangesnotonlytheHTvoltagebutalsotheheatervoltage.TheDCconditionsof thedifferentialpairsareforced tobecorrectbytheconstantcurrentsourcesandHTregulation,andthecathodefollowershaveplenty of feedback, but the output valves are sensitive to heater voltage.Fortunately,becausethe13E1heaterscanbeconfiguredtooperatefrom26 V,each pair of valves requires only 2.6 A, which can be regulated reasonablyefficiently.

TheFirstDifferentialPair,ItsHTSupply,andLinearity

Bycomparisonwiththeseconddifferentialpair, theconsiderationsinvolvedinthedesignofthedifferentialpairoftheinputstagearetrivial.Thestageonlyhasto furnish ≈3.3 V RMS from each output, so distortion really isn’t a problem.Nevertheless, theSN7/N7 family requiresV a≥150 V for reasonable linearityevenatverysmallvoltageswings,soa>300 VHTwouldbeideal.The second differential pair required a negative HT of −350 V, and if atraditional centre-tapped rectifier/transformer combinationwasused to providethis voltage, it could also provide the positive HT. As a further measure toprotect theoutputvalves,wecoulduseavalverectifier for thepositiveHT.Ifpowerwasbriefly interrupted to theamplifier, thevalverectifierwouldensurethatattheinstantofpowerreturning,theoutputvalveswouldinitiallybebiassedoff,butwouldgentlybeturnedonastherectifierwarmed.Unfortunately,valverectifiersdropmorevolts,sothepositiveHTislikelytobe≈300 V.AlthoughDCconditionsdonotrequiretheHTforthefirstdifferentialpairtoberegulated,itisprobablythebestwayofachievingasufficientlylowHTripple.Toensurethattheregulatordoesnotdropoutofregulationwhenmainsvoltagedrops,wecouldsetitsoutputto+270 V.

ThefirstdifferentialpairnowhasquitealowHTvoltage,andtheonlywaytomaintainlinearityandvoltageswingistoreduceIa.ReducingIaallowsVatoswingcloserto0 V,whichincreasesmaximumoutputswing,anddistortionisgenerally inversely proportional to maximum output swing. Slithering atransparent ruler over the anode characteristic curves resulted in an operatingpoint of V a =125 V and I a =2.9 mA for each valve, using a 50 kΩ loadresistor.

ValveMatching

2.9 mApertriodeiswellbelowtheideal8 mA,butthedifferentialpaircancelsthepredominantsecondharmonicdistortion,andthevoltageswingisverylow,so this is tolerable,but the requireddistortioncancellationwouldbenefit frommatchedvalvesinthedifferentialpair.AlthoughtheLoctal7N7/14N7valvestendtobequitewellmatched,individualtriodes such as the 6J5GT allow even better matching. If we decided tostandardise on single triodes, we would need twelve 6J5GTs for a stereoamplifier.Theadvantageofneedingsomanyvalvesofagiventypeisthat theprobabilityof findingmatchedpairs increasessubstantiallywith thenumberofvalves,sobuyingtherequireddozenvalvesoffersafarbetterchanceoffindingmatched pairs than buying two. Itwas the decision to use a dozen 6J5GTsofcomplementary appearance to the 13E1 output valves that prompted the name‘CrystalPalace’forthisamplifier.Ingeneral,whentwoapparentlyidenticalvalveshavethesameanodevoltagesin a differential pair, their gain is likely to bematched under those operatingconditions. Thus, we can test 6J5GTs in the amplifier by inserting a valvedeemed to be the reference valve in one side of the differential pair, andsequentially test all the other valves against this reference. The valves withclosestanodevoltagesareinpairs.

TheEssentialTwiddlyBits

We have made the broad brushstrokes, and chosen our stage topology, valvetype,anodecurrentsandloadresistances.Itisnowtimetogetdowntothenitty-grittyandensurethatthoseconditionsaremet.Forthisweneedto:•settheDCconditionsofeachstagebydesigningtheirconstantcurrentsinks;•considerthermalstabilityoftheconstantcurrentsinks;• considerRF stabilityby includinggrid-stopper resistors andbypassing the

HTsuppliescorrectly;•designtheHTregulators.

TheCascodeConstantCurrentSinkandStabilisationAgainst

MainsVariation

WeknowthatVgk≈−10 Vfortheseconddifferentialpair,soweshouldbeableto design a cascode that operates at this voltage, thus avoiding a subsidiarysupply.For reasons thatwill become apparent in amoment,we need a low referencevoltage,sowewilluseaninfraredLED,whichwewillbiasfromthe0 Vrailviaalargeresistor.Becausetheresistorhas≈350 Vacrossit, itcanonlypassquiteasmallcurrenttokeepwithinitspowerrating.Ifwechoosea150 kΩ3Wresistor,itwillpass2.3 mAwhilstdissipating0.83 W.2.3 mAwouldnotnormallybeconsideredtobeanidealreferencecurrentforanIRLEDbecauserinternalrisessignificantlyatlowercurrents(16.4 Ωat2.3 mA,asopposedto5.4Ω at 10 mA). However, because the slope resistance helps compensate formainsvoltagevariations,thisisn’taproblem.To consider the effect ofmains variation,wewill assume a 1% rise inmainsvoltage.Intheoutputstage,wewanttoholdIaconstantdespitechangingVa,andfindtheVgkthatwouldopposethischange.Thisiseffectivelythedefinitionofμ.SincetheoutputstageHT=400 V,1%riseimplies+4 V.Forthe13E1,μ≈3.9,soVgkmustfallby≈1 Vtocombattheanodechange.1 V fall at an anode of the second differential pair would be caused by anincreaseinindividualanodecurrentof

Buttherearetwovalves,sothetailcurrentmustincreasebytwicethis,thatis40μA.Forour infraredLEDV ref.=1.10 Vat2.33 mA,so thecurrentprogrammingresistorintheemittercircuitofthecascodemustbe

Achangeof 40 μA in the40 Ωprogramming resistorwouldbe causedby achangeinvoltageofV=IR=40 μA×40 Ω=1.6 mV.

Assumingconstantbase–emittervoltage,V ref.mustriseby1.6 mVtocombatthechangeinoutputstagecurrent.The 150 kΩ resistor passes 1% more current due to the 1% rise in mainsvoltage.Itnormallypasses2.33r mA,sotheincreaseincurrentis23.33r μA.Wenowknowthechangeincurrentandchangeinvoltageacrossanunknownresistance,sowecanfinditsvalue:

TheIRLEDpasses2.33 mA,andcontributesrslope=16.4 Ω,soweneed68.6–16.4=52 Ω.But52 Ωdrops121 mVat2.33 mA,soVref.risesto1.10 V+0.121 V=1.22V.Therefore, thevoltageacross theprogramming resistorbecomes521 mV,andsinceitmustpass10 mA,itsrequiredresistancechangesfrom40 Ωto52 Ω(seeFigure6.40).

Figure6.40Biassingtheseconddifferentialpair

As can be seen, the values of the programming and compensating resistorsinteract, so we will need to use variable resistors and adjust them on test asfollows:(1)Setthecompensatingresistortoitsmaximumvalue,settheprogramming

resistortoitsminimumvalue(2)Adjusttheprogrammingresistorforcorrectoutputstagecurrent(3)Usingavariac,raisemainsvoltageby5%(4)Adjustthecompensatingresistortorestorecorrectoutputstagecurrent(5)Restorecorrectmainsvoltage.

Repeatsteps(2)–(5)untiltheoutputstagecurrentvariationwithmainsvoltageisminimised.Thetransistorsdonotneedtowithstandlargevoltages,soBC549Cisideal.Weknowthatweneedtobeabletoadjusttherelativevoltagesonthegridsofthe output valves to equalise individual anode currents, so a variable resistorbetweenthecathodesoftheseconddifferentialpairallowsthisvariation.Ifweusea200 Ωvariableresistorandnotionallymovethewipertooneextremeend,theresistorwillpassthecurrentofonlyone6J5GT,whichis≈5 mA,soitwilldrop≈1 V.Thegainofthedifferentialpairis≈18,sotherewillbeagrid-to-gridchangeof≈18 Vattheoutputvalves.Becausethewipercouldbemovedtotheoppositeendoftheresistor,wecouldachievethesamevoltagechangebutintheoppositedirection.Thus,eachvalvecaneffectivelyhaveitsVgkvaried±18 V,which isquitesufficient toachieveanodecurrentbalance. (Asoriginallybuilt,theauthoruseda100 Ωvariableresistortobalanceoutputstageanodecurrentbutthisdidnotalwaysprovidesufficientvariation.)Thecollectorofthelowertransistorhardlyhastochangevoltage,soVCE=2 Visperfectlysatisfactoryforthistransistorat10 mA.Becausethecollectorofthelowertransistorisconnectedtotheemitteroftheuppertransistor,VCEisequalto the voltage between the two emitters. Because we drop 0.7 V across thebase–emitterjunctionofbothtransistors,VCEforthelowertransistorisequaltothevoltagebetweenthetwobases.Whenweputaresistorbetweenthebases,weknowthatitpassesthe2.33 mAsourcedviathe150 kΩresistor,soitsrequiredvalueis2 V/2.33 mA≈820 Ω.

The334ZConstantCurrentSinkandThermalStability

Referringtothedatasheet[20],thecurrentprogrammingresistorforthe334Zcanbecalculatedusing:

whereTistheabsolutetemperature.

Ifweassumeanambienttemperatureof300 K(27 °C),thissimplifiesto

Thus,toset5.8 mA,weneed≈12 Ωresistor.However,itwasworthseeingthefirstequationbecause it remindsus thatallelectronicsdriftswith temperature.The usual reason for drift is the temperature dependence of V be for silicontransistors,butthiscanusuallybecompensatedbyaddingasilicondiodeinthereference chain. The fundamental assumption is that the diode is at the sametemperature as the junction producing the error, so the compensating diodeshouldbegluedtotheoffendingdevicewithepoxyadhesive,andtheentiremassinsulatedfromconvectioncurrentsbyasmallexpandedpolystyreneshroud.Sure enough, the data sheet gives a circuit that compensates for thermal drift,and simply requires that the additional resistor is 10 times the programmingresistor(seeFigure6.41).

Figure6.41Compensatingthe334Zagainsttemperaturevariations.

Havingcompensatedthe(uncritical)334Z,weshouldconsidercompensatingthecascodeconstantcurrentsinkbecausethis iscritical.Thetraditionalmethodofcompensatingthecascodeaddsasilicondiodeinserieswiththereferencediodetocompensate for thechangingVbeof the lower transistor.Theassumption ismade that the referencediodehas zerodriftwith temperature, and this isverynearlytrueifa6.2 VZenerisused,butwehavechosentouseanLED.BecausetheforwarddropofanLEDfallswithincreasingtemperature,italreadytendstocompensatethetransistor,sonoextracomponentsarerequired.

HighFrequencyStability

High-gmvalvessuchasthe13E1arepronetoparasiticoscillation,butthiscanbepreventedby1 kΩgrid-stopperresistors.Becausecathodefollowersoperatewith 100%negative feedback and feed a capacitive load, there is a danger ofoscillation,sotheyneed10 kΩgrid-stoppers.Differentialpairsrarelyneedgrid-stoppers, but shorting a grid directly to ground is inviting RF oscillation (nodampingwhatsoever),so10 kΩgrid-stopperswerefittedtothefirstdifferentialpair.Adding10 kΩgrid-stoppers to theseconddifferentialpairwould reduce the f−3 dBpointduetoMillercapacitanceandsourceresistancefromanacceptable130 kHztoanunacceptable60 kHz,sogrid-stopperswereomitted.AnotherpossiblecauseofHighFrequencyoscillationisnon-zeropowersupplyimpedance.Tocounterthisproblem,theoutputofthe+160 Vregulatorshouldbe a star point, and the −350 VHT should also feed a star point.A 470 nFcapacitorcanthenbeconnectedbetweenthesestarpointstoensurestabilityoftheseconddifferentialpairanditsassociatedcathodefollowers.Similarly,a470nFcapacitorshouldbeconnectedfromthecentretapoftheoutputtransformertothejunctionofthe1 Ωcurrentsenseresistorsintheoutputstage,andanother470 nFcapacitorfromthestarpointofthe270 Vregulatortothebottomofthe1N4148diodeinthe334Zconstantcurrentsink.Finally,weneedaTHINGYtosetVhkappropriately.THINGYdesignhasbeencoveredpreviously,sowenowhaveourfinalaudiodesign(seeFigure6.42).

Figure6.42Finalaudiocircuitof‘CrystalPalace’poweramplifier.

HTRegulators

Theseconddifferentialpairrequiresa160 VregulatorfreefromDCdrift,andavariation of the Maida regulator was used. The first differential pair is notcritical, but there is no real reason to use an alternative, so another Maidaregulator is used. Supplying the 160 V regulator via the 270 V regulatorensures that the270 V regulatorpasses sufficient current tooperate correctly.Withtwocomponentchanges,thesamedesignisusedforboththe270 Vand160 Vsupplies(seeFigure6.43).

Figure6.43Regulatordesign.

StereoversusMass

TheauthorbeganthemetalworkandlayoutoftheCrystalPalaceamplifierasastereo amplifier before buying accurate scales. At over 90 lb, this is not anamplifierforthefaint-hearted.The reason for building the amplifier as a stereo amplifier is that the totallybalancedaudiotopologyrenderstheamplifierinsensitivetopowersupplynoise.Thereisthereforenoneedtohaveseparateleftandrightpowersupplies,andaconsiderable reduction in support circuitrycanbeachieved.Lastbutnot least,theauthorhadmanyofthepartstoachieveastereoamplifier,butapairofmonochassis would have doubled the metalwork and required the purchase of twolarge HT chokes. Youmight have a different opinion about the benefits of astereochassis.

PowerSupplyDesign

Havingdecidedonastereochassis,weneedanHTsupplycapableofsupplying1 Aat≈400 V.AquickcheckwithaspreadsheetrevealedthatachokeinputHTsupplywouldneeda2 H1.5 Achokeanda455 VRMSmainstransformer.Theauthortookonelookatthesizeofhis1 H1 Achoke,anddecidedthataneven larger choke was not acceptable. A capacitor input HT supply wastherefore necessary. 1,200 V soft recovery diodes are used for the bridge

rectifier. In order to protect the 13E1 output valves, the output stage’s HTtransformercanbeswitchedbyathermaldelayrelay.The13E1heatersrequire26 Vat2.6 Aperchannel,soa2 × 25 VRMS300VA toroid was chosen because a 160 VA transformer would have beenmarginal, and the300 VA transformercostnomore thana250 VA,yetwasslimenoughtofitinsidethe2″chassis.Theregulatorarrangementsarestandard,butthereservoircapacitorsaredeliberatelysmalltoreduceregulatordissipation.Traditional centre-tapped HT transformers are intended for use with valverectifiers,soonlyone-halfofthewindingisinuseatanyinstant.Ifwederiveapositiveandanegativesupply,bothwindingsareinusesimultaneously,sowemustbecarefulnottoexceedtheVArating.Thesimplestwaytoensurethisisto say that the sumof thepositiveandnegativecurrentsmustbe less than thewindingrating.Thus,ifweneed78 mAforthepositivesupplyand61 mAforthe negative, the total current is 139 mA, so a 150 mA 275 V–0–275 Vwindingisfine.Fortuitously,thesalvagedHTtransformeralsohadthebonusofapairof6.3 V4 Acentre-tappedwindingssuitableforthedrivervalves,EZ81rectifieranddelayrelay(seeFigure6.44).

Figure6.44MainPSUdesign.

Designer’sObservations

In one significant respect, this amplifier is even worse than the ScrapboxChallenge–itisfartooheavy.Theauthoraimstoavoidrepeatingthismistake.The other problem is sample variation between 13E1s. Given that it wasdesigned to be a power supply regulator valve, close tolerances were notnecessary,sowecan’treallycomplain.Thosetwoproblemsaside,theauthorisverypleasedwiththisamplifier,andespeciallywiththedriverphilosophy.

ExceedingVg2Overtheyears,theauthor’smisgivingsaboutexceedingVg2ratingshaveprovenwell-founded.Althoughsomevalveswerehappyat180 mA,othersneeded tobebackedoffto150 mA,andoneortwojustgothotunderthecollar,nomatterwhatcurrenttheypassed.

WecaneasilydropVg2to200 VDCbyinterposingalargeZenerdiodebetweenitandtheoutputtransformer,butalthoughthiswouldworkforsmallsignals,fullpowerwouldcauseg2toswitchoff.Thus,wewouldalsoneedtoattenuatetheaudiosignal fed tog2and thiswouldmeanchanging from triodeoperation tobeamtetrodeBlumleinconfigurationusing43%outputtransformertaps.Realistically,theauthorhastoconcedethatalthoughthe13E1isveryprettyandpermitsalowprimaryimpedanceoutputtransformer(ensuringexcellentoutputtransformer performance), it could be bettered. Keeping that excellent outputtransformerrequireshighgmintheoutputvalves,sowearebacktothechoicesfaced at the start of this design, and multiple pairs of EL34s are the bestsolution.

GM70

If multiple pairs of output valves are deemed unacceptable but high anodevoltages (and impedances) are acceptable, then the ColdWar GM70 125 WtriodeoperatedatVa=1,250 V,Ia=100 mAbecomesapossibility.Undertheseconditions,Vgk=−125 V,sothe90 VRMSdriverswingrequiredforclassAisalittle more than is comfortable from 6J5GT but well within the capability of6S4A(V a(maxDC)=550 V).Thus,6S4Acouldbe substituted for thecathodefollowers (10 mA each) and driver (6 mA each). Grid current is always aproblemwithtransmittervalves,buta6S4Acathodefolloweroughttobeabletoachieve a 500 Ωoutput resistance, so if 0.1%THDwas tolerateddue to gridcurrent,thenthiswouldbe100 mVRMSdevelopedacrossthesourceresistanceof 500 Ω, equating to a non-linear grid current of 200 μA – which isconsiderablymorethanthe4 μAspecifiedontheGM70datasheet,suggestingthatgridcurrentshouldnotbeaproblem.

MeasuringIkIt didn’t take many burnt knuckles before the author realised that pluggingDVMsinto4 mmsocketsdirectlyadjacenttohotoutputvalveswasadaftidea,sohesplashedoutontheluxuryofapostagestampDVMpervalve.SincetheirFSDis200 mV,the1 Ωcathoderesistorconvertedthemdirectlyinto200 mAmeters.Theyonlyneeded1 mAapiecesoeachobtaineditssupplyviaaresistorandZenerfromthenearby26 V13E1heatersupply.Althoughnotcheap,thiswasaveryworthwhilemodification.

GlobalNegativeFeedback

GlobalNegativeFeedback

As presented, the amplifier does not have global negative feedback. Thetraditionalwaytoapplyfeedbacktoadifferentialpairistolifttheunusedinputfromground and apply feedback to this point (transistor power amplifiers usethistechnique).Theauthortriedthisconfigurationforawhilebutitisnotideal.Thesensitivityoftheamplifierbeforefeedbackis400 mVRMS.Ifweapplied20 dBoffeedback,sensitivitywouldfallto4 VRMS ,buttherewouldstillbe400 mVRMSbetweenthetwogridsoftheinputdifferentialpair,sothefeedbacksignal must be 3.6 V RMS and it must be of the same polarity. Moresignificantly,wecouldobservethatthegridsaremovingupanddowninvoltagetogetherat≈4 VRMS ,withvery littlevoltage (400 mVRMS )between them.Moreformally,wewouldstatethatourfeedbackhasimposedalargecommon-modesignalonthegrids.Ifthegridshavealargecommon-modesignal,thenthecathodesmustbefollowingthissignal,andthisiswheretheproblemstarts.TheLM334Z only has 3.5 VDC across it, and drops out at 1.2 VDC , so it hasinsufficient voltage compliance to copewith a superimposed≈4 VRMSaudiosignal.Itisthissortofnastylittlehiddenproblemthatmakestheauthorsokeentousecascodeconstantsinkssuppliedfromanauxiliarynegativesupply–sucha supply gives the CCS enough voltage compliance to copewith a 4 V RMSsignalandhaveasubstantiallyunchangingoutputcapacitance(Ccb∝1/√Vcb).Fortunately,thereisawayaroundtheproblem,anditfittedanewrequirementratherneatly.Ratherthanapplyingseriesfeedback,wecanapplyshuntfeedbacktomakeaninvertingamplifier(seeFigure6.45).

Figure6.45ApplyingglobalnegativefeedbacktotheCrystalPalace.

Theeffectistomaketheinputgridavirtualearth,sowecannowapplyasmuchfeedbackastheoutputtransformerwillpermitwithoutdisturbingtheLM334Z.Thereisaslightdisadvantageinthattheamplifiernowinverts,butswappingthecolouroftheloudspeakerterminalsandreconnectingloudspeakerwiresishardlydifficult. However, we can now take a further step and apply two loops offeedback,onefromeachloudspeakerterminaltoeachgrid,togivetheamplifierabalancedinput.Thiswouldbeparticularlyhandyiftheamplifierneededtobedrivenfromadigitalcrossoverwithabalancedoutput(seeFigure6.46).

Figure6.46ApplyingbalancedglobalnegativefeedbacktotheCrystalPalace.

NotethatverysmallPTFEtrimmercapacitorsarerequiredacrossthefeedbackresistors, and it is the practical minimum value of these capacitors thatdeterminesthemaximumvalueoffeedbackresistorswhich,inturn,determinesthe series input resistors and input resistanceof the amplifier.Asusual, it hasbeennecessarytoaddastepnetworkattheanodesofthefirststage,butbecauseitisadifferentialpair,asinglenetworkbetweentheanodesispossible,leaving0Vacrossthe39 pFcapacitor.Theauthorapplied18 dBofbalancedfeedbackbutwasinitiallymystifiedbytheresults.Bearinmindthattheamplifieroutputnolongerhasonelegconnectedtoground,sobothlegshadtobemonitoredontheoscilloscope,yetitsimplywasn’tpossibletoachieveidentical(andperfect)10 kHzsquarewavesoneachleg.Alittlethoughtsuggestedthatthismightbebecauseofimbalancesintheoutputtransformer,andthatsincetheloadrespondstothedifferenceinsignals,thisiswhatshouldbemonitored(seeFigure6.47).

Figure6.47CrystalPalaceoutputwaveforms(Math=Ch1−Ch2=thevoltageacrosstheload).

As can be seen from the oscilloscope traces, the difference between the twochannels (Math, centre trace) isa clean10 kHz squarewave even though thetwolegsdonotmatch.Notethat1 kΩresistorsfromeachoutputlegtogroundarenecessarywhenbalancedfeedbackisusedinordertoreferencetheoutputtoground, otherwise inter-winding capacitanceswithin the transformer can causeinstability.Itwouldbebetterifthetransformersecondarycouldbecentre-tappedto ground, but the author needed a secondary configuration that didn’t permitthat.

Conclusions

Whattheworldneedsisasmaller,lighterCrystalPalace.

TheBulwer-LyttonScalableParallelPush–PullAmplifier

“Itwasadarkandstormynight;therainfellintorrents–except at occasional intervals, when it was checked by aviolentgustofwindwhich sweptup the streets (for it is inLondon that our scene lies), rattling along the housetops,and fiercely agitating the scanty flame of the lamps thatstruggledagainstthedarkness.”

‘PaulClifford’E.G.Bulwer-Lytton(1830)

The first laboratory testof thisamplifier’soutput stagewasmadeona typicalBritish summer afternoon– the skywas dark and itwas about to bucketwithrain.Oncesuggested,theBulwer-Lyttonnamestuck.

Background

Itistraditionalforamplifiersandloudspeakerstobeuniversal–anyloudspeakercanbeusedwithanyamplifier.Butsuchversatilitycarriesthepriceofforcingcompliance with an interface standard of zero source resistance rather thanallowingtheloudspeakerandamplifiertobedesignedtogetherfortheoptimumperformanceofboth.Bycontrast,theBulwer-Lyttonamplifierhassomeunusualcharacteristics,andrather thanengineer themout, theauthorchose todesignaloudspeaker that could capitalise on them. That loudspeaker uses the FostexFE166Efull-rangedriverandfulldesignandconstructiondetailsoftheauthor’sArpeggioloudspeakermaybefoundinthe‘Articles’sectionofdiyAudio.com.Experiment showed that a pair of push–pull 6S4As could produce 2 W (seeFigure6.48).

Figure6.486S4Aoutputstage.

Moresignificantly,theinclusionofaharmonicequaliserresistorenabledthat2WbeobtainedwithdistortionasshowninTable6.7.

Table6.7DistortionofPush–Pull6S4AOutputStageUsingHarmonicEqualiserH2 H3 H4 H5 H6 H7

Level(dB) −42.6 −68.6 −66.6 −78.6 −97.6 −80.6

Notethatnotonlyisthedistortionbelow1%,butthatitisdominatedbysecondharmonic.

DesigningtheFollowerstoDrivetheOutputValves

The amplifier was required from the first to be scalable, with driver circuitrycapable of drivingmany pairs of output valves, and that immediately impliescathodefollowers.HavingmadethedecisiontousesmalloutputvalvesbutdrivethemDCcoupledfromcathodefollowers,itseemsterriblywastefultohavea−300 VHTsupplysimply for cathode followers that only need to swing to 26 V pk–pk . If wereplace the resistive loads in the cathode followers with a semiconductorconstant current sink not only do we improve linearity, but also we improveefficiency because the sink only needs a few more volts than the maximum

required peak negative swing to ensure correct operation.Thus, ifwe need toswingto−26 V,a–35 Vsupplywouldbeperfectlyadequateandfarcheaperthan−300 Vatthesamecurrent.Westillneedatleast100 Vacrossthecathodefollower,butwe’veavoidedwastingvoltageacrossaresistiveload.Evenbetter,a−35 Vsupplywouldenableacascodeconstantcurrentsinkasthetailfortheinputdifferentialpair–slightlycheaperbutfarbetterthantheCrystalPalace’s334Z.We saw in the Crystal Palace amplifier that DC coupling to the output valvegridsmeansthatthecathodefollower’scathodeisslightlynegative,sowemusteither choose a valve that can tolerate V ak >300 V (perhaps the expensive*SN7GTA),orwedrop the300 VHT from theoutput stagedown toamoresuitablevoltageforthecathodefollower.Drivingalargenumberof6S4Aoutputvalves impliesa largeMillercapacitance thatmustbechargedanddischarged,sothisimpliesasubstantialquiescentcurrentthroughthecathodefollowerand,combinedwiththeVakproblem,thissuggestsalotofpowerisbeingwastedasheat. The obvious solution is to determine the ideal positive voltage for thecathodefollowersthenprovideitfromadedicatedmainstransformerwinding.Havingacceptedthatthecathodefollowersneeddedicatedtransformerwindingsfortheirpositiveandnegativesupplies,it’stimetoquestionthesuperiorityofacathode follower, andwhetherornotanFETsource followermightbe just asgood(butalotcheapertoimplement).Itwastimeforsomemeasurements.

ComparingCathodeandFETSourceFollowers

Weknow that a cathode follower has 100%negative feedback, so high open-loopgain(high-μ)impliesmoredistortion-reducingnegativefeedback.Further,wewouldwant tominimisedistortionbefore feedback,and that impliesa lowdistortionvalve.Weknowthatweneeda lowoutputresistance,so thatmeanswe also need high g m . There is only one valve that meets all of theserequirements and it is the 6C45Π. We know that distortion is minimised byensuringthatRL /ra>50,andthisconditioniseasilysatisfiedbythecascodeconstantcurrentsinkthatwealreadyneedtoavoidwastingnegativeHTvoltage.Thus, a 6C45Π cathode follower sitting on a cascode CCS is as good as athermionicfollowergets.WealwaysneedtheefficiencyofthecascodeCCS,soanFETsourcefollowershouldhavethesameload.Thereversebiasseddrain/gatedepletionlayerwithinapowerFEThascapacitance thatvarieswith the inverse square rootofVdg ,potentiallycausingnonlinearity, soweneed tochoosea lowcapacitanceFET,

suchasthe500 V1.4 AFairchildFQP1N50.Unfortunately, these(likemanyothermodern FETs) are optimised for switching rather than linearity, and theauthor soon found that the FQP1N50 has a feature not revealed by themanufacturer’sdatasheet(seeFigure6.49).

Figure6.49FQP1N50Pdraincharacteristics;notethenegativeresistancetetroderegionatVDS≈25V

Ascanbeseenfromthemeasuredcurves, thereisa tetroderegionofnegativeresistanceatVds≈5 V,andsubsequentdistortionmeasurementsshowedthatVds should not be allowed to drop below 30 V. Nevertheless, this is still lessonerousthanthe150 Vrequiredbythe6C45Π.It’sjustashamethattheninthFQP1N50tobetestedprovokedsmokefromtheauthor’sTek571curvetracer(again).Whether the follower is a cathode follower or source follower, it still needs aquiescentcurrentof10 mA,andpossiblymoreinordertobeabletosupplythecurrent neededby the input capacitanceof theoutput stage.Bothdeviceswilloscillate given half a chance, so power supply decoupling is important andcarbon grid or gate stopper resistors are essential. Further, we know that thefollowers are likely to be driven from a high source resistance, and that thiscould cause distortion due to grid current in the 6C45Π or due to signal-dependent depletion region capacitance in the FQP1N50, so a test sourceresistanceof100 kΩwaschosen to revealeitherof theseproblems.Thus, thetest circuit for the Device Under Test (DUT) comparison can be drawn (seeFigure6.50).

Figure6.506C45ΠvsFQP1N50followertestcircuit.

TheonlycircuitchangewhenexchangingbetweenDUTswasthatthetriodewasallowed+150 V,whereas theFETwas finewith+100 V.Each followerwasdrivenwith+23 dBu(31 Vpk–pk)becausethiswasthemaximumsingle-endedvoltage that the author’s audio test set could provide. 1 kHz distortion wasindistinguishablefromthetestset’sowndistortion,someasurementsweremadeat10 kHzinthehopeofrevealingdistortionduetosignal-dependentdepletionregion capacitance.Withonly the60 kΩof the test set to load the followers,bothachieved<0.01%THD,dominatedbysecondharmonic.In an effort to provoke some clearlymeasurable distortion, each followerwasloaded by a resistance box adjusted to increase distortion in 3 dB steps (seeFigure6.51).

Figure6.51Comparisionof6C45ΠvsFQP1N50distortionagainstloadresistance.

We can finally see a difference between the two followers, and the FET issuperior.This seriesofmeasurements shows that ifappreciable loadcurrent isneeded,themostimportantpropertyofthefollowerdeviceishighgm,andtheFEThashighergmthanthevalve.Thus,theBulwer-LyttonamplifierusesFETsourcefollowersbecausetheyallowlowerdistortion.

OutputStageBias,BalanceandCoupling

JustliketheCrystalPalace,wemustmakeprovisionforadjustingoutputstagequiescent current and balancing the anode currents in the output transformer.Therequiredharmonicequaliserresistorforeachpairof6S4Aswasdeterminedempiricallyasbeing91 Ω.Attheoptimumcurrentof45 mAperpairof6S4As,thissharedcathoderesistordrops4.3 V.Butthe6S4AneedsVgk=−13 Vtoset45 mAperpairfromthe320-VHT,soif−4.3 Visprovidedbycathodebias,theremaining−6.7 Vmustbeprovidedbygridbias.Thus, theBulwer-Lyttonamplifier is an example of mixed bias and is more stable than the fixed biasCrystalPalace.Withonly9 VRMSneededateachoutputvalve’sgrid,theBulwer-Lyttonneedsvery little gain, and twodifferential pairs are unnecessary.This implies that asingledifferentialpairwillprovidethegainandthatthedrivercircuitry’ssingleLow Frequency time constant must be the coupling capacitors between thedifferential pair and the FET source followers. Thus, output stage quiescentcurrent and DC balance must be adjusted at the inputs of the FET sourcefollowers.Thetraditionalwaytodothis is tomakeapairofpotentialdividersusing the ends of a variable resistor with the wiper connected to a negativevoltage.Movementofthewiperadjustsrelativeattenuationsofthetwopotential

dividers so that one voltage rises while the other falls. Quiescent current isadjustedbyavariableresistor inserieswith thewiper thatcontrols thecurrentsunkintothepotentialdividersandthereforethevoltagedevelopedacrossthem(seeFigure6.52).

Figure6.52Adjustinganoutputstage’sDCbalanceandbias.

The best way to design such a bias arrangement is with a spreadsheet. TheequationsarebestdeterminedbytreatingthequiescentcurrentvariableresistorR1anditsassociatedlimitingresistorR2asfixedresistorsinaNortoncurrentsource, thenapply thecurrentdividerequation toeacharmof thebiasbalanceresistorR4anditsassociatedlimitingresistorsR3.Oncethecurrentsdowneacharmofthecurrentbalanceresistorareknown,theresistanceofeacharmofR4canbeaddedtoitsR3andOhm’slawisappliedtothatresistancetodeterminetheoutputvoltage.Finally,copytheequationsdownfordifferentproportionsofR4,thenplotagraphofthetwooutputvoltagesagainsttheseproportions(seeFigure6.53).

Figure6.53Carefuladjustmentofvaluesallowsadequatebutnotexcessiverangeofbiasadjustment.

Having set up the spreadsheet, set R 1=0 and chooseR 2 to give the highestvoltageat50%ofR4 rotation thatyou thinkyouwillneed, thenadjustR1 togive the expected quiescent voltage.R 4 andR 3 can then be adjusted to giveadequate variation. The process tends to be somewhat iterative, but once theequationshavebeenwritten,experimentationisquick.Finally,adjustR1togivethemostnegativevoltageyouthinkyouwillneed,andthiswillbethevalueofthisvariableresistor.Although the previous schemeworkswell atDC, the resistances seen lookinginto the circuit from the coupling capacitors become unequal once the biasbalancecontrolisadjustedfromitscentreposition,andunequalloadresistancesdisturbdifferentialpairACbalance.Furthermore,thetimeconstantsofthetwocouplingcapacitorsandloadresistancesbecomeunequal,causingimbalanceandconsequentdistortiontowardstheircut-offfrequency.The problem can be solved by buffering the DC from the ends of the biasbalance controlwith emitter followers so that the output resistance becomes afewtensofOhms.Onceweaddour1 MΩgate-leakresistor,anyvariabilityornonlinearityintheemitterfollower’soutputresistancebecomesinconsequentialand a constant load resistance is seen irrespective of bias balance adjustment.Theemitterfollowersdrop0.6 Vacrosstheirbase–emitterjunctions,soitmaybenecessarytotakeaccountofthatandrevisitthespreadsheet.Inaddition,itisnowpossibletoincludesomepowersupplysmoothingtothecircuitbyputtingacapacitor across each R 2 . However, it is not a good idea to make thesecapacitors too large as they will slug the speed of adjustment, which is veryirritating.Atimeconstantof100 msallowssomesmoothingwithoutnoticeablysluggingadjustmentspeed(seeFigure6.54).

Figure6.54BufferingthebiasadjustmentpreventsinteractionwithACconditions.

TheFQP1N50hasitsdrainconnectedtoitstab,andasthedrainisconnectedtothe +39 V rail, there is no problem in heatsinking it to the chassis via aninsulatingwasher.However,theMJE340transistorsintheconstantcurrentsinkhavetheircollectorconnectedtotheirtab,soheatsinkingthesetransistorstothechassisviaaninsulatingwasherwouldadd≈8 pFinparallelwiththeiroutput,whichisnotideal.Thus,theMJE340shavetheirownheatsinks.Sincetheamplifierisdesignedtodriveadedicatedloudspeakerhavingaknownf−3 dB=83 Hz,thereseemslittlepointinsaturatingtheoutputtransformerbyapplyingfullamplitudebassdown to10 Hz,so thePTFEcouplingcapacitorsare only 10 nF and feed1 Mgate-leak resistors, setting the amplifier’s f−3dB=16 Hz.

ProvidingGain

Having designed an output stage that doesn’t generate higher harmonics anddrivers with low distortion FET source followers, it would be unfortunate tospoil this performance with poor gain circuitry. Thus, although we mightconsider0.6%distortionintheoutputstagetobeacceptableonitsown,itmustbedrivenbyaperfectundistortedsignal.Inthiscontext,‘perfect’wouldmeanthatanydriverdistortionshouldbe>20 dBbelowthatoftheoutputstageandbecomposedsolelyof loworders.Although thedifferentialpaircanproduce lowdistortion, it does so by cancelling even harmonics and summing odd, so thetriode’sdominantH2tendstocancelbutthelesserH3issummed.WethereforeneedavalvethatinherentlyproducesverysmallamountsofH3,andthattakesusstraightbacktotheSN7/N7familychosenfortheCrystalPalace.

EachoutputvalveisbiassedsothatVgk=−13 V,soitrequiresaswingof≈9 VRMS todrive it intogridcurrent (Vgk=0 V).Thesource followershaveverynearlyunitygain,butnot all6S4Asare the same, soweought toassume thateachanodeofthedifferentialpairmustswing≈10 VRMS.Experiencesuggeststhat a SN7/N7 differential pair should be capable of producing H2≈−69 dB(0.035%)andH3≈−80 dBat this level–whichisgoodenough.The7N7wasbiassed to <8 mA in order to allow a flatter loadline that would allow lowdistortionandgoodswingfromthelimitedHTvoltage.

GainStageCCSandGainBalance

Thegainstageusestheauthor’sstandardcascodeCCSbutitissuppliedfroma337L(lowpowerTO92variant)regulatortoguaranteelowhum.Because the test amplifier was designed to operate without global negativefeedback, it is entirely possible that component variation (especially valves)couldcauseaninter-channelgainerror.Asimplemethodofcompensationistoallow adjustment of DC tail current in each differential pair by adjusting theCCSprogramming resistor; adjusting tail current changes r aand thus slightlychangesgain.Onlya little adjustmentcanbeobtained in thisway,but ifbothstereochannelshavetheadjustmentitbecomespossibletomatchthem.

BalancedInputsonPowerAmplifiers

Unlike thesignal leavingamicrophoneoramoving-coilcartridge,signalscanbetransferredeasilytopoweramplifierswithnegligibleriskofinterference,yetpower amplifiers with balanced inputs are becoming increasingly fashionable.Popular reviews comparing balanced and unbalanced inputs on the sameamplifierhaveoftenclaimedthatthebalancedinputsoundedbetter,yetitishardtoseehowadomestic lengthof interconnectingcablecouldpickupsufficientinterference to make balanced operation desirable. However, there is another(and much more likely) possibility, and that is interferencewithin the poweramplifier.Fundamentally,therearetwowaysofachievingabalancedinput:eitherwithatransformer, or with a differential pair. Transformers having good windingbalance,wide frequency response, and lowdistortion tend to be expensive, sothedifferentialpairisunderstandablymorepopular.Consider the differential pair driven from a balanced source. Two equalamplitude signals of opposing polarity are applied to the grids, resulting inperfectbalancewithinthedifferentialpair,andnoaudioonthecathodes.

Nowconsiderthedifferentialpairdrivenfromanunbalancedsource.Oneinputgrid isgrounded,and theotherhasa signal,but thedifferentialpairmaintainsoutput balance because a large cathode resistance (whether explicit or aCCS)prevents audio current out of one anode from flowing anywhere but into theotheranode.Ifonegridisgroundedbuttheanodeofthatvalvecarriesasignal,thatvalvemustbeactingasagroundedgridstageandtheinputsignalmustbeatitscathode.However,thereiscapacitancebetweenthecathodesandtheheater(Chk≈7 pFper triode for 7N7), and the heater transformer could easily have 1 nFcapacitancetothemainswinding,pickingupcommon-modeinterference.Thus,byunbalancingtheinputsofthedifferentialpair,weforceittoamplifysignalson its cathodes, rendering it sensitive to mains interference coupled throughheater transformer inter-winding capacitance – and that is why the balancedinput sounds better, not because of better rejection of interference on audiocables.Note that the previous argument hinges on a very particular definition of‘balanced.’Theoverridingrequirementofbalancedaudioisthatimpedancestoearthareequalfromeachleg–nomentionofaudiovoltages,yetthisdifferentialpair‘balanced’inputalsorequiresequalsignalsofopposingpolarity.Standalone digital to analogue converters have once again become popularbecause of their versatility in dealingwith disparate digital sources (computermusic server, broadcast receiver, conventional CD player). Many digital toanalogueconvertersimprovetheirdistortion/noisebyinternallyoperatingapairofDACs inpush–pullbecause taking thedifferencebetween these twosignalsincreases the (correlated) signal by 6 dB, but the sum of the two DACs’distortion/noise(whichisassumedtobeuncorrelated)onlyrisesby3 dB,thusimproving dynamic range by 3 dB over a single DAC. Thus, many modernDACsinherentlyproducebalancedaudio,anditischeaptomakeafeatureofitbybringingitoutontoanXLRconnector.Giventhatdomesticbalancedaudioisnowreadilyavailableandthatapush–pullamplifierwithabalanced-capable inputworksbetterwithabalancedsignal, itnowmakesagreatdealofsenseforavalveamplifier toexpectbalanced line-levelsignals–butnotbecauseofthetraditionalcableinterferenceissues.

TheVolumeControlandBaffleStepCompensation

HavingdecidedthattheBulwer-LyttonamplifierwillbedrivenprimarilyfromabalancedoutputDAC,wenowknowthat the required inputsensitivity is4 VRMS (differential). This doubling of voltage occurs because balanced output

DACs invariablyproduce2 VRMSoneach leg, so if theother leg is invertedpolarity, the differential signal must be 4 V RMS . There’s no engineeringnecessitytochoosethisconvention–itisjustthewayitseemstobedone.The6S4Asneed≈10 VRMSeach,equivalent to≈20 VRMS(differential),andthegainofa7N7differentialpairis≈14,resultinginaninputsensitivityatthegridsof1.4 VRMS(differential).Wethereforeneed≈9 dBattenuationfromthe4 VRMSsource,whichisjustaswellbecausetheArpeggioloudspeakerneeds2.4 dBbafflestepcompensationattheinputofitsdedicatedamplifier(causing2.4 dB attenuation), and balanced volume controls have to be Type C (seeChapter7) thatcannotachieve0 dBattenuation.TypeCvolumecontrolsarealways a delicate balance between excessive output resistance and low (andvariable)inputresistanceloadingthesource.SinceithasbeenassumedthattheBulwer-LyttonamplifierwillprimarilybedrivenfromaDAChavinglowoutputresistance, the balance can be swung towards low input resistance, enablingloweroutputresistance.Theissueoflowoutputresistanceisimportantbecausethe volume control precedes the baffle step equaliser, so minimising outputresistance minimises the (unavoidable) changes in equalisation as the volumecontrolisadjusted(seeFigure6.55).

Figure6.55Bulwer-Lyttonvolumecontroloutputresistanceagainstattenuation.

Thevolume control’s output resistance changes from2.73 kΩ to 109 Ω, andthischangingsourceresistanceaddedtotheequaliser’sseriesresistorschangesits attenuation by 0.17 dB, manifesting itself as a shelf error. Fortunately,although shelf errors are the most audible, discriminating between a 0.2 dBerrorandnoerrorataconstantlevelismarginal,soa0.17 dBerrorbetweenfullandminimumvolumeshouldpassunnoticed.TypeCattenuatorshabituallyselectanindividualresistorfortheirshuntbutitis

mucheasiertoobtainagoodlogarithmiclawifthewipermovesupanddownaseries chain of resistors so that it picks up the sum of a number of seriesresistors. Using this technique, the Bulwer-Lytton’s volume control deviatesfrom logarithmic linearity by <0.05 dB and has perfect channel matching (Table6.8).

Table6.8Bulwer-LyttonVolumeControlResistorValuesAttenuation(dB) Individualresistor

0 –1 2k72 1k83 1k54 1k15 820 Ω6 680 Ω7 560 Ω8 430 Ω9 390 Ω10 330 Ω11 270 Ω12 240 Ω13 200 Ω14 160 Ω15 150 Ω16 130 Ω17 120 Ω18 91 Ω19 91 Ω20 75 Ω21 68 Ω22 56 Ω23 51 Ω24 47 Ω25 39 Ω26 36 Ω27 33 Ω28 27 ΩTailresistor 221 Ω0.1%+2 Ω1%

WecannowdrawtheentirecircuitdiagramoftheBulwer-Lyttonamplifier(seeFigure6.56).

Figure6.56EntireBulwer-Lyttoncircuitdiagram.

AudioCircuitComments

Thecircuitappearscomplex,butmostof it ishousekeepingcircuitry toenablethesimpleaudiodepartmentofdifferentialpairandsourcefollowerstoworkattheirbest.Although theamplifier as awholewasdesigned tocomplement theauthor’sArpeggio loudspeaker, the housekeeping circuitrywas designed to begeneric.Eachchannel’sentirehousekeepingcircuitrywasbuiltonasinglePCB;justaddachassis-mountingvalvesocket tosuit thegainvalveandyouhaveacompletedriver.Further,theFETsourcefollowerisspecificallydesignedtobeabletocopewiththehighervoltagesneededbyvalvessuchastheKT88,hencethe300 VMJE340uppertransistorintheCCSandthe500 VFET.Obviously,detailed resistor values would need to be changed and the MJE340 wouldprobably need bigger heatsinks because the higher voltages would increasedissipation,buttheboardlayoutwouldremainunchanged.

PowerSupplies

Eachpairof6S4Asneeds45 mA,andtherearefourpairs,sothatmeans180mA,andeachdifferentialpairrequires8 mA,givingatotalrequirementof196mA at 315 V DC . Traditionally, a GZ34 would have been the obvious HTrectifier but these are now expensive, so a pair of 12CL3/12CK3was chosen,necessitating a 12.6 V 1.2 A heater supply. The FET source followers andhousekeepingcircuitryrequire+39 VDCat44 mAand−39 VDCat72 mA.The author detests ‘wall-warts,’ so rather than leaving an ugly plug-mountedmainstransformerpermanentlypowered(gettinghotandwastingelectricity),a

12 V1.5 AwindingwasaddedtopowerhisDacMagicaudioDAC.ACLCfilterwasidealforHTtotheoutputstages,butthegainstageneededasmuchHTaspossibletominimisedistortion,soitalsousedLCsmoothing.Asisnow the norm, PSUD2 was used to analyse the supplies and check for lowfrequencystability–whichrevealedthattheinductorfeedingthegainstagehadtoo high a Q and needed a small series resistor to prevent Low Frequencyringing.Similarly,two100 μF400 VKelvincapacitorswereneededtosmooththeHTtotheoutputstagesnotforanyreasonsofstereoseparation(sincetheyare in parallel) but because 200 μF was needed to prevent Low Frequencyringing.Alloftheprecedingsuppliescanbederivedfromacommontransformer,buttheaudiovalveheatersneedtheir6.3 Vat6 Afromaseparatetransformer(ideallya split bobbin EI type) to avoid interference from rectification spikes.Unfortunately,theauthordidn’thaveroomonthetopofhischassisforacannedEIheater transformer, sohewas forced tousea6 V50 VAtoroidunder thechassisthatgave6.2 Vbecauseitwasslightlyunder-run(under-runninga6 Vtransformertoobtain6.3 Visausefultrick).

GlobalNegativeFeedback

WesawinChapter3thatBaxandall’sanalysisoffeedbackshowedthatprovidedopen-loopdistortionis<1%anddominatedbysecondharmonic,anyamountofnegativefeedbackfrom0 dBupwardsproportionatelyreducestheamplitudeofallharmonicsandself-generationofhigherharmonicsisnegligible.Ontest,the6S4A push–pull output stage produced 0.6% THD just below grid current,dominatedbysecondharmonic,sothisamplifierisanidealcandidateforglobalnegativefeedback.IntheBulwer-Lyttonamplifier,globalfeedbackwouldhavebeenundesirablebecause itwouldhave reduced theoutput resistance requiredby the Arpeggio loudspeaker, but a more forceful version employing sixteen6S4As per channel (BL) (2) to give 16 W could drive a more conventionalloudspeaker and 20 dB of negative feedback would reduce its maximumdistortionto0.06%–stilldominatedbysecondharmonic.

Thetaskofapoweramplifieristoamplifyaprocessedsignalanddeliverpowerintoaloadsuchasaloudspeaker.Itshoulddothiswithoutintroducingspurioussignals, such as hum, noise, oscillation or audible distortion, whilst driving awiderangeofloads.Additionally,itshouldbetolerantofabuse,suchasopenorshortcircuits. Itwillbeappreciated that this isnota trivialobjective,andwillthereforerequirecarefuldesignandexecutionifitistobeachieved.

[1]Hafler,D;Keroes,HI,Anultra-linearamplifier,AudioEng(November)(1951)15–17.

[2]BlumleinA.Improvementsin/orrelatingtothermionicvalveamplifyingcircuits.BritishPatent496,883;1937.

[3]MolloyE,editor.Highfidelitysoundreproduction.2nded.GeorgeNewnes;1958.p.52.

[4]McIntosh,FH;Gow,GJ,Descriptionandanalysisofanew50 Wamplifiercircuit,AudioEng(December)(1949).

[5]Futterman,J,Apracticalcommercialoutputtransformerlessamplifier,JAudioEngSoc(October)(1956);[alsoUSPatent2,773,136;December1959].

[6]Schmitt,OH,Cathodephaseinversion,JSciInst15(136)(1938)100–101.

[7]Clare,JD,Thetwintriodephase-splittingamplifier,ElectronEng(February)(1947).

[8]CarpenterREH.Improvementsrelatingtoelectrondischargeapparatus.UKPatent325,833;1928.

[9]MasatsugoKobayashi.Electricoscillator.USPatent1,913,449;1929.[10]TheWilliamsonAmplifier.Acollectionofarticlesreprintedfrom‘Wireless

World’April1947,May1947,August,OctoberandNovember1949,December1949,January1950,May1952.

[11]Hafler,D;Keroes,HI,Ultra-linearoperationoftheWilliamsonamplifier,AudioEng(June)(1952).

[12]Mullard:Tubecircuitsforaudioamplifiers;1959[nowreprintedbyAudioAmateurPress,Peterborough,NewHampshire,USA;1993].

[13]WalkerP.Privatecommunication;1993.[14]Williamson,DTN;Walker,PJ,Amplifiersandsuperlatives,JAudioEng

Soc2(April(2))(1954).[15]Anapproachtoaudiofrequencyamplifierdesign.GeneralElectric

CompanyLtd;1957[nowreprintedbyAudioAmateurPress,Peterborough,NewHampshire,USA;1994].

[16]Colloms,M,Highperformanceloudspeakers.6thed.(2005)Wiley;pp.327–43.

[17]HedgeLB.CascadeAFamplifier.WirelessWorld;June1956.[18]Langford-Smith,F,Radiodesigner’shandbook.4thed.(1957)Iliffe.[19]PhilipsQE5/40valvedatasheet;12thDecember1958.

[20]LM134-LM234-LM334datasheet.SGS-Thomson;October1997.

References

FurtherReading•Spicer,S,Firstsinhighfidelity.(2001)AudioAmateurPress,New

Hampshire,US.

Chapter7.ThePre-Amplifier

Thetraditionalpre-amplifierperformedanumberoffunctions:•Inputselection•Volumecontrol•Balancecontrol•Cabledriver•Tonecontrol•RIAAstage.

Ifthelasttwofunctionsarenotneeded,thenthefirstthreecanbeimplementedpassivelywithinthepoweramplifier,negatingtheneedfortheextraelectronicsofacabledriverandmakinganexternalpre-amplifierentirelyredundant.

Differentsituationsrequireadifferentmixofthepreviousfunctions,sowewillinvestigate how each function may be implemented, allowing us to mix andmatchtoaparticularapplication.Ingeneral,theproblemisdefinedeitherbytheneedtoputanaloguecontrolsconvenientlytohandatthelisteningpositionortolimit the length of cable carrying a low-level signal. Thus, there are fourcommonsituationsthatrequireapoweredboxbeforethepoweramplifier:• Traditional pre-amplifier with full controls : Placed adjacent to vinylturntable,andbothplacedconvenientlytohand.•Limitedcontrolpre-amplifier :Inputselector,volumecontrol,plusbalancecontrolwithcompensatinggain–placedconvenientlytohand.•Volumecontrolplusunity-gainlinedriver:Althoughthiscouldbeanevensimpler version of the above, it is more likely to be a six-channel steppedattenuator placed after a digital active crossover as a means of achievingstereovolumecontrolwhilstmaintainingeachDAC’sfulldynamicrange.•RIAAstage:Vinylcartridgesneedtheiramplificationnearby.

InputSelectionAlthoughinfrequentlyused,whentheinputselectorisused,attentionisfocusseduponit.Thus,inputselectionshouldnotoffend,andwaysitcanoffendare:•Disparatelevelsbetweensources•Crosstalkbetweensources•Noise.

Analogue switches such as the 4016 (but ideally not the 4066 because ofcrosstalk from its control lines) can switch audio signals. However, thesesemiconductor switches are based on Field Effect Transistors (FETs) having‘off’ capacitancesproportional to the inverse square rootof thevoltage acrosstheir depletion region, so they need virtual earth techniques to minimisedistortion, implying semiconductor op-amps. Valve electronics therefore usesmechanical switches, sowewill investigate theirdefects andhow tominimisethem.

DisparateLevelsbetweenSources

Strictly, there’s no switch defect if source levels do not match, but that finedistinction is lost on the non-technical user. It ought to be possible to switchbetween Bach arriving via analogue radio, remote digits, optical disc player,computer server or LP without hearing any appreciable volume differencebetweenthesources.Mostsignalswitchingisnowdoneinthedigitaldomain,andtherearenowonlyafewanaloguesources.CDistheoldestsourceofdomesticdigitalaudio,andits2 V RMS maximum undistorted sine wave definition of analogue level hasbecomethedefactostandard.Thus,weshouldensurethatallsourcesarriveattheinputselectormatchingthisstandard.Inthisinstance,broadcastterminologyhas been adopted across the industry and most quality sources have internalengineeringadjustmentsmarked‘linelevel’,soitisthesethatshouldbeadjusted(ifnecessary)tocorrectlevel.Quarter-inchtapemachineshavebecomefashionableonceagain,andEuropeanex-broadcast machines typically have their line levels set to reproduce peakseither 8 dB (UK) or 9 dB (Germany) above 0.775 V RMS or 0 dBu. Thesignificanceisthat+8 dBu=1.95 VRMS,sonoadjustmentisnecessary.Sadly, FM tuners commonly produce quite small signals, and this is a tunerrather than pre-amplifier problem becausewe should only send robust signals

downcables. If,as iscommon, there isn’ta line-leveladjustment,apiggybacklinedriverboardwillbeneededtoprovidetheadditionalgain.

AdjacentContactCapacitance(CrosstalkBetweenSources)

The simplest way to select between sources is with a rotary switch.Unfortunately, all such switches suffer adjacent input crosstalk due tocapacitance between adjacent contacts (typically 0.4–0.8 pF). If we had anumber of sources plugged into the pre-amplifier, but selected an inactive orunplugged source, that ≈0.6 pF would form a high-pass filter in conjunctionwiththetypical100 kΩinputresistanceofthevolumecontrol.Theearismostsensitive at ≈4 kHz, and at this frequency the RC combination would causecrosstalk ≈53 dB below an expected signal. On high-quality traditional pre-amplifiers, this irritation was solved by having two ganged switches: oneselected the sourceand theotherdeselected the short-circuit togroundon thatsource. Sadly, such wafer switches are no longer available, but a goodalternative is to use alternate contacts for inputs and connect intermediatecontactstogroundtoguardbetweensignalcontacts(seeFigure7.1).

Figure7.1Blockdiagramofpre-amplifier.

Although crosstalk on an open-circuit input could easily be at −53 dBwith atraditional switch, once an active source having a low source resistance isselected, thecrosstalkfallsrapidly.Asanexample,selectingasourcehavingrout≈300 Ωwould cause the crosstalk to fall to−107 dB.Thus, thegroundedintermediate selector switch contacts aremainly there to avoid crosstalk if an

unused input is selected,but theyalsoprovideamute settingbetween sourceswithoutaddingcontactstothesignalpaththattheauthorhassubsequentlyfoundtobeveryconvenient.

ContactandLeakageResistance(Noise)

Ideally, contact resistance would be zero, but this is never achieved. Contactresistanceisnotaproblemprovidedthat it is low(milliohm)andconstant,butcauses noise when it rises and particularly if it fluctuates. Contact resistancerisesovertimeasaresultofoxidationofthecontacts,waningcontactpressureandcontactwear.Becauseofitsresistancetoatmosphericcorrosion,gold-platedcontacts are sometimes used, despite the fact that the resistivity of gold isconsiderablyhigherthanthatofsilverorcopper,butbewarethatgoldissofterthansilver,sothewipingcontactsofarotaryswitchweargoldfasterthansilver.All switches have leakage resistance, which is usually specified by themanufacturer,andwillbeslightlyworsenedbyincreasinghumidity,butsurfaceleakage currents can easily be generated by failing to deflux the wafer aftersoldering (flux remaining after soldering contains solder droplets and iselectricallyleaky).Surfaceleakagecurrentsinvariablygeneratenoiseand,onaselectorswitch,crosstalk.

SolutionsandProblemsPeculiartoElectromechanicalSwitches

(Relays)

Although a changeover relay could be used for input selection, allowingcrosstalkduetostraycapacitance,practicalimplementationsuseonerelay(andassociated coil) per input. Because the coil is relatively large, the enforcedphysical separation between source wiring effectively eliminates straycapacitance across the distributed switch – although this could always berestoredbyspectacularlyincompetentPrintedCircuitBoard(PCB)layout.The ideal signal switch was the mercury wetted relay because a droplet ofmercury wetted the contacts to ensure minimum, and constant, contactresistance. Because the relay had to be hermetically sealed to prevent the(poisonous) mercury vapour from escaping, the contacts did not oxidise. Thecontactswere non-wiping, sowearwasminimised.Unfortunately, they are nolongermanufactured,mostlybecause theirmainusewas in telegraphrepeaters(long obsolete), but also because safety legislation concerning substanceshazardous to health has made it all but impossible to sell any productincorporating legislated substances no matter how great their benefit or how

smallthehealthrisk.Restrictedavailabilityofmercurywettedrelaysnotwithstanding,relayswitchingis an excellent solution. If we had a series relay on each source, we couldprecedeitwithashuntrelaytogroundthatwouldnormallybeclosed,andthiswould ensure almost perfect attenuation of unwanted sources. To protect thesourcefromtheshort-circuit,a1 kΩseriesresistorisnormallyfittedbeforetheshuntrelay,whichfurtherimprovesattenuation(seeFigure7.2).

Figure7.2Modifyingatypicalpentodeinputstagefortriodeoperationtoreducenoise.

Eachrelayshouldbemountedascloseaspossibletoitsassociatedinputsocket,allowing the signal wiring to be as direct as possible (minimising straycapacitance),andthefrontpanelselectorswitchmerelycarriesDC.5 Vrelaysareanobviouschoice,sincethesecouldbepoweredbya5 Vregulatorfedfromthesametransformerwindingasthevalveheaters.However,whilst thiswouldbeaperfectlyvaliddesignchoiceifweusedsimpleDCorcombinationallogictodrivetherelays,itismorelikelythatwewoulduseamicrocontrollerandaddremote control. The key virtue of combinational logic is that it is quiet as amousewhennotbeingcontrolled,whereas thesequentialmicrocontrollermustcontinually poll its inputs to see if anything has changed, so its clock andfirmware run continuously, polluting the heater winding and capacitivelycouplingnoise intocathodesof theaudiovalves. Ifyouuseamicrocontroller,either filter its supply very carefully or give it a dedicatedmains transformer(alsoenablingremotecontrolofpowerON/OFF).

VolumeControlThevolumecontrolisthemostfrequentlyusedcontrol,soit isessentialthatitdoesnotoffend.Waysthatitcanoffendasitisadjustedare:•Disturbingfrequencyresponse•Perceivedvolumenotchangingsmoothlywithrotation•Disturbingchannelmatching.

Wewillinvestigatehowtominimiseeachoftheseproblemsinturn.

LimitationsontheControl’sValue(DisturbingFrequency

Response)

Themaximumoutput resistance of a 100 kΩ volume control is 25 kΩ. Thismaximumoutput resistancemayeasilybeverifiedbymoving thewiper to theelectricalmid-positionofthetrack.Theresistancetoeachendmustbehalfthetotalresistance,andassumingzerosourceresistance,eachendisatACground.Looking back into the potentiometer, we see the two halves in parallel, andthereforetheoutputresistanceisequaltothetotalresistanceofthepotentiometerdividedbyfour.Ifthewiperisateitherendofthetrack,outputresistancewillbezerobecauseitisconnectedtogroundeitherdirectlyorviathe(zeroresistance)source.Maximum output resistance therefore occurs when thewiper is as farawayfromeachendaspossible,whichisthecentreposition.Thequestionofpotentiometermaximumoutput resistance iscrucialbecause itforms a low-pass filter in conjunctionwith loading capacitancewhose f −3 dBcut-offfrequencywecancalculatefrom:

However,wewouldlikethehighfrequencyroll-offwithintheaudiobandtobefarlessthan3 dB,soweneedtobeabletorelateanf−3 dBfrequencytoagivenlossatagivenfrequency,whichwecanfindfromthefollowingformula:

wheref(dBlimit)=theoutermostfrequencyofinterest

dB=thedeviationfromflatresponseatthatfrequency.

Thedifferencebetween0 dBand0.1 dBroll-offat20 kHzisnegligible,soifwewanted a volume control that caused negligible frequency response errorsoveritsrange,wewouldsetourlimitto0.1 dBat20 kHz,resultinginf−3 dB=131 kHz.Thus,whenthevolumecontrolisatitsmaximumoutputresistanceof25 kΩ,wefindthatitsmaximumtolerableloadingcapacitanceis≈49 pF.Obviously, a lower-resistance volume control tolerates higher loadingcapacitancebutattheexpenseofloadingthesourcemoreheavily.Modernvalveelectronicscantoleratea100 kΩloadwithoutanyproblem,butdistortionrisesas the load resistance falls. Thus, 100 kΩ has become the de facto standardvolume control because it is a standardvalue that offers a usable compromisebetween high frequency roll-off due to loading capacitance and increaseddistortionduetoasteeploadline.

LogarithmicLaw(PerceivedVolumeNotChangingSmoothlywith

Rotation)

Incommonwithotherhumansenses,theearhasalogarithmicresponsetosoundpressure level, so if we want a volume control that has a uniform perceivedresponse to adjustment throughout its range, we need a logarithmicpotentiometer.Thisistherootcauseofallourproblems.Itisnotaproblemtomakealinearpotentiometer.Wesimplydepositastripofcarbonofuniformwidthand thicknessontoan insulator,put terminalsateachend,andarrangeforacontacttoscrapeitswayalong.Ifwedon'tbotherwithacasing,itisknownasaskeletaltype.Inanattempttoproducealogarithmiclaw,thecoatingthicknessismadevariable,then,indeferencetoaudiosensibilities,apressedmetalscreeningcanisfitted,andtwopotentiometersaregangedtogetherononeshaftontowhichwecanfitabig,shiny,spunaluminiumknob.Makingthe coating thickness continuously variable would be expensive, so thelogarithmiclawisapproximatedbyaseriesofstraightlines(seeFigure7.3).

Figure7.3Approximationoflogarithmiclawbystraightlines.

It isamazinghowgooda fit to the ideal logarithmiccurvecanbemadeusingonlyfourdifferentresistancetracks,butitwillcomeasnosurprisetolearnthatthisstillresultsinstepsintheresponseastheknobisrotated.Worse,whenwemechanicallygangthemweexpectthechannelstomatchallthewayfrom0 dBto60 dBandthatjust isn’tgoingtohappen.Somearequitegood,butgangedcarbontracklogarithmicvolumecontrolsbelonginlandfill.

SwitchedAttenuators(DisturbingChannelMatching)

If quality is paramount, and we can accept a control that is not continuouslyvariable, we could use a switched attenuator that works by selecting fixedresistorsinordertocontrolvolume.Thelogarithmiclawcannowbeperfect,ascan the much more important channel matching. However, just because avolume control has detents, this does not guarantee that it is a true switchedattenuator – it could be a carbon track potentiometer in masquerade. Realswitchedattenuatorstendtobequitelarge.Aquicktest,ratherthandismantlingitintheshop,whichmighthaveyouthrownout,istomeasuretheresistanceofthe lower armof each gang at themaximumattenuation settingwith a digitalmultimeter.Ifthereisanymeasurabledifferencebetweengangs,itislikelytobeacarbontrackpotentiometer.Theswitchedattenuatorhasa longandnoblehistory.TheBBCusedquadrantfaders (switched attenuators without detents) on sound desks until the 1970sbecausethereisnothingworsethangentlyfadingoutaprogrammeandhearingan abrupt change in the rate of attenuation – the ear expects to hear anexponential decay akin to reverberation decay. Once Penny & Giles sliderattenuators using conductive plastic tapped linear tracks became available, the(farmore expensive) quadrant fader could be safely relegated to broadcasting

history.Surprisingly,switchedattenuatorswithamereninestepsweremadebyErieforconsumerusein1949[1],buteventhentheadvantageofthesuperiorlawwasrealised.Commercial switched attenuators having thick film resistances inked directlyontotheceramicsubstrateoftheswitchwaferareavailable(ataprice),andtheirperformanceisfarbetterthanacarbontrackvolumecontrol,althoughnotquiteasgoodasyoumightexpectowingtothepoortoleranceoftheinkedresistors.Nevertheless,anAlpssteppedattenuatorguaranteeditssteperroras<±0.5 dBand its farmore important channelmatching error as<0.5 dB, implying10%tolerance inked resistors. More recent commercial solutions solder a PCBpopulatedwithsurfacemountresistorsdirectlytotheswitchwaferandthereadyavailabilityof closer tolerance resistorspotentially allowsmuchbetter channelmatchingerrorstobelegitimatelyclaimed.Thepracticaldisadvantageoftheswitchedattenuatoristhatwecanonlyhaveasmany different volume levels as switch positions. Although common rotaryswitches have detents at 30° (11 usable positions), Elma makes a popularminiature15°(23usablepositions)studswitch,UKType72studswitchesare12° (29 usable positions), and the author recently bought some very splendidSoviet dualwafer 10° (35 usable positions) stud switches that looked entirelyappropriatefordetonatingexplosivesyethadalightactionthatbeliedtheirsize.Shallco’sEandFseriesofrotaryswitchesofferarangeofdetentanglesdownto6°,potentiallyallowingexcellentresolutionandwiderange.Thedesignersofthe15°detentAlps-steppedattenuatorassumedthatweneededa−60 dBposition,thenprovidedcoarsestepsfollowedby2 dBuniformstepsupto0 dB.The60 dBattenuationrangeallowedforswitchingbetweensourceshavingdisparate levels.Thus, thepreviousrequirementforallsourcestoreachthe input selector control at the same level was not only ergonomic, but alsoreduced the range needed by the volume control, making switched attenuatorvolumecontrolsmuchmorepractical.2 dBstepsarealittletoocoarse,andtheauthorprefers1 dB.Providedthat levelsarematchedat theinputselectorandcorrectlymatchedtopoweramplifiersensitivity(only justable tooverload theamplifier on the last two or three steps), 1-dB steps on a switch having 12°detents(orbetter)allowaperfectlypracticalvolumecontrol.

SwitchedAttenuatorDesign

Assumingthatwehaveasuitableswitchfortheattenuator,weneedtocalculatetherequiredresistorvalues.Wecoulddothisbyhand,butacomputermakeslife

mucheasier.Therearethreefundamentalattenuatortypes(seeFigure7.4).

Figure7.4μ-Followeraspre-amplifieroutputstage.

TheTypeAattenuatorinFigure7.4issimilartothecarbontrackattenuatorinthat it has a chain of resistors fromwhichwe choose an appropriate tap. TheTypeAattenuatorhasagood logarithmic lawandexcellent channelmatchingbecause for most attenuations each potential divider resistor is made up of anumber of resistors, improving the tolerance of each composite resistor. As aresult, even2% tolerance resistorsallowanaveragechannelmatchingerrorof<0.1 dB provided that the tail resistor at the bottom of the ladder is 0.1%tolerance.TheTypeBattenuator inFigure7.4uses individualpotentialdividersforeachvolume setting,which dramatically reduces the number of soldered joints andcomponents in the signal path at the expense of twice as many wafers andresistors.Unfortunately,maintainingconstantinputresistanceyetprovidingtheexact attenuations required to give a good logarithmic law, requires awkwardvaluesand thereforeE96resistors.Further,becauseeachattenuator ismadeofonlytworesistors,thereisnoneoftheaveragingeffectthatreducederrorsintheTypeA attenuator, so the resistorsmust be 1% tolerance (preferably 0.1%) tominimisedeviationsfromlogarithmiclawandachieveclosechannelmatching.Thus, the Type B attenuator is unpopular because it costs more than doublecompared to theTypeA,yethasworse logarithmic lawandchannelmatchingsolelytoreducethenumberofcomponentsandjointsinthesignalpath.The Type C attenuator in Figure 7.4 uses a single fixed series resistor and aselectionofshuntresistors inorder toachievethesamesignalpathcomponentcountastheTypeBbutatthecostoftheTypeA.However,inputresistanceisno longer constant, and the series resistor must be equal to the maximumtolerable output resistance because when this attenuator is set to maximumattenuation,itsinputresistanceisequaltothatoftheseriesresistor.Thus,inputresistancefallstoaminimumof25 kΩ,whereastheTypeAandBattenuatorshadaconstantinputresistanceof100 kΩandamaximumoutputresistanceof

25 kΩ.Providedstraycapacitancesareminimisedandtheattenuatoronlydrivesalowinputcapacitancecathodefollower,theseriesresistormaybeincreasedto100 kΩ to tame its input loading. Despite its loading issues, the Type CattenuatorisfarmorepopularthantheTypeBbecauseitissomuchcheaper.ThefollowingQBASICprogramsgeneratetheresistorvaluesfortheattenuatorsinFigure 7.4 .They are notmiracles of programming, but they are quick andeasytouse,andcaneasilybemodifiedforotherprogramminglanguages,orthekeyequationscanbeextractedandusedinaspreadsheet.Theprogramsaskfor the loadresistanceacross thewiper; this is thegrid-leakresistorof thefollowingvalve.It is temptingtotrytousethepotentiometerasthegrid-leak,but this ispoorpractice andcancausenoiseproblemswhen thecontactsbounce, and it is alsounnecessary, since theprogramsaccount for itsloadingindesigningtheattenuator.This program finds individual resistor values for the Type A attenuator. Thefinal value given by this program is connected between the last usable switchcontact and ground, and it is often convenient to use the spare contact on theswitchasagroundterminal.Thetailresistorisinvariablyanawkwardvalue,yetitmustbe0.1%tolerance,butitisperfectlypermissibletomakeitupfromtheseries combination of a 0.1% tolerance resistor and a 1% tolerance resistorprovidedthatthe0.1%tolerancecomponentismorethan10timesthevalueofthe1%component.CLS

A=0

B=0

N=0

PRINT "This program calculates individual values of resistors

between"

PRINT"tapsoftheTypeAattenuator."

PRINT"Howmanyswitchpositionscanyouuse";

INPUTS

PRINT"Whatstepsize(dB)";

INPUTD

PRINT "What value of resistance will be across the output of the

potentiometer";

INPUTL

PRINT"Whatvalueofpotentiometerisrequired";

INPUTR

DOUNTILN=S-1

Y=((R-L/10^(-A/20))+SQR((L/10^(-A/20)-R)^2+4RL))/2

C=R-Y-B

PRINTA;"dB";C;"ohms"

B=B+C

A=A+D

N=N+1

LOOP

PRINTA;"dB";R-B;"ohms."

ThefollowingprogramisfortheTypeBattenuator.CLS

A=0

N=0

PRINT"Thisprogramcalculatesupper(X)andlower(Y)armsof"

PRINT"individualpotentialdividersfortheTypeBattenuator"

PRINT"Howmanyswitchpositionscanyouuse";

INPUTS

PRINT"Whatstepsize(dB)";

INPUTD

PRINT "What value of resistance will be across the output of the

potentiometer";

INPUTL

PRINT"Whatvalueofpotentiometerisrequired";

INPUTR

DOUNTILN=S

Y=((R-L10^(-A20))+SQR((L10^(-A20)-R)^2+4RL))/2

X=R-Y

PRINTA;"dB";"Y=";Y;"ohms";"X=";X;"ohms"

A=A+D

N=N+1

LOOP

ThefinalprogramcalculatesshuntresistorsfortheTypeCattenuator.Notethatitnever achieves zero attenuation, and therefore the program also predicts theminimum unavoidable loss through the volume control and grid-leak resistor(basic loss). In effect, this volume control must be considered to be a fixedattenuatorplusavariableattenuator.CLS

N=0

PRINT "This program calculates shunt resistors for the Type C

attenuator."

PRINT"Howmanyswitchpositionscanyouuse";

INPUTS

PRINT"Whatstepsize(dB)";

INPUTD

PRINT "What value of resistance will be across the output of the

potentiometer";

INPUTL

PRINT"Whatvalueofseriesresistorisrequired";

INPUTR

B=((-100LOG(L/R+L))8.686)\1)/100

REMTHE8.686FACTORARISESBECAUSEQBASICUSESNATURALLOGS

PRINT"Basicloss=";B;"dB,addedshuntisinfinite"

PRINT"Addedattenuation:"

A=B

DOUNTILN=S-1

A=A+D

C=R*10^(-A/20))/(1-10^(-A/20))

Y=1/(1/C-1/L)

N=N+1

PRINTN*D;"dB,shunt=";Y;"ohms"

LOOP

SpreadsheetsandVolumeControls

Asmentioned,thefundamentalequationsfromthepreviousQBASICprogramscan be used in a spreadsheet. Although harder to debug, the advantage of aspreadsheet is that it can be set up to predict exact values, substitute neareststandardE24values,andthenplottheconsequentdesignerrorsonagraph.Themost common requirement is for aTypeAattenuator loadedbya1 MΩgrid-leak resistor that emulates a perfect 100 kΩ logarithmic potentiometer.Fortuitously, once practical E24 values were substituted for the calculatedvalues, this combination produced quite low design errors (10 othercombinations were tried but all were worse), and some tweaking away fromobviousvalues improved it further–hence the resistorchange to910 Ωfrom984 Ω(chain)andto3k92from3,995 Ω(tail).Alternatively,wecoulduseE96resistors,renderingthedesignerrorsentirelynegligible(seeFigure7.5).

Figure7.5AttenuationerroragainstattenuationforE24andE96TypeAattenuator.

Theerrorbarsassociatedwitheachdesignsteperrorinthegraphassumetheuseof E24 1% or E96 0.1% tolerance chain resistors and a 0.1% tolerance tailresistor,resultinginanentirelynegligiblemaximumchannelmatchingerrorof0.053 dBandanaveragechannelmatchingerrorof0.045 dBevenfortheE241%option.The reason for including the E96 0.1% option is not to further improve thealready entirely adequate channel matching but because E24 1% toleranceresistors tend to be thick film, whereas E96 0.1% tolerance resistors are thinfilm.Thesignificanceisthatthedistortionofsurfacemountthin-filmresistorsisbetterthan−100 dBforthevaluesneeded(providedthat0805or1206casesizeareused),whereasthick-filmresistorsaresomewhatworse[2].Ifsurfacemountresistors are used, they should be the 1206 case size to minimise distortion,irrespectiveofwhethertheyarethickorthinfilm.NotethattheE24valuesinthetable7.1aresubtlydifferenttothosegiveninthethirdeditionofthisbook,enablingslightlylowerdesignerrors(maximum0.053dB)anda(moreconvenient)single-tailresistor.

Table7.1ResistorValuesfor100 kΩTypeAAttenuatorLoss(dB) R(ideal) E241% E960.1%

0 0 0 01 10068 10 k 10 k2 9261 9k1 9k313 8456 8k2 8k45

3 8456 8k2 8k454 7675 7k5 7k685 6932 6k8 6k986 6237 6k2 6k347 5594 5k6 5k498 5005 5k1 4k999 4470 4k3 4k4210 3987 3k9 4k0211 3553 3k6 3k5712 3164 3k0 3k1613 2816 2k7 2k8014 2506 2k4 2k4915 2229 2k2 2k2116 1983 2k0 1k9617 1764 1k8 1k7818 1569 1k5 1k5819 1396 1k3 1k4020 1242 1k3 1k2421 1105 1k1 1k122 984 910 Ω 976 Ω23 875 910 Ω 866 Ω24 779 750 Ω 787 Ω25 694 680 Ω 698 Ω26 618 620 Ω 619 Ω27 550 560 Ω 549 Ω28 490 470 Ω 487 ΩTail 3996 3k92(0.1%) 3k92(0.1%)+75 R

VolumeControlsforDigitalActiveCrossovers

Versatile digital active crossovers intended for the professional soundreinforcement market are deservedly becoming popular for domestic Hi-Filoudspeakers because economies of scale mean that they are surprisinglyaffordable.However,toachievethatprice,theDACsandanalogueelectronicsinsuchcrossovers tendtobegoodrather thanexcellentquality,withnodynamicrangetospare,sotheHi-Fisolutiontoretainingtheirfulldynamicrangeatallvolumesettingsistoplacethevolumecontrolafterthecrossover.Although driver deviations with frequency are far greater, inter-driver levelerrors of 0.2 dB are just perceptible when setting up an active crossoverloudspeakerbecausetheearissensitivetotheaveragedresponseandnoticesifthere is a shelf in the relative response between adjacent drivers. Thesignificanceofa0.2 dBerrorbeingjustperceptibleisthatifthevolumecontrolis to be placed after an active crossover, its channelmatching errorsmust be<0.1 dB,implyingthataTypeA-steppedattenuatorusing2%toleranceresistorsispermissible,but1%preferable.Sadly,aTypeBattenuatorwouldbeunsuitableunlessallresistorswere0.1%orbetter,substantiallyincreasingcost.

VolumeControlValuesandTheirEffectonNoise

Avolumecontrolusingresistancetoachieveattenuationmustproducenoise.Aresistivevolumecontrol’snoisecanbecalculatedeasilybyassuming that it isdrivenfromasourceofzeroresistance.Thisassumptionfoldsthetoparmofthepotential dividerover, and the (zero resistance) signal source canbe removed,leaving two resistors in parallel, which can be combined into one resistorproducingnoise(seeFigure7.6).

Figure7.6Thenoisesourcesinapotentialdividervolumecontrol.

Thethermalnoiseiscalculatedusing .Ifwesetbandwidthto19,980 Hz(20 Hzto20 kHz)andtemperatureto20°C,thissimplifiesto:

Theabsolutelevelofthermalnoisegeneratedattheoutputofavolumecontrolisnot especially useful because the output level changes with volume controlsetting.Whatisneededistoapplyastandardlevel(2 VRMS)totheinputofthevolumecontrolanddeterminetheS/N(Signal-to-Noise)ratioattheoutputofthevolumecontrolforeachattenuationsettingandplotitasagraph(seeFigure7.7).

Figure7.7TheeffectonS/Nratioofself-generatednoiseinavolumecontrol.

ThegraphcomparestheS/Nratioofa100 kΩTypeA(tappedchain)againstaTypeC(switchedshunt)usingafixed100 kΩseriesresistor,andshowsthatasattenuationincreasesthetwocontrolsbecomecomparable,butthattheTypeAhasaclearadvantageatlowattenuations.Theshapeofthecurvesisalwaysthesame,sotheycanbeusedtopredictS/Nratioforanyresistancevalueorsignallevel.Resistorsproducenoiseproportionaltothesquarerootoftheirresistance,soitfollowsthathighervaluevolumecontrolsproducemorenoise,andthechangeinnoisecausedbychangingthevalueofavolumecontrolcanbefoundusing:

Scalingavolumecontrol’svaluebyafactorof10changesthenoiseby10 dBandafactorof5by7 dB,soexchanginga100 kΩcontrolfora1 MΩcontrolincreasesnoiseby10 dB,whereasexchanginga100 kΩcontrolfora20 kΩcontrolreducesnoiseby≈7 dB.Reducing the input level reduces the S/N proportionately, so transistorelectronicsstandardisedon400 mVRMSusesa5 kΩvolumecontroltoachievealmostidenticalvolumecontrolS/Ntovalveelectronicsusinga100 kΩvolumecontrolbutstandardisedon2 VRMS.AnotherwayofgeneratingnoiseatavolumecontrolistoallowDContoit.Thisshould never occur because the preceding stage will always have a couplingcapacitortoblockitsDCfromthenextstage,butaleakycapacitorwouldcausenoise,ascouldsignificantgridcurrentfromthenextstage.

Grid-LeakResistorsandVolumeControls

Thegrid-leakresistorof thefollowingstagecausesaproblemfor tworeasons.Firstly, although the previous stepped attenuator programs were designed toaccount for it, any error in its value increases attenuation errors. Secondly, itcauses the input resistance of the volume control to vary as attenuation ischanged from maximum to minimum. These two potential problems warrantfurtherinvestigation.TheTypeAsteppedattenuator inTable7.1wasdesignedtobeloadedbya1MΩ grid-leak resistor. Changing the value of this load resistance affects themaximumattenuationerror(0.053 dB),so+10%causesthemaximumerrortorise to0.060 dB,and−10%causes it to rise to0.073 dB.Although this isan

almostnegligibledegradation,itisnotdifficulttoensurethattheloadresistanceiswithin1 MΩ±10%.When the volume control feeds a self-biassed cathode follower, the grid-leakresistorisbootstrapped(seeFigure7.8).

Figure7.8Aself-biassedcathodefollowerbootstrapsitsgrid-leakresistor,greatlyincreasinginputresistance.

Bootstrapping increases the effective resistance of the grid-leak resistor (seeChapter2)andthereforetheloadingresistanceimposedonthevolumecontrol.Forminimumerror,theloadingresistanceshouldbemeasuredorcalculatedand,ifnecessary,aresistoraddedinparallelwiththeoutputofthevolumecontroltomaintaintheexpectedloadingresistanceof1 MΩ.A1 MΩgrid-leak resistance inparallelwith a100 kΩvolumecontrol set tominimumattenuationcausestheinputresistanceofthevolumecontroltobe91kΩ,butasmaximumattenuationapproaches, its input resistancerises towardsits nominal value of 100 kΩ. If the volume control is part of a filter, thischanging resistanceupsets theaccuracyof that filter. If the filter is simply thearbitrary 7,950 μs (20 Hz) high-pass filter of an RIAA stage, then a 10%changeisnotaproblem,butifitwerepartofthecritical75 μssection,a10%changewouldbecompletelyunacceptable.Thereisthereforeagreattemptationtodiscardtheformalgrid-leakresistor,recalculatethevolumecontrolandgainthebenefitofanunchanginginputresistance(seeFigure7.9).

Figure7.9Bewareusingthevolumecontrolasthegrid-leak.

The switch contacts are typically projecting studs, and the wiper is pressedagainstthembyaspring.‘Makebeforebreak’switchesaredesignedsothatthewipercontactsthenextstudbeforeleavingthefirst(therebymaintainingcontactwith theresistorchainatall times),butas thewiperrotatesandtransfersfromone stud to another there is apossibility that itmaybounceandbreakcontactwithbothstuds.Ifthewiperdoesbounceandwehaveomittedtheformalgrid-leakresistor,thefollowingvalve’sgridfloatsanditbecomesadiodewithonlytheanodeloadresistortolimitcurrentflow.Theanodevoltagefallssharply,andwhenthewiperresumescontact,theanodereturnstoitsdesignvoltageequallysharply.Dependingonthedesignofthestage,wiperbouncecouldeasilycause>50 V pk–pk spikes at the anode. Because the spikes are (hopefully) of shortduration, theyarecomposedmostlyofhigh frequenciesandwillbeattenuatedby any shunt capacitance; nevertheless, they could be sufficient to damage asucceedingtransistoramplifierorribbontweeter.

BalancedVolumeControls

Itmay be that youwant to build a balanced pre-amplifier. Inwhich case, thevolume control should be balanced too. Curiously, people persist in placingnotionally identical controls ineachpath of each channel.This iswrong.Thetwomechanicallygangedattenuatorscannothaveperfectchannelmatching,soacommon-mode noise signal such as hum must be attenuated unequally,converting a proportion of it to differential mode, to which a balanced pre-amplifier is sensitive.Thecorrectway toconstructabalancedvolumecontrol,using the minimum number of components, is to use a balanced Type Cattenuatorhavingafixedseriesresistorineachleg(seeFigure7.10).

Figure7.10Balancedvolumecontrol.

ThereasonthatthebalancedTypeCconfigurationinsuperioristhatdegradationof common-mode rejection is reliant solely on thematching of the two fixedseries resistors,which should thereforebe0.1% toleranceorbetter. Ifyouusethecomputerprogramtodeterminevalues,rememberthattheseriesresistorthatthe program uses is twice the value of the series resistor in each leg.Unfortunately, the Type C attenuator has the disadvantage of a high outputresistancewhensetforasensibleinputresistanceand,incombinationwiththeinput capacitance of the following stage, this causes high frequency loss ifignored.

Light-SensitiveResistorsasVolumeControls

Cadmium sulphide (CdS) light-sensitive resistors such as the ORP12 areoccasionallymootedaspossiblevolumecontrolelements.Asanexperiment,theauthorfittedapairofORP12light-sensitiveresistorsintoacarefullymachined2"-longaluminiumtube,oneateachend,andaddedlight-tight seals. A 28 V 40 mA incandescent lamp was fitted axially midwaybetween the two resistors with a light-tight seal. One ORP12 had a darkresistanceof≈5 MΩ,andtheother100 kΩ.Whenfullyilluminated,onehadalightresistanceof69 Ω,andtheother63 Ω.Clearly,wewouldneedtoselectthesedevicestohaveanyhopeofmakingastereovolumecontrolthattracked.Whena1 kHzsinewaveat+30 dBuwasappliedviaa10 kΩseriesresistor,withtheresistorsdark,1%distortionresulted(puresecondharmonic).Oncetheinputlevelwasreducedto+8 dBu(2 VRMS),thedistortionfellto0.02%.Astheresistorswereilluminated,bothoutputvoltageanddistortionfell(Table7.2).

Table7.2ComparisonBetweenLight-SensitiveResistorandTypeASwitchedAttenuatorCdSattenuator TypeAswitchedattenuator

Distortion Benign(secondharmonic) Barelymeasurable

Distortion Benign(secondharmonic) BarelymeasurableChannelmatching Poor,needstobeselected Easilybetters0.05 dBLogarithmiclaw Poor EssentiallyperfectEaseofconstruction Difficulttomakelight-tight Slightlyfiddly

Providedthatlight-sensitiveresistorselectioncouldreducethechannelmatchingerror to acceptable levels, the logarithmic law problem could be solved byadding a correction signal to the illumination control current derived via amicrocontroller’s internal 8-bit DAC driven by a look-up table; look-up tablevalueswouldbeadjusteduntilthelawwasacceptable.BewarethatLEDseasilyrespond to 1 μs pulses and although CdS resistors tend to be sluggish bycomparison,noisecouldstillbecoupledintotheaudiofromthecontrolcurrent,soincandescentilluminationcouldbeabetterchoice.Classicvalvecompressorssuccessfullyusedilluminatedlight-sensitiveresistorsas a means of controlling gain because 0.02% of pure second harmonicdistortion is quite good performance for an electronically controlled gainelement. A volume control doesn’t need fast-responding electronic control ofattenuation,sowhytolerateeven0.02%distortionandpoorchannelmatching?

TransformerVolumeControls

The previous volume controls have all attenuated the signal by interposing avariable resistance, but in doing so their output resistance has always beenhigherthanthesourceandtheyhaveaddednoise.Arecentlyfashionablemethodofcontrollingvolumehasbeentouseaswitchtoselect between different tappings on a transformer. The stated advantages arethat the transformeractually reduces source resistancebecause it isdividedbythesquareoftheselectedturnsratio(althoughwindingresistancesareinseries)and that there isno lossof signalenergy (true,but irrelevant).Perfectchannelmatching is a given with transformer volume controls because attenuation isdetermined by the turns ratio (counted by a machine), and the significantlyreducedinternalresistancereducesnoisecomparedtoaresistiveattenuator.Justliketheresistiveswitchedattenuator,thecontrolhasalimitednumberofsteps,notjustbecauseofswitchlimitations,butalsobecauseofthepracticaldifficultyofmakingalargenumberoftransformertaps.Fortuitously, the large number of taps tends to force a large coil former andcorrespondingly largecore,and the levels tobecoupledarequite low,socoreflux densities are low, enabling a mu-metal core, which greatly increasesprimary inductance over grain oriented silicon steel. Taken together, low coreflux density and high primary inductancemean thatwe should not expect theusual transformer bugbear (distortion at low frequencies (LFs) and high

amplitudes)tobenoticeable.Lowfrequencydistortionfallswithlevelbutriseswith source impedance, so the<0.1%distortion at 20 Hz froma 5 Ω sourceeven at +30 dBu (24.5 V RMS ) achieved on test by a Stevens& BillingtonTX102transformervolumecontrolconfirmsthatlowfrequencydistortionisnotaproblem.However, high frequency response is somewhat more problematic because asattenuation increases, the secondary tappingmoves to use less and less of thecoil, so coupling becomes poorer and leakage inductance rises, causing eitherultrasonic ringingorhigh frequency loss,dependentonvolumecontrol settingand source resistance.With good design, these defects can beminimised, buttheyremainlargerdefectsthanfoundinaresistiveattenuator.Therealadvantageoftransformervolumecontrolsisnotthattheyattenuatethesignalmore faithfully than a resistive attenuator (they don’t), but that becausetheyarea transformer, theybreak theearth loopsbetweenequipment that addbroadband noise. Noting the eyebrow-raising price of volume controltransformers and their limited number of coarse taps, the authorwould ratherbreakearthloopswithawell-balancedinputtransformer,andthenusearesistiveattenuator.

BalanceControlIt isperfectlypossibletomakeabalancecontrolusingapairofreducedrangeswitched attenuators, but we will see shortly that law-faked balance controlsusingconductiveplasticlinearpotentiometerscanbesogoodthatit’ssimplynotworththetrouble.

LawFaking

Onewayof approximating a logarithmic lawwith a linear potentiometer is toadd a stand-off resistor between its lower leg and ground and a law-fakingresistorbetweenwiperandground(seeFigure7.11).

Figure7.11Fakingalogarithmiclawfromalinearpotentiometer;arrangementofresistors.

Thissimplesolutioncan’tturnalinearpotentiometerintoaperfectlogarithmicpotentiometer,but asTable7.3 shows, itworksverywell forbalancecontrolswhereonlyalimitedrangeofattenuationisrequired.

Table7.3RequiredResistorValuesforLawFakingMaximumattenuation(dB) Worsterror(dB) Stand-offresistorratio Fakingresistorratio Minimuminputresistanceratio26 2.4 0.0582 0.1674 0.145±8 0.51 0.25 0.5916 0.402±6.1 0.22 0.4706 1 0.595±4 0.085 1 1.988 ≈1±3 0.025 1.5 3.204 1.404

Example:A100 kΩlinearpotentiometerisavailableandneedstobelawfakedtogivethebestapproximationtologarithmicattenuationover0–26 dBofrange.Thestand-offresistorbecomes100 kΩ×0.0582=5.82 kΩ(5k6 Ωinserieswith220 Ω), and the law-faking resistor becomes 100 kΩ×0.1674=16.74 kΩ (18kΩ in parallel with 240 kΩ). However, the input resistance of the volumecontrolisnolongerconstantandfallstoaminimumof100 kΩ×0.145=14.5 kΩ

–wepayaheavypriceforattemptingtolawfakeoversuchawiderange.The remaining four attenuators are intended tobeusedasbalancecontrols, sothey are defined by their deviation from mid-position rather than maximumattenuation,anditisassumedthateachisfollowedbygainequaltoitsdeviationfrommid-position.Although the±8 dBoption still has a somewhat onerous input resistance, theremainingthreeoptionsareperfectlyusableandallhavebeendesignedtogivesymmetricalattenuationaboutmechanicalcentre(seeFigure7.12).

Figure7.12Deviationfromlogarithmiclawagainstrotationforthefourlaw-fakedbalancecontrols.

If we pan a camera across a small bright light, we don’t expect the light’sbrightnesstochangeaswepan,sowedon’texpectanaudiosourcetochangeitsvolume if we use a balance control to alter its apparent position between theloudspeakers.Balancecontrolsshouldbeconstantvolume.Symmetricalattenuationisanessentialrequirementforaconstantvolumestereobalance control because although the attenuator in one channel is wiredconventionally (attenuation decreases clockwise), the attenuator in the otherchannel must be wired in reverse (attenuation increases clockwise).Asymmetrical attenuation could still allow electrical centre to correspond tomechanicalcentre,butadjustmentofthecontrolawayfromcentrewouldchangeperceivedvolume.Thesignificanceofthe±6.1 dBattenuatoristhatitusesafakingresistorequalto its value, implying that an existing 100 kΩ volume control could beimmediatelyprecededbya tandem100 kΩlinearpotentiometer (perhapswithcentre detent) plus 47 kΩ stand-off resistors, making a very simple constant

volumebalancecontrolhavingarangeof±6.1 dB.However,theadditionofsuchabalancecontrolmeansthatthevolumecontrolisno longerdriven froma sourceof zero resistanceand thatmust affect its law.Worse, once the balance control is moved from its centre position, eachchannel’s volume control is driven from a different resistance and there is adanger that rather than the balance control causing the desired fixed inter-channelbalancedifference, itmightcauseadifferencethatvarieswithvolumecontrolsetting(seeFigure7.13).

Figure7.13Worstcasebalanceerroragainstattenuationfornominal100kΩTypeAattenuatorplus±6.1 dBbalancecontrol.

Thegraphshowsthecalculatedinter-channelbalanceerrorofanominal100 kΩTypeA-steppedattenuatorprecededbya±6.1 dBlawfakedbalancecontrolasdescribed.Thebalancecontrolhasbeenswunghardtooneendtoproducea12.3dBdifference in level between the channels and it canbe seen that theworstdeviation from this is0.2 dBat full volume.At a farmore reasonable settingwherethebalancecontrolcausesa3 dBleveldifferencebetweenchannels,theworstcaseerrorfallstoanentirelynegligible0.042 dBatfullvolume.The±6.1dBlaw-fakedbalancecontrolhas tworemainingniggles thatwillprobablygounnoticedinpracticebutshouldbementionedforcompleteness:•Retrofittingthebalancecontroltoasteppedattenuatorsignificantlyworsensits deviations from true logarithmic law (typically from±0.06 dB to±0.27dB)becausesourceresistanceisnolongerzero.However,sincetheprimaryjustification for a stepped attenuator was good channel matching, and thisremains unchanged, so <0.3 dB deviations from strict logarithmic law areentirely acceptable. If absolutely necessary, the stepped attenuator could beredesigned to account for the mid-position output resistance of the balancecontrol.• Input resistance drops to 59.5% of volume control resistance. This isunlikely to be audible, but the change from 100 kΩ to 59.5 kΩ input

resistance just might cause a measurable change in frequency response ordistortion of the previous stage. If this is a problem, dropping to ±4 dBbalancerangebyusinga50 kΩbalancepotentiometerwith100kΩstand-offresistor raises the minimum input resistance to that of the original volumecontrol.

Althoughthe±4-dBand±3-dBoptionscanbeusedasconstantvolumebalancecontrols, their more likely use is as analogue fine gain trimmers in activecrossovers.Asanexample,ifanactiveloudspeakerhadjustbeenbuiltandwasbeingcalibrated,itwouldbeveryhandytouseVishayT73trimpotsas±3 dBgaintrimmersbecauseeachoftheirmarkingswouldcorrespondto1/2 dB,soameasured 3/4 dB gain discrepancy on one driver could be quickly correctedwith confidence. The ±3 dB option can be particularly convenientlyimplemented using a 50 kΩ potentiometer plus 75 kΩ stand-off and 160-kΩfaking resistors (or in semiconductor electronics, 5k potentiometer, 7k5 Ωstand-off,16 kΩfaking).Finally, remember that the centre attenuation of any balance control must bemadeupelsewhere,sofittingthe±6.1 dBbalancecontrolrequirestheadditionof6.1 dBgain.

CableDriverThemostcommonreasonforneedingacabledriveristhatthepoweramplifiershavebeensitedadjacenttotheloudspeakersinordertominimisethelengthandconsequent resistance of loudspeaker cable, but that the sources and volumecontrol have been placed conveniently to hand at the listening position,necessitatingalongcabletothepoweramplifiers.

DeterminationofRequiredQuiescentCurrent

Once cable is routed inconspicuously from one point to another, its requiredlengthquicklyescalates.Ifweassumethatthecableis20 mlong,typicalcablecapacitance of 100 pF/m would produce a capacitance of 2 nF. If we alsoassumetransistorpoweramplifiers (!),weshouldadda further1 nF,givingatotalloadcapacitanceof3 nF.Ifwewanttorestrictthelossat20 kHzto0.1dBwhendrivingthiscapacitance,wemustsetf−3dB=131 kHz,whichrequiresasourceresistanceof≈400 Ω.Almostanyvalveusedasacathodefollowercanachievethissmall-signaloutputresistance,butthemoresignificantquestioniswhetheritcansupplytherequiredcurrentwithoutdistortion.Thereactanceofacapacitorfallswithfrequency,sowetaketheworstcase,andfindthereactanceat20 kHz:

Ifweassumethat thepoweramplifiershaveasensitivityof2 VRMS ,drivingthemtofullpowerat20 kHzimpliesapplying2 VRMSacross thisreactance.ByOhm’slaw,thisrequiresacurrentof:

Whenwe consider loadlines and valve operating conditions,wemustwork inpeakcurrentsandvoltages,so750 μARMS≈1 mApk .Becausethiscurrentisrequiredbyacapacitor,itforcesatypicalloadlinetochangefromastraightlinetoanellipse(seeFigure7.14).

Figure7.14Ellipticalloadlinecausedbycapacitiveload.

The diagram is somewhat exaggerated to aid clarity because our cathodefollower will not need to swing as many volts as shown, but the effect of acapacitiveloadcanbeclearlyseen.Drivingthecablecapacitanceforcesourlinestagetoswingvertically±1 mAwithoutanychangeinvoltage(thisisduetothe90° lagbetweencurrentandvoltage inacapacitor).Asanabsoluteminimum,the(ClassA)linestagemustpass1 mAofquiescentcurrentsothatitcanswing1 mAtotheloadwithoutswitchingoff.

ChoiceofFollowerValve

Toachievegoodlinearityinthefaceofaheavyreactiveload,acathodefollowerneedsplentyofdistortion-reducingnegativefeedback,soμneedstobeaslargeas practicable. More importantly, we need g m to be constant with currentbecause we know that our elliptical loadline forces changing current. Sadly,constantgm inthefaceofchangingIa is impossible,but thevalvethatcomesnearest is the Russian 6C45 π single triode (other possibilities are triode-strappedD3a,or6H30P)(seeFigure7.15).

Figure7.156C45πanodecurves.

Looking at the curves, we find that once I a >5 mA, the curves are nearlystraight, and bunching (which reducesgm andμ ) is almost non-existent.Weknowthatourquiescentcurrentmustbe1 mAclearofbunching,sowecouldoperatethevalveatIa=6 mA,butthiswouldbealittlemarginal,and10 mAwouldbebetter.NowthatwehavechosenIa,weneedtosetVa.ThemainlimitationonVaisthatitmustallowustoavoidgridcurrentatourchosenIa .IfwechooseVgk=−2.5 V, this isnicelyclearofgridcurrent,andsetsVa=170 V.Ifweusea390 V HT (in common with the EC8010 RIAA stage), we must drop 390V−170 V−2.5 V=217.5 V,and if thispasses10 mA,a22 kΩ load resistorwould be required. Even for the 6C45 π, this is amoderately steep loadline,which increases distortion before feedback, sowewill use anEF184 constantcurrent sink (CCS) to force the resistive component of the loadline to behorizontal(seeFigure7.16).

Figure7.166C45πoperatingconditionsinunitygaincabledriver.

PracticalConsiderations

Adding the EF184 CCS dramatically reduces distortion, but adds practicalproblems related to g 2 . Firstly, under these conditions, to sink 10 mAat itsanode,theEF184requires4.4 mAofg2current,increasingtheHTcurrentforastereopairtoalmost30 mA.Secondly, if the6C45 π should fail todrawcurrent for any reason,g 2of theEF184wouldactasananodeandpassthefullprogrammedcurrentof14.4 mA,causingitsdissipationtoriseto2.5 W whichwoulddestroyg2.Thisg2problemiscommontoallpentodecircuitry,andiscommonlysolvedbysupplyingg2viaaresistor,whichlimitscurrent,sothe39 kΩresistorprotectsg2inthiscircuit(seeFigure7.17).

Figure7.17Lowdistortionunitygaincabledriver.

However,wecanimprovetheperformanceofanypentodecircuitbysupplyingg2fromalowimpedancesupply(becauseIaisfarmoredependenton thanVa ), but this offers no protection against the g 2problem. If a simple regulatorsuchas theTHINGY(seeChapter5 )wereused to supplyg 2 , the largeandexpensive3.3 μF400 Vcapacitorcouldbereplacedbyasmallercollectionofcheap components offering better performance, but there would then be noprotectionagainsttheg2problem.AlthoughtheEF184ischeap,wewouldstillpreferthemtodieofnaturalcausesratherthanbeingmugged.If thiscircuitwaspoweredinthetraditionalfashionusingavalverectifierandallsuppliesoriginatingfromonetransformer, theEF184mightheatfaster thanthe6C45π,leavingtheEF184vulnerabletotheg2problem.Thus,theTHINGYwasreluctantlyrejected,andthelowerperformanceoptionofsupplyingg2viaaresistorwasadopted.The 6C45π is self-biassed by the voltage dropped across the 240 Ω cathode

resistorbecausefixedbiasfromapotentialdividerchainwouldinjectHTnoiseinto thegridcircuit.Because themeasured inputcapacitancewasonly11 pF,this factor does not restrict the choice of volume control, but distortion roseslightly(from0.02%to0.05%at+20 dBu)whenthesourceresistanceexceeded150 kΩ, suggesting that therewas some grid current.A subsequent test on amodified AVO VCM163 confirmed the hypothesis, as DC grid current wasfoundtobeconstantat≈0.1 μAwhenVgkwassweptfrom−1 Vto−3 V.Givenhalfachance,the6C45πoscillatesenthusiasticallywhenconfiguredasacathode follower. The HT must be locally bypassed to ground at radiofrequencies, hence the 100 nF polypropylene capacitor from the anode pin toground (polyester might be too lossy at radio frequencies to adequatelydecouple).Inaddition,1 kΩgridstopperand200 Ωcathodestopperresistorswere essential to suppress oscillation at 70 MHz. If you don’t have anoscilloscopethatcanreliablyseesuchahighfrequencyatitsprobetip,itmightbeworthwhile toraise thegridstopper to4.7 kΩ.Similarly,becausegm≈16mA/Vattheoperatingconditions,thecathodestopperresistorcouldberaisedto330 Ω,andstillkeeproutbelowtherequired400 Ω.PassingIa=10 mAthroughtheEF184withVa=221 VmeansthatitdissipatesP a=2.2 W, which is close to the 2.5 W limit, but the EF184 is cheap andplentiful,soweneednotworryaboutareducedlifetime.TheDCconditionsofthe EF184 were determined in the usual way, but the value of the cathoderesistoriscriticaltosettheanodecurrentcorrectlyto10 mA,soitmayneedtobeadjustedontest.Theeasiestwaytomeasureanodecurrentistomeasurethevoltageacrossthe240 Ω6C45πcathoderesistorusingaDVMandthenadjusttheEF184cathoderesistoruntil2.4 Visseen.

AddingGain

Once a balance control has been added, its mid-position attenuation must becorrected, and the easiest way to achieve this is to direct couple a commoncathode gain stage to a cathode follower, and then wrap negative feedbackaroundbothtoachievetherequiredlowgain(probably6.1 dB).Parallelderivedfeedback further reducesoutput resistance,but the feedbackcouldbe seriesorparallelapplied.Seriesappliedfeedbacktotheinputvalve’scathodeforcesaverylowvalueoffeedback resistor, steepening thecathode follower’s loadlineand increasing itsdistortion before feedback. Parallel applied feedback allows a larger feedbackresistor but requires a large resistor in series with the input valve’s grid that

increases thermal noise and potentially converts input valve grid current intodistortion.Theinputvalvemusthavelowgridcurrent,andhigh-μallowsmorefeedback,making an ECC83 loadedwith a CCS a good choice because its gain is thenequaltoμ(typically90).AninsipidgreenLEDdropsabout1.8 Vat300 μA,convenientlybiassingtheECC83.Theinputresistorloadsthevolumecontrol,soitmustbe1 MΩ,andthiswillgenerate18 μVRMSofnoise;−101 dBreferredto2 VRMS,soitisjusttolerable.Rearrangingthestandardfeedbackequation,wehave:

Fromwhichwecanfindthefeedbackresistor:

The standard E24 value of 2M2 will do and certainly not load the cathodefollower.Wehavereducedgainfrom90to2,correspondingtoafeedbackfactorof45,sothecathodefollower’soutputresistanceanddistortionwillbereducedby a factor of 45. Such a large reduction in output resistance and distortionmeansthat,provideditpassessufficientcurrent(≈10 mA),weneednotworrytoo much about its exact operating point (just as well, because the ECC83’sanodecouldbeanywherebetween130 Vand200 V),soanE88CCloadedbyaCCSwilldoverynicely(seeFigure7.18).

Figure7.18ECC83/E88CCanodefollower.

Itappearsasifthevolumecontrolisbeingusedasthegrid-leak,andthiswouldnotbeideal,buttheECC83’sgridhasaDCpathto0 Vviathe2M2feedbackresistorand1 Moutputresistor–soitisvitaltoincludethatoutputresistor!

PolarityInversion

Notethataddinggaintothecabledrivercausedaninversionofoutputpolarity.Everysooftena fuss ismade in theHi-Fipressabout ‘absolutephase’,1withclaimsthatsometracksofsomerecordingssoundmorerealisticwheninverted.There is a reason why reproduction could sound different with one polarityratherthantheother,butit’snothingtodowithincorrectrecordings.Distortionoccurs once a loudspeaker cone changes the volumeof air in its enclosure by>5%,andbecausethatdistortiondiffersbetweencompressionandexpansion,asoundsuchasabassdrum(whichcontainsasignificantDCcomponent)soundsdifferentreproducedonsuchaloudspeakerdependentonsignalpolarity.Thisisanother reason for the author’s earlier assertion that any loudspeaker smallerthanadomesticwashingmachineissmall–a15″driverinawashingmachine-sized enclosure reproduces bass with far lower distortion than a long-throwdriverstrainingashoebox.1. Strictly, it’s polarity, but an engraved “Φ” takes up far less roomon amicrophone body or clutteredcontrolpanel.

Polarity is importantwhen recording andparticularlymixing. It is common tousetwomicrophoneswhenrecordingasnaredrum,oneinside,oneoutside–therelative balance between the two microphones adjusts the recorded sound’stimbre.When the skin is struck, it moves towards onemicrophone and awayfromtheother,soonemicrophonemusthaveitspolarityinvertedtopreventLFcancellationwhen they are summed in themixer. Butwhich has the ‘correct’polarity?Theinsidemicrophone,ortheoutside?Inshort,theauthorconsidersabsolutepolaritytobefloobydustwhenitcomestoreproduction,butyoumighthaveadifferentviewandwish toensure thatanyunavoidablepolarityinversioniscorrected.

ToneControlIfatonecontrolistobeincludedtocompensateforpoorrecordings,thenitmustbe implemented carefully. Experimentation with the Tone Stack Calculatorfreeware (available from theDuncanampswebsite) will quickly convince youthatalthoughtheJames[3]controlistheleastworstofthepassiveRCbunch,itrequireslogarithmiccontrolstoevenapproximatetoaflatelectricalresponseatmechanicalmid-position.TheonlyplausibleHi-Fi tonecontrol (asopposed toelectricguitareffects)isthenegativefeedbackBaxandall[4]controlbecauseitachieves a flat response with linear controls at their mechanical mid-position(seeFigure7.19).

Figure7.19Noiseintheinputstage.

As originally presented, Baxandall’s tone control offers an absurd amount(theoretically20 dB)ofboostandcut.Althoughsuchanamountmightbeusedto achieve a particular sound when recording, 20 dB of ‘correction’ duringreproductionisexcessiveand±10 dBisquiteenoughtoallowthesweetspottobefoundquicklybyapplyingtoomuchcorrectionthenbackingoff.Notethatthereisn’tanexplicitgrid-leakresistor–thecontrolgrid’spathto0 Visviathewiperofthebasscontrolandthecentretapofthetreblecontrol.Thisisnotagoodpracticeasitwillultimatelyleadtonoiseasthebasscontrol’swiperismoved.Rememberingthatthestageisessentiallyaunitygaininverter,Baxandallstatedthatahigh-slope(highgm)pentodewasnecessaryfortworeasons:

•Cagispartofthefeedbackimpedance,soitshouldbeminimised,otherwisethefulltrebleboostwillnotbeavailable.EF37A:Cag<0.02 pF;6SN7:Cag≈4 pF.

•ItensuresthatA0≥100inorderthatthereisstillenoughfeedbackavailableevenwhenfullboost(A=10)isinvokedtokeepdistortionlow.

Reducing themaximum correction from 20 dB to 10 dB slightly relaxes theopen-loop gain requirement, butminimisingC ag stillmakes sense. Baxandallrecommended the EF37A (precursor to the EF86) because its top-cap gridconnection avoided the grid to heater leakage resistance of the phenolic octalbasethatwouldotherwisecausehum.Top-capgridsareanuisance,sopossiblealternativesareshowninTable7.4.

Table7.4ComparisonofPossiblePentodesforBaxandallToneControl

aManufacturer’sspecificationusingcentre-tappedACheater.

Cag(fF) Typicalgm(mA/V) Humatgrid(μV)a CommentsEF37A <20 1.8 Notspecified NOSavailableEF86 <50 2.2 2 NOSrare,expensiveandoftennoisyE180F <30 7 100 NOSavailableEF184 <5.5 15 Notspecified NOScheapaschips

BoththeEF37AandEF86havehelicallywoundheaterstoreducethemagnetichumfield.SacrificinganE180FandanEF184tosciencerevealedthatbothhadconventional loop heaters, explaining the far poorer E180F hum specificationandsuggestingthatbothEF184andE180FwouldneedDCheaters.Humaside,the EF184 is the stand-out modern contender because not only does it havesuperior specifications to the other valves, but it’s also cheap. Itwas time forsomeEF184pentodemeasurements.Perusing the Mullard EF184 pentode mutual characteristics suggested that

,andVgk=−2 Vought toresult inIa≈10 mAand .For a sensible HT voltage, this indicated a 10 kΩ anode load and a 27 kΩscreengridresistor;theauthorhad11 kΩ5 Wand27 kΩ2 W,andagoodfittotheforwarddropofatypicalinsipidgreenLEDis:

Thus,aninsipidgreenLEDdrops≈2 Vat14.5 mAandcanbeusedtocathodebiastheEF184(seeFigure7.20).

Figure7.20EF184pentodedistortiontestcircuit.

AbogeyEF184havingDCcharacteristicsthatreasonablymatchedtheMullarddatasheetandaveragedistortionwasselectedfromastockof33EF184s.Thestage produced 3% distortion at the author’s standard test level of +28 dBu,dominatedbythirdharmonic,whichwasn’tatallpromising.Thegainof42 dBwas a little lower than expected, so a 4,700 μF cathodebypass capacitorwasadded to see if the LED’s predicted 112 Ω slope resistancewas significantlyreducing gain. Adding the capacitor increased the gain by 1 dB but rosedistortionby2 dB,soitwaspromptlydiscarded.Sincewe know that a tone control invariably follows the volume control andprecedesthepoweramplifier,wealsoknowthatitisunlikelytohavetodevelopmorethan2 VRMS(+8.2 dBu)atitsoutput,sotheoutputtestlevelwasdroppedto +8 dBu.At +8 dBu, the distortionwas 0.28% (which iswhat one shouldexpect, dropping level by 20 dB), but more importantly distortion wasdominated by second harmonic. Itwas clear that itwas necessary tomeasureindividualharmonicsagainstlevel(seeFigure7.21).

Figure7.21EF184pentodedistortionharmonicsagainstlevel.

It’s best not to look at EF184 pentode distortion after looking at SN7/N7distortion,butprovidedlevelis<+10 dBu,it’snottoobad.Moresignificantly,mostofthe42 dBopen-loopgainwillbeusedasnegativefeedbacktoreducedistortion.Asaroughexample,if30 dBofthegainwasusedasfeedback,at+8dBuweshouldexpectH2≈−80 dBandH3≈−105 dB(becauseTHD<1%,H3generatedbynegativefeedbackwillbenegligible).Testingthestageasaunity-gaininverterat+8 dBu,theauthormeasuredH2=−83 dBandH3=−95 dB(theH3wasprobablytestsetresidual).Moresignificantly,thestagedidn’tburstintoRFoscillationwithacapacitiveloaddirectlyonitsanode,presumablybecauseoftheEF184’sastonishinglylowCag.Likeallfrequency-selectivefeedbackamplifiers,theBaxandalltonecontrolhasan input impedance that changes horribly with frequency, so unless thepreceding stage has plenty of feedback and current capability, this frequency-dependent loadline is converted into frequency-dependent distortion, which isalmostcertainlywhytonecontrolsaresofrequentlyvilified.It’snotthatthetonecontrolstageitselfdistorts,butitmakesthepreviousstagedistort,andworse,itcauses frequency-dependent distortion that is especially fatiguing because itforcestheeartoattempttorejectacomplexpatternthatchangeswithfrequencyrather than a simple fixed pattern. The Baxandall tone control stage must beprecededbyastagecapableofdrivingachanging impedancewithconstantornegligibledistortion.GiventhattheBaxandall tonecontrolinvertspolarity, itwouldbeusefulif theprecedingstagealsoinvertedpolaritybecausethiswouldrestorecorrectpolarity.Combinedwith the current drive anddistortion requirement, this suggests that

theidealprecedingstagemightbeanotherunity-gainpentodeinverteridenticalto that in the tone control.Admittedly, this becomes expensive inHTcurrent,but that’s the price of a decent tone control. Self [5] offers a much fullerdiscussionoftherelativemeritsofthedifferentformsofBaxandalltonecontrol,so this author will simply content himself with presenting a version that hebelievesisappropriatefordomesticreproduction(seeFigure7.22).

Figure7.22ContemporaryimplementationofBaxandalltonecontrol.

The high gm of the EF184 allowed a much smaller anode load resistor thanBaxandall’s,enablingalowerimpedancefrequency-selectivenetworkusing100kΩ potentiometers. Thus, a fully featured pre-amplifier could use the samemodelofconductiveplasticcentredetentlinear100 kΩpotentiometerforbass,treble and stereo balance. The 33n capacitors associatedwith the bass controlneedtobe1%tolerancetoensureaflatresponseat thecontrol’smid-position.Note that the lossof the treblecontrol’scentre taprequires the inclusionofanexplicitgrid-leakresistor.Thetonecontrolhasbeenconfiguredtobeasymptoticto≈9.6 dBofboostandcutforbothbassandtreble,althoughaslightlysmallerrangeisseenwithinthe20 Hzto20 kHzaudiobandwidth(seeFigure7.23).

Figure7.23BasicRIAApre-amplifier.

Ratherthanusinginfinitelyvariablepotentiometers,themeasuredresponsewasobtainedbyconstructingtwochainsoften10 kΩ1%resistorstomake100 kΩcontrols.Thus,accuratetappingswereavailablecorrespondingto10%intervalsofmechanical rotation. In addition, theEF184 gain stage used a 5 μF outputcouplingcapacitorinordertoplaceitslowfrequencylossatasufficientlylowfrequencythatitcouldnotdisturbtheBaxandallcurves.Ascanbeseen,notonlydoes the control have a flat response at mechanical centre, and very nearlysymmetricalboostandcut,butalsotheamountofboostandcutnearlyfollowsalogarithmic law with mechanical rotation, implying that the control will feelnaturaltouse.Thediscontinuitiesat1 kHzoccurbecausebassresponseswereplottedupto1 kHzandtrebleresponsesdownto1 kHz,butbothresponseshadtailsthatextendedalittlefurtherinfrequencythatwerenotplotted.Because the control has plenty of feedback at all settings, output resistance islow,andwith10 mAofanodecurrent the stage shouldbecapableofdrivingcablecapacitance.Thecontrolsweresetformaximumbassandtreble,andthestagedrivenat20 kHztoproduce2.5 VRMSatitsoutputwithaloadof≈300pF,andthiswaveformwasstoredasareference.Whenloadedwith6 nF,thedifferencebetweenthisandthereferencewasbarelyvisible,butsubtractingonefrom the other revealed a small sawtoothwaveform indicative of the onset ofslewratelimiting(seeFigure7.24).

Figure7.24Tonecontrolslowratelimitingat2VRMSat20 KHZcausedby6 nfload.

The subtractionwaveform reverted to a sinewavewhen load capacitancewasbackedoffto3 nF,implyingthatthestageiscapableofdrivingfulloutputat20kHzinto3 nFunderitsmostonerousconditions.Interestingly,althougha20kHz squarewaveprovokedovershoot, novalueof load capacitanceprovokedringing even though the output was taken directly from the anode. It wouldprobably be wise to check whether a different construction needed a smallresistor(afewhundredohms)betweenanodeandcable.

ObtainingaCleanSignalfromAnalogueDiscBeforewecaninvestigatethedesignofRIAAstages,weneedtoquantifylevelsandlookatthepracticalitiesofobtainingacleansignalfromthecartridge.

ComparisonofAnalogueLevelsbetweenVinylandDigitalSources

Toallowswitchingbetweensourceswithnegligiblevolumechange, theRIAAstage shouldmatch digital sources by producing 2 VRMS atmaximum level.Although digital sources define their 2 V RMS output as being themaximumamplitudeofundistortedsinewavethattheycanreproduce,analoguecartridgesdefinetheiroutputvoltagereferredtoarecorded(sinusoidal)velocityof5 cm/s(sometimes3.54 cm/s) at a frequencyof1 kHz.Howcanwe reconcile theseentirelydifferentmethods?VinylisnotnearlyastightlyconformedasCD,andmaximumrecordedlevelistotally dependent on the skill and audacity of the cutting engineer. Recordedlevelmaybereducedbyasmuchas6 dBinordertoallow40 minratherthan20 min to be recorded per side of a 33⅓ record. Since vinyl noise and dustclicksareconstant,thisautomaticallymeans6 dBhasbeensubtractedfromthatrecording’sdynamicrange,soBeethoven’sninthsymphonyrequiresfourvinylsides, not two. RIAA equalisation further complicates matters, but whenequalised vinyl typically has peaks (measuredwith a PeakProgrammeMeter)reaching12 dBabovethenominal5 cm/sline-uplevel.The significanceof this is thatwecouldnowconsider a cartridge specified toproduceanominal2 mVRMSat5 cm/sascapableofproducingmusicalpeaksof8 mVRMS ,whichwhenmultipliedby the1 kHzgainofa suitableRIAAstagewouldgiveasignalleveldirectlycomparabletodigitalsources.

RIAAandReplayRumble

RIAAis theabbreviationfor‘RecordingIndustryAssociationofAmerica’andis the de factoworldwide post-1954 standard for equalisation ofmicrogrooverecords, as opposed to the numerous standards for 78s. Because the RIAAstandardwasnotinventedinEurope,butaworldwidestandardwasneeded,theIEC invented an LP equalisation standard thatwas almost identical. The onlydifferenceisthattheIECstandardrecommendsbasscutonreplayonly,witha−3 dBpointat20 Hz(7,950 μs)inordertoreducerumble.Mostmanufacturersofhigh-qualitypre-amplifiersassumethattheirproductswillbecomplementedbyequallygoodturntablesandthatreplayrumblewillnotbeaproblem,sothey

ignoretheIECrecommendation.TheirequalisationisthereforeRIAA.Nevertheless,thereisconsiderablepressuretomodifyRIAAstagestoincludealow-frequencyroll-offbecause:• Some valve power amplifiers are susceptible to output transformer coresaturationifhigh-amplitudesignalsareappliedatlowfrequencies(<50 Hz).•Bass reflex loudspeakers are easilyoverloaded at low frequenciesbecausethere is negligible damping of cone motion below their roll-off frequency.Bookshelf reflex loudspeakers tend to roll off below 100 Hz, whereasfreestandingreflexloudspeakerscouldimprovethisto50 Hz,orless,butthisstillleavesbothvulnerabletolowfrequencynoise.• Vinyl records contain low frequency (<20 Hz) noise due to warps andrumble.

It is therefore argued that these problems could be avoided by implementingsomeformofLFroll-offwithintheRIAAstage.Onepossibilityistoimplementthe IEC 7,950 μs recommendation, but a more sophisticated approach is toincorporate a properly designed high-pass filter having a final slope of 12dB/octave,ormore,setat≈10 Hz.TheauthorfirmlybelievesthatneitheroftheprecedingelectricalapproachesiscorrectandthatRIAAequalisationshouldbereservedsolelyforcorrectingtherecord equalisation applied by the manufacturer at the time of cutting. CDplayers do not add a 10 Hz high-pass filter to solve the problems of poorlydesigned loudspeakers or questionable output transformers, so why adulteratevinyl?Warpsandrumblearemechanicalproblems,andshouldhavemechanicalsolutions,notelectrical‘fixes’.

TheMechanicalProblem

Fortunately,a12 dB/octavehigh-passmechanicalfilter isunavoidablyformedbythecomplianceofthecartridgesuspensionandtheeffectivemassofthearmpluscartridge.Thelowfrequencyarm/cartridgeresonancemaybefoundusingthestandardresonanceequation:

whereC=cartridgedynamicverticalcompliance(oftendifferenttothestaticvalue)mtotal=totaleffectivemass.

Typicalvaluesmightbe:Cartridgemass 5 gMountinghardware(screwsandnuts) 1.5 gArmeffectivemass 12 gTotaleffectivemass(mtotal) 18.5 g

Cartridgedynamicverticalcompliance(C): 15×10−6 dyne/cm

ThepreviousfiguresappliedtoaunipivotarmdesignedforanOrtofonQuattromoving coil cartridge with its outer body removed, and resulted in the idealresonant frequency of 10 Hz. The significance of determining this resonantfrequency is that it is also the cut-off frequency of the high-pass mechanicalfilter.Ithasbeensuggestedthatahigherresonantfrequency(12–15 Hz)shouldbeset,as this would be more effective at filtering LF noise, and this is quite true.However, we live in a practical world and dramatically reducing an arm’seffective mass (to raise the resonant frequency) inevitably produces a flimsystructureonlysuitableforcartridgesthatdonottransfermuchvibrationintothearm.Unfortunately,suchcartridgesarehighcompliance,andwearebackwherewestarted.Additionally, even setting the resonant frequencyas lowas10 Hzmeans that thereproducedresponse(whenRIAAequalised) is likely tobe−1dBat20 Hz,dependingondamping.Asanaside, thebestwayof reducingeffectivemass is to removemassat theheadshell.Modernarmsareusuallyfixedheadshell,sothisleavesthecartridge.Amoving coil cartridge often has a heavy outer shell that can save valuablegrammes if it can be removed without damaging the internal workings. Evenbetter,provided that themagnetsystemis firmlyanchored, removing thebodyeliminates box resonances. The stylus cantilever is now completely exposed,whichmakescueingandalignmenteasy,butleavesitfrighteninglyvulnerabletodamage.Allfactorsconsidered,thetradeiswellworthwhile,whichiswhysomecartridgesaresoldnaked.Evenifthearm/cartridgeresonantfrequencyiscorrect,themechanicalhigh-passfiltercanoperatecorrectlyonlyiftheresonanceiscorrectlydamped,andsomecartridgesrequireextradamping.Thegeneralprincipleisthatthemovingpick-uparmisfittedwithapaddlewhichisforcedtomovethroughaviscousliquid,thusdamping themotionof thearm. Ideally,dampingwouldbeappliedat theheadshell because thiswould also attenuate high frequency energy transferredfrom the cartridge into the arm, and thereby reduce excitation of unavoidablehigh frequency structural resonances, but damping near the pivot, as used byalmostallunipivots,dampsthelowfrequencyresonanceequallywell.Additionaldampinghastobesetbytrialanderror,andcommonly,fartoomuch

damping isapplied– the fluid iseither tooviscous,or there is toomuchof it.One way to set damping is to play a badly warped record with no dampingapplied, and observe cartridge movement as the warps are traversed. If thecartridgeappearstobouncerelativetotherecordsurface,addalittlefluid,andtry again. Use as little damping as possible, as too much will increase lowfrequencynoiseandcausetrackingproblemsathigherfrequenciesasundistortedstylus displacement is squandered by tracking warps rather than recordedsignals.Setting themechanical high-pass filter correctly has twomajor consequences.Firstly, itmeans thatwenolongerneedanelectricalhigh-passfilter,butmoreimportantly itmeans thatstylusverticaldeflection isconsiderably reducedanddistortiongeneratedbythecartridgefalls.

ArmWiringandMovingCoilCartridgeDCResistance

Once universally ignored, the wiring resistance of a pick-up arm can becomesignificant,particularlywhena lowoutputmovingcoilcartridge is steppedupbyatransformer,becausethetransientresponseofthattransformeriscriticallydependentonsourceresistance.Theauthormeasuredtheresistanceofa5 mlengthofthefinewireusedwithinhispick-uparm,andfoundthatithadaresistanceof0.45 Ω/m,soatypical9″arm requiring 600 mm ofwire for each channel (loop to cartridge and back)contributes0.27 Ωresistance.The1 mloopof0.7 mmsilvertwistedpairfromthearmbasetothepre-amplifieradded0.12 Ω,bringingthetotalarmresistanceto 0.39 Ω. Pick-up arm wiring modifications are popular, and to reduce thenumberofsolderedjoints,sometakethefinewirerequiredwithinthearmtubeall theway to the pre-amplifier input plug. 600 mm leads are typical, so thiswould increase the loop resistance to 0.81 Ω. To put these values intoperspective,thepreviouslymentionedOrtofonQuattrocartridgehadaspecifiedcoilresistanceof3 Ω.High levels at high frequencies imply high acceleration of the stylus tip. Tominimise the force required by the vinyl to accelerate the tip ( F = ma ),cartridgemanufacturers strive tominimise stylus tipmass. Themost effectivewayof reducing tipmass is to use a smaller diamond, because so little of thediamondactuallyconstitutesthestylustipbutthismakesthediamondhardertogrip whilst grinding and lapping, and increases the chance of trapping dustbetween record surface and cantilever. However, the mass of the coils in amoving coil cartridge is also significant, so a useful improvement can beobtainedby reducingwirediameter.Unfortunately, cartridgemanufacturersdo

notalwaysupdatetheir technical informationastheydevelopaproduct,sothemeasuredDC resistance of the coils can be higher than specified. The authorrecentlymeasuredanominal6 Ωcartridge,and found itsDCresistance tobe10.5 Ω.TheidealpointtomeasurecartridgeDCresistanceisat thepre-amplifierinputplugbecausethistakesarmwiringresistanceintoaccount.Thefinewirewithinacartridgewouldberupturedbypassingahighcurrentthroughit,sotheauthorfirstmeasuredthecurrentsuppliedbyhismeterwhensettothelowestresistancerange,andfoundittobe0.1 mA–quitelowenoughnottodisturbacartridge.ThesafestmeasurementmethodistouseacomponentbridgetomeasuretheACresistance(andinductance).Oncethesourceresistanceseenbythestep-uptransformerisaccuratelyknown,itsoptimumoutputloadingcanbefound(seeChapter4).

HumLoopsandUnbalancedInterfaces

Allunbalancedinputstagesaresusceptibletothenoisecurrentcirculatinginahumloop,buttheproblemcanbereducedeveniftheloopcannotbebroken:• Always bond the 0 V signal ground to chassis at the input of the RIAAstage’sfirstactivedevice–thisisanunbreakablerule.•V=IRforcesthehumvoltagetobeproportionaltotheresistanceofthe0 Vsignal conductor, so a thicker conductor reduces hum. Unfortunately, thisimpliesthatturntablesneedheavyearthbondwiresthatwouldtendtoshort-circuit any acoustic suspension they might have. One way of avoiding theproblem of finicky cable dressing to a suspended sub-chassis is to take thefine armwires to the plinth before connecting to the heavier external cableneededtoconnecttotheRIAAstage.•Stop treatingcartridgesasunbalancedgenerators–balanced interfacesarefarmoreforgivingofhumproblems.

BalancedWorkingandPick-UpArmWiring

Abalancedsourceissimplyonewhereeachterminalofthesourcehasbalanced,or equal, impedances to ground. Frequently, the only path to earth from theterminalsisviastraycapacitances(noDCpath),andthesourceisthensaidtobefloating.Connectingcablesforbalancedsystemsthereforerequiretwoidenticalsignal wires, or legs , to maintain this balance, plus an overall screen. Tomaintainbalance, theinputstageofthefollowingamplifiermusthaveitsstray

impedances carefully balanced to ground and is based on either a differentialpair(cheap)oracarefullydesignedtransformer(best,butmoreexpensive).Professionalaudioisinvariablybalancedinordertoprotectaudiosignalsfromexternal electromagnetic interference. TV studios and stages are particularlyharshenvironmentsbecausemicrophonecablesmayunavoidablyhavetobelaidadjacent to lighting cables fed from triac dimmers (which generate copiousmainsharmonics).Whenwe immerse a balanced connecting cable in a changing electromagneticfield,anidenticalnoisecurrent is inducedintoeachwire.Theseriesresistanceofthecableisthesameoneachleg,andtheshuntcapacitancesandresistancesto ground are also equal, so the noise current develops a voltage of identicalamplitude and phase on both legs at the amplifier input. Because this is acommon-modesignal, it isrejectedbytheamplifier,whereasthewantedaudiosignalisdifferentialmodeandisamplified.Atypicalmovingcoilcartridgeproduces≈200 μVat1 kHz5 cm/s,butbeforeRIAA equalisation the level at 50 Hz is ≈17 dB lower at only 28 μV.Achievingourgoalofinaudiblehumonasignalatthislevelisnottrivial,andwe need all the help that we can get. The cartridge is inherently a balanceddevice,sowhyunbalanceit?Weshouldimmediatelyrewirethecableleavingthebaseofourpick-uparmtomaintainthisbalancebythrowingawayanycoaxialcableandreplacingitwithatwistedpairhavinganoverallscreenforeachchannel.(Apairofcoaxialcablesfor each channel would not be a good idea because the increased spacingbetween the inner conductors would cause slightly different noise currents ineachleg,greatlyreducingcancellation.)Theauthor’spick-uparmusesaninterconnectfromthearmbasecomprisingatwistedpairof0.7 mmsolidcoresilverthreadeddownapolytetrafluoroethylene(PTFE) sheath, coveredwith a braid electrostatic screen.Both cables are thenthreaded down one overall braid screen, which also serves to hold the cablestogether.Thebraidmustnothavevoids,sodomesticaerialcableisunsuitable;broadcast quality video cable and multicore umbilical cable are both idealsourcesofnon-voidedbraid.Oncetheplasticoutersheathhasbeenremoved,thebraid easily concertinas off the inner conductors. Finally, the cable should besleevedwithnylonbraid toprevent thenoise thatwouldotherwise result fromthescreenintermittentlytouchinganotherearthedmetalpart.Allthreescreeningbraidsshouldbefirmlybondedtothemetalworkatthebaseofthepick-uparmandalinktakenfromtheretotheturntablechassisinordertoearthturntableswithlowvoltagemotorsthatwouldotherwisebefloating.Attheotherend,makesuretheinterconnect’sscreenisconnectedfirmlytotheRIAA

stage’schassis.Turntablesusingmainsmotorswill/shouldalreadyhavetheirchassisbondedtoearth by their ownmains earth safety bond, and the first active device in theRIAAstagewillhaveits0 Vsignalgroundconnectedtochassis(alsobondedtoearth) to minimise hum. Connecting the two earth bonds together via theinterconnect’sscreencreatesahumloop,butbecausethebalancedaudiosignaldoesnotpassdownthescreen,thecirculatingcurrentintheloopdoesnotcauseaproblem.Intheeventthattheloopdoescauseaproblem,itisthelinkbetweenarmandturntablechassisthatshouldbebroken.Phono plugs should not be used for connecting the audio cable to the pre-amplifieras theyareunbalancedconnectors,anda ‘professional’qualitymetalbodiedfive-pinDINplugorXLRis ideal,although itscableentrywillalmostcertainlyneedtobeenlarged.Alternatively,andmoreclumsily,apairofthree-pinXLRs could be used, but this requires individual (double-screened) cablesfrom the armbase, or a ‘Y’ split in the cable near the pre-amplifier,which isquitedifficulttomakeneatly.Withinthearmtube,mostpick-uparmslightlytwistallfour(thin,non-screened)wires from the cartridge together because this makes the harness easier tohandle. Crosstalk between channels, and hum rejection, can be improved bytightlytwistingeachindividualchannelpairasitpassesdownthearmtube,butperhaps reverting to the four-wire twist (often required for low friction)as thewirespass through thebearings to theoutput cable.Because thismodificationprimarily affects longitudinal currents, it tends to be of more value to pre-amplifierswith balanced inputs, but it is stillworthwhile on unbalanced ones.MartinBastin(ofGarrardmodificationfame)reportsthathehasbeenusingthismethodforyears.Bearinmindthattheprimaryrequirementforpick-uparminternalwiringislowfriction, and that pick-up armwire is fiddly stuff anddifficult to stripwithoutdamaging the internal conductors, although the specialist adjustable wirestrippershavingcalibratedsettingsdownto0.25 mmareveryeffective.Leavewellaloneunlessyoureallyarecompetentwithsuchfinewire,andbewarethatitbecomesbrittlewithage.Balancedwiring is particularlybeneficial formoving coil cartridges, and evenhelpshumrejectionwhenthepre-amplifierisunbalanced.

RIAAStageDesignThe RIAA stage has to satisfy so many contradictory requirementssimultaneously that its design and execution is fraught with problems –microphone amplifiers and RIAA stages are the two hardest analogue audioproblems.Whenwe investigated power amplifiers,we looked at some classic designs tosee how the goals were achieved. There were no classic RIAA stages, theyvariedfrommediocretoplainawful.Thiswasnotalwaysduetoincompetenceonthepartofthedesigners.Theyhadpoorerqualitycomponentsandcouldnotuse regulatedHT supplies as is habitual today.However, themain factorwasthat therewas simply no incentive to design superbRIAA stages because thesignal leaving the turntablewas not very good.Vinylwas regarded as a verypoor quality source, often requiring low-pass filtering at 8 kHz to reducedust/clickdisturbance.Amazingly,goodvinyl,turntablesandcartridgeswereallavailable, but the appallingmechanical/acoustical failings ofmost of the armsandchassis/plinthsmeant that the electronics engineerswerenever exposed tocriticism.

DeterminationofRequirements

WeneedtodefinetheRIAAstage’sdetailedrequirementsbeforewecanbegindesign:(1)Lownoiseandnohum:Wehavetoconcedethatvalvesarenotquiteasquietasthelatestgenerationoflow-noiseICop-amps,butDCheatersupplieseliminate hum and slightly reduce valve noise. Pentodes are complete non-runners,andwewillneedtobecarefulinouruseoftriodes.(2)Constantinputresistanceandcapacitance:Thismightseemobvious,buthigh outputmoving coil cartridges can be sensitive to changes in electricalloading.(3)AccurateRIAA :The author is delighted to report thatwildly inaccurateRIAA is now becoming a rarity on new designs. Nevertheless, it’s easy tomakeamistake.Onemistakeistousepolyester(polyethyleneterephthalate)capacitors–theircapacitancechangeswithfrequency.Polystyreneisthebestpracticaldielectric,butpolypropyleneisacceptable.(4)Lowsensitivitytocomponentvariation:Valveswearout,andastheydoso,rarises.Similarly,whenavalveisreplaced,thenewvalueofCagmaynotbethesameasthatoftheoldvalve.Neitheroftheseeffectsshouldnoticeably

affecttheaccuracyofRIAAequalisation.(5)Good overload capability : But what capability is necessary? Using aTektronixTDS420oscilloscope,themaximumoutputofLPswasinvestigatedin conjunctionwith a highquality record playing system.TheTDS420wasfirstusedin‘envelope’modetofindthemaximumoutputofthecartridgeandmonitoredanentiredayoflisteningtomusic.Thelargestmusicalpeakswerefound whilst playing a Mobile Fidelity pressing of Beethoven’s NinthSymphony. Before equalisation these peaks rose to +16 dB above thenominal5 cm/slevel,butclicksduetodustorscratchesrosetoabouttwicethislevelat+22 dB(seeFigure7.25).

Figure7.25Unequalisedenvelopedmusicoutputfromcartridge(peaksaredust/clicks).

Individual clickswere then captured, and itwas found that the vinyl/tipmassresonancewasbeingexcitedandthatthisproducedaheavilydampedoscillationat56 kHzforthisparticular(movingcoil)cartridge(seeFigure7.26).

Figure7.26Unequalisedoutputfromcartridgeshowingexcitationofvinyl/tipmassresonance.

Ultrasonic overload could either generate intermodulation products that comebackdown into theaudioband,orworse, it couldcauseblocking.Blocking isparticularly undesirable because it converts a momentary overload that mighthave been almost unnoticeable into a protracted low frequency disturbancewhoseseverityisamplifiedbyRIAAequalisation.Ifapoweramplifierblocks,theusercanturnthevolumedown,butthisisnotpossibleinanRIAAstage,soblockingmustbeavoidedatallcosts.We shouldnowallow for variable cartridge sensitivityof about 6 dB– ifweneedmorethanthis,weshouldreconfiguretheRIAAstage.Agooddesign shouldnotoperatepermanentlyat its limits, soa further6 dBmarginisdesirable,togiveatotalheadroomof28 dBintheaudioband,risingto34 dBormoreatultrasonicfrequencies.VeryfewRIAAstagesofanyageachievethisrequirementandlownoisesimultaneously.Worn/olddiscsgeneratemoreultrasonic energy thananewdisc.Thismaybeduetodirtgroundintotheirgroove,orbecausetheywerepreviouslyplayedbyacartridge that mistracked, causing wall damage as its stylus flailed helplesslyfrom side to side of the groove. Inadequate ultrasonic overloadmargin is thereasonwhyapoorRIAAstageexacerbatesawornrecord’sdefects,yetagoodonerendersthempalatable.(6)Lowdistortion:Thisisanobviousrequirement,andislinkedto(5).(7)Lowoutputresistance:TheRIAAstageshouldideallybeabletodrivetheinput resistance of a semiconductor recording device such as a computersoundcard.(8)Lowmicrophony : Valves are alwaysmicrophonic, but it is possible tomake them worse. A low value of anode load combined with high anode

currentreducesnoise,butincreasesthepowergainofthestage,whichcausesmicrophony to rise.Ultimately,we have to isolate the valvesmechanically.Thisislessofaproblemthanitseems,sincemostofthestructuralresonancesof theelectrodesareabove1 kHz,andamechanical filter todealwith thiscan bemade by floating the RIAA stage sub-chassis on springs of knickerelastic. (Metal springs tend to ring at the same frequencies as the internalstructuresofvalves.)

ImplementingRIAAEqualisation

Nowthatweknowourrequirements,wecanconsiderourtopology.The low noise and constant input resistance requirements eliminate shuntfeedback. Low noise rules out the pentode. We are therefore left with acombination of triode stages having active equalisation determined by seriesfeedback,orwithpassiveequalisation.Eitherofthesecontendersmaybefurtherbrokendownintoperformingtheequalisation‘allinonego’,orsplittingitoveranumberofstages.To see howwe need to tackle the problem ofRIAA equalisation,we need todefine RIAA equalisation. The equalisation is specified in terms of timeconstants:3,180 μs,318 μsand75 μs.TheequationthatgeneratesthegainGsrequiredbytheRIAAreplayequalisationstandardis:

where

Thisisnotafriendlyequation,andaspreadsheetistheeasiestwayofsubduingit. The graph shows the required amplitude response of the equaliser only aperfectlypre-equalisedsignalpassedthroughaperfectequaliserwouldyieldanamplitude response deviation of 0 dB and a phase response of 0° at allfrequencies(seeFigure7.27).

Figure7.27RequiredRIAAreplaygainagainstfrequency(includes3.18μs).

Thegraphshowsthat19.9 dBofgainisneededatlowfrequencies,whilsthighfrequencyattenuationmustcontinueindefinitely,whichapparentlyexcludestheseriesfeedback‘allinonego’topology,becauseitsgaincannotfallbelowunity.However, this failing can be compensated after the feedback amplifier, but itdoesmeanthattheresponsebeforecompensationisrising,whichcompromisesdistortionandultrasonicheadroomwithintheamplifier.Since the RIAA replay curve appears in almost all discussions about vinylequalisation,thereisatemptationtothinkthatitreferstothevinylcut,butthisisnotquitetrue.TheRIAAreplaycurvealsocorrectsforthefactthatvirtuallyall cartridges are magnetic and therefore velocity transducers that need acorrectionthatfallsat6 dB/octave.IfwesubtractvelocitycorrectionfromtheRIAAreplaycurveandinvertit,weobtainaresponsethatreflectsthevinylcut(seeFigure7.28).

Figure7.28RIAAamplitudeagainstfrequencyresponseminusvelocityresponse.

Notethatthereplay(less3,180 μs)responseisconstantamplitudeexceptforthe318 μs/75 μs12.5 dBshelfequaliserthatcorrectsfortherecordedequalisationthattamedrecordingvelocities.ThesignificanceoftheRIAAcurvelessvelocitycorrectionistwo-fold:•Ifwehadaperfectdisplacementtransducer(perhapsbasedonstraingaugeorelectrostaticprinciples),wewould require replayequalisationconformingto the replay (including3,180 μs) curve ifwewere tomatch the frequencyresponseof an equalisedmagnetic cartridge.However, the few straingaugecartridges that the author has seen have incorporated the 318 μs/75 μsequalisationmechanically,yetdonotappeartoinclude3,180 μsequalisation,effectivelygiving themsignificantbassboostbelow100 Hzcompared to amagneticcartridgepluselectricalRIAA.• The vinyl cut curve gives the relative amplitudes of the groovewidths atdiffering frequencies and, in principle, a good USB microscope withmeasurement capabilities supported rigidly just above the surface of a testrecordshouldbecapableofcalibratingittowithin1 dB(rememberthat1 dBis 12%, so it’s actually quite a sizeable uncertainty even for a pixellatedopticalmeasurement).

‘AllinOneGo’Equalisation

Because the 1 kHz level is ≈19.9 dB below the maximum level at low

frequency,any‘allinonego’passivenetworkmustalsohave≥19.9 dBofloss.Ingeneral,anRIAAstagehavinganacceptablebalanceofnoiseandoverloadcapabilityusing this technique requires ahighgain input stage.Beware that ifthegrid-leakresistorofthefollowingvalveisacrosstheoutputofthenetwork,thiscausesadditionalattenuation(thiscanbeavoidedbymoving thegrid-leakcapacitortobeacrosstheinputofthenetwork).Ifweshoulddecidetouse‘allinonego’equalisation,therelevantformulaearegiveninthedefinitiveJAESpaperbyLipshitz[6].OfthefourpossiblenetworksthatLipshitzgives,thesereducetotwoforpassiveequalisation.Of these two, onlyonehas a capacitor inparallelwith the lowerarmofthenetwork.ThisfeatureisimportantbecauseitallowsustoaccountforstrayandMillercapacitanceandisthereforetheonlyfeasiblenetworkinavalvepre-amplifier(seeFigure7.29).

Figure7.29PassiveRIAAde-emphasisnetwork.

Therelevantequationsforthispassivenetworkare:

Thesenumbersareexactandhavenotbeenrounded.Remember that any grid-leak resistor in parallel with the lower arm of thenetwork,ornon-zerooutputresistanceofthedrivingstage,changestheeffective

valueofR1asseenbythenetwork.Therefore,thevaluesforthenetworkmustbecalculatedusingtheThéveninresistanceseenbythatnetwork.Likewise, any stray, or Miller, capacitance must be subtracted from thecalculatedvalueofC2.Forany‘allinonego’topologyotherthantheabovenetwork,itisessentialtorefertotheLipshitzpaper,andreaditthoroughlybeforeembarkingondesign.

SplitRIAAEqualisation

Wearenowleftwithonlytwopossibilitiesforequalisation,splitactiveandsplitpassive, sowemust define how to split the equalisation. Fortunately, there isonlyonerationalwaytosplit theequalisation,andthat is topair the3,180 μswiththe318 μs,buttoperformthe75 μsseparately.The75 μstimeconstantdefinesalow-passfilterwhosef−3 dB≈2,122 Hzandrollsoffat6 dB/octavethereafter.Thiswouldbeanidealfiltertouseearlyinthepre-amplifiersinceitallowsHFoverloadcapabilityafterthatstagetoriseat6 dB/octave above cut-off, which is exactlywhat we need with a magneticcartridge.The 75 μs time constant can be implemented passively following the inputstage,whichhastheadvantageofensuringthattheloadseenbythecartridgeisconstantwithfrequency.Moving-magnetcartridgesoftenusetheloadcapacitanceinconjunctionwiththegenerator’sself-inductancetoformaresonantequaliserthatcorrectsthefallingmechanical response of the cartridge. Thus, the value of load capacitance iscritical,but thiscanbesetquicklyandeasilybyaddinga twin-gang≈300 pFair-spaced variable capacitor salvaged from a (probably valve) medium waveradio(seeFigure7.30).

Figure7.30Typicalvariable300pFair-spacedcapacitor.

Themainreasonforthechoiceofapassive75 μsRIAAequalisationnetworkisthat a series feedback amplifier cannot make A v <1, and a shunt feedbackamplifierwould have noise problems.Additionally, although itwas not notedearlier,theoutputstageofafeedbackamplifierattemptingthisresponsefacesaheavycapacitiveload.Briefly,thecapacitiveloaddemandsalargecurrentatHFand is equivalent to changing the AC loadline to a far lower value of loadresistance, which results in additional distortion before closing the feedbackloop,althoughthisisnotaproblemwiththebetterICop-amps.The3,180 μs,318 μspairingdefinesashelfresponsewithalevelvariationofexactly 20 dB. Using IC op-amps it is equally convenient to perform thisactively or passively, but with valves it is more convenient to use passiveequalisation.

TheFinalChoice

Feedback RIAA is best suited to semiconductor op-amps because theirextremelyhighopen-loopgainandfallingresponsewithfrequencyallowafairlyconstant(andhigh)amountoffeedbackatallfrequencies.Passiveequalisationisbest for valves, and the choice between ‘all in one go’ and split equalisationdependsonthesignalamplitudeleavingthefirststage.Asausefulroughguide,thedecisionpointtendstobearound200 mVRMSat1 kHz5 cm/s–belowthisamplitudethebestbalancebetweensecondstagenoiseanddistortionislikelytobeobtainedusing splitRIAA (passive75 μs at the input to the second stage,

passivepaired3,180 μs,318 μsattheoutput),whereasabove200 mVRMS‘allinonego’atthesecondstage’sinputislikelytobesuperior.

ASimplifiedExampleRIAAStageRather thangoingstraight toadetailedpracticaldesign,wewill introduceandinvestigate some generic problems using a simplified example having splitequalisation because this will allow background understanding before delvingintothemorecomplexanddetailedissuesofpracticaldesigns.

NoiseandInputCapacitanceoftheInputStage

Bearing inmindour low-noise requirement, the first stage is thecrucial stageand must have low noise above almost every other requirement. This isreasonablebecauseeven+34 dBref.5 mVisonly700 mVpk–pk,solinearityoughttobeaminorproblem.Designingforlownoiseusuallymeanswringingtheutmostgainoutofthefirststage such that noise considerations in succeeding stages are irrelevant. Thiswouldimplyacommoncathodestageusingahigh-μtriodesuchastheECC83orECC808(electricallyalmostidentical,butECC808haslowerhumandnoise,and completely different pin-out), but with a typical gainA v=70 this wouldresultinaninputcapacitanceof≈120 pFincludingstrays.Most moving magnet cartridges are designed to be loaded by a specificcapacitance,andolderShuresandOrtofonsneeded400–500 pF,butonelastinglegacy of CD4 (quadraphonic sound with the rear channels on a supersoniccarrier)isthatmoderncartridgestendtoexpect250 pF.Onceweincludepick-up arm wiring capacitance and connecting cable capacitance to the 120 pFcontributedby theECC83, the loadingcapacitanceseenby thecartridgecouldrise to300 pF.TheECC83isprobablynowoutof therunning,unlessweareprepared to rewire the arm (whichmight not be such a bad idea), andwe arebacktotheE88CCwithalowergainandlowershuntcapacitance.Althoughhigh-μLoctalvalvessuchasthe7F7areapossibility,high-μoctal-basedtriodesarealmostcertainlyforbiddenbecauseoftheirexcessiveCag.The6SL7GT,whichwithμ=70isthepredecessoroftheECC83,hasCag≈2.8 pF(RCAvalue: depends onmanufacturer/source).With a typical gain of 50, thiswould result inan inputcapacitance, includingstrays,of160 pF.This isnowuncomfortably close to our 250 pF limit, and once armwiring capacitance isincluded, could only be achieved bymounting the entire RIAA stage directlybelowthepick-uparmmountingsothattheinternalwiresofthearmconnecteddirectlytothegrid.MountingtheRIAAstageontotheplinth,directlybelowthearmmounting,has

enormous advantages in termsof input capacitance, rejectionof inducednoiseandmicrophony.Italsomakestheturntablecompletelynon-standard,andmaynotevenbephysicallypossibleduetolimitedspaceorlimitedweight-carryingability. A delicately suspended sub-chassis turntable will not take kindly to apoundor two(500–1,000 g)ofpre-amplifierhangingfromthearmmounting.Conversely,a turntable suchas theGarrard301 thatmustbedirectlymountedontoaveryheavyplinthwouldscarcelynoticetheextramass.TheE88CChasanadditionaladvantageinthatra is lowand,aswewillsoonsee, this helps noise performance. Additionally, a low r a forms a smallproportion of the total resistance that defines the 75 μs roll-off, which thensatisfiesourearlierrequirementofreducedsensitivitytocomponentageingandchanges.Noise in the input stage is determined not only by the valve, but also by theassociatedresistors,ofwhichRL isbyfar themost important(seeFigure7.31a).

Figure7.31Noiseintheinputstage.

Tobeabletocalculatethenoiseperformanceofthestage,weneedtoredrawthecircuit as a simple equivalent circuit,whichmakes analysis easier (see Figure7.31b).WehavereplacedtheoutputofthevalvewithaperfectThéveninvoltagesource,andr ahasbeen included.Amovingmagnetcartridgecanbe representedasa

resistor in series with an inductor, and since a Thévenin source has zeroresistance, we could replace it with a short circuit, and redraw the circuit yetagain(seeFigure7.31c).Wearenowinapositiontoaddsomenoisesourcestoourequivalentcircuit(seeFigure7.31d).Thederivationof this finalequivalentcircuitwas taken inmanystepsbecausethe final circuit bears very little resemblance to the original circuit. Beforeembarkingoncomplexcalculations,wecanmake some important, anduseful,observations.Allofthenoisesources(withtheirassociatedresistances)afterthevalveareinparallel, so a source of zero resistance will short-circuit any other source,providedthatthereisnoadditionalseriesresistance.ModerndesignsaimforRg≈100ra,andRL≈10ra,soratendstoshunttheseothersources.Thisshouldmake the contributionofR g insignificant so that any convenient value ofR gcouldbeused,buttheseriescouplingcapacitorreducestheshuntingeffectofra.Thereactanceofthiscapacitoris:

Foratypicalgrid-leakof1 MΩ,wemightuseacouplingcapacitorof100 nFtogivea−3 dBfrequencyof1.6 Hz.Ifweassumethatthelowestnoisefrequencyofinterestis20 Hz(andthisisdebatable),thenwefindthatat20 Hz,XC=80kΩ.Thisissuchahighvaluethatitnullifiesanypossibleshuntingeffectbyra,untilXcfallstoavaluelowerthanra.Theresultofthisisthattheusualchoiceofcouplingcapacitordoesnotallowratoshunt thenoisefromthegrid-leakresistorat frequenciesbelow1 kHz.Theresistor therefore produces noisewhose amplitude is inversely proportional tofrequency (1/ fnoise),but that rises to themaximum theoretical thermalnoiseforthatvalueofresistor( ).To prevent this excess noise, we might decide to use a value of couplingcapacitorsufficientlylargethatraisabletoshuntRgatallfrequencies,whichwould require a value ≈10 μF. This is a large capacitor, andDC coupling ispreferable if possible, but the technique has been used in a number ofcommercialRIAAstages.Assuming that we have dealt with the grid-leak resistor and the couplingcapacitor,weareleftwiththeanodeloadresistorRL,andthevalveitself,whichleavesuswithasimpleequivalentcircuit(seeFigure7.32).

Figure7.32Finalequivalentcircuitfornoisesourcesintheinputstage.

R L generates thermal noise, and unless it is a wirewound resistor, it alsogenerates excess noise. Excess noise is generally specified by resistormanufacturersintermsofμV/VofappliedDC.Wewillthereforeinvestigateatypicalstage(seeFigure7.33).

Figure7.33Typicalinputstagefornoiseanalysis.

TheDCvoltageacrossRL≈200 V.Atypical100 kΩ2 Wmetalfilmresistorgenerates 0.1 μV/V of excess noise, so 20 μV would be generated in thiscircuit.Thethermalnoiseofaresistorisgivenby:

where

k=Boltzmann’sconstant≈1.381×10−23 J/KT=absolutetemperatureinK=°C+273.16B=bandwidthinHzR=resistanceinΩ.

For a typical internal temperature of 40°C (313 K), with a bandwidth of 20kHz,thisismoreconvenientlyexpressedas:

Usingthisequation,wefindthataperfect100 kΩresistorgenerates5.9 μVofthermal noise. In this instance, the resistor’s thermal noise has been greatlyexceededbyitsexcessnoise.Tofindthetotalnoiseoftheresistor,wemustaddtheindividualnoisepowers,which,ifwerememberthatP=V2/R,meansthat

Thisgivesatotalnoisefortheresistorof21 μV,andwasrathertedious,butitdemonstratestwopoints:• For wirewound resistors we need only calculate the thermal noise. (Noexcessnoise.)• For metal film resistors we need only calculate the excess noise. (Thissimplificationworksbecauseinpracticalcircuits,astheDCvoltageacrosstheanodeloadresistorfalls,sodoesitsrequiredvalue,andthereforeitsthermalnoise.)

Nowthatwehavesimplified thenoisesources in theresistor,wecanseehowtheywillbeshuntedby ther aof thevalve,andredrawthecircuit (seeFigure7.34).

Figure7.34EffectofraonnoiseproducedbyRL.

It is now easy to see that the circuit is a potential divider and that the actualcontributionof resistor noise to the circuit is equal to the open circuit resistornoisemultipliedbytheattenuationofthepotentialdivider.Inourexample,thisreducesthenoiseoftheresistorfrom21 μVto1.26 μV.ItshouldbenotedthatifRk is leftunbypassed,rarisesdramaticallyandit isnolongerabletoshuntresistornoise.IfwedividethenoisevoltagebythegainofthestageAv=29,wecanfindtheinputreferrednoise,whichis43 nV.Thesignificanceofthisisthatitenablesus to sum this noisewith any noise sources at the grid, such as the grid-leakresistor. Inpractice, ifwecalculate the thermalnoisegeneratedbyR gand itsattenuationbythecartridge,wegenerallyfindthatitisinsignificantcomparedtothevalvenoise.Inanyevent,wedonothaveachoiceaboutRgsinceitissetbythecartridge.

ValveNoise

Weshouldnowconsider theshotnoisewithin thevalve itself.ValvesproduceshotnoisebecauseIaismadeupofindividualelectronsthatshowertheanode,andalsobecauseelectronsleavethecathodewithrandomvelocitiestojointhespacecharge,sothisimpliesthatcathodechemistrycouldaffectnoise.Fortriodes:

Thissaysthatthewhiteshotnoisegeneratedwithinthevalveisequivalenttothethermal(white)noisegeneratedbyaperfectresistorreqattheinputofthevalve.

For our example triode, g m ≈5.3 mA/V, so the equivalent noise resistancewouldbe470 Ω.Using , the input voltage noise produced by the valve istherefore≈400 nVandswamps the43 nV(input referred)noiseproducedbytheanodeloadresistor(asitshould,inagooddesign),andweneednotsumthenoisepowersofthevalveandtheresistor.Forpentodes[7]:

Applying this equation to the low-noise EF86 pentode operating at I a=1.25mA, predictsanoiseresistanceof3.9 kΩandanoisevoltage(20kHz bandwidth) of 1.2 μV. However, Mullard measured 2 μV for a noisebandwidth of 25 Hz to 10 kHz under the same DC conditions, whichcorrespondsto2.8 μVfora20 kHzbandwidth,makingit7.4 dBnoisierthantheprediction.ForJFETs[8]:

JFETs are common in hybrid valve/transistor circuits, and as the previousequation shows, they are quiet. Their equivalent noise resistance is not onlysubstantiallylowerthanforatriode(effectively5.5 dBquieterforagivengm),but they also tend to have highergm for a given anode or drain current. ThequietestJFETscurrentlyavailablearetheLinearSystemsLSK170(derivedfromthe Toshiba 2SK170) and Philips BF862 – both produce ≈1 nV/√Hz noise,makingthementirelysuitableformovingmagnetcartridges,butnotquitequietenoughformovingcoils.

1/fNoise

Unfortunately,theprecedingnoiseequationsdonottellthewholestoryataudiofrequenciesbecausetheydonotaccountfor1/fnoise,buttheydoindicatethatpentodes are much noisier than triodes and that g m should be maximised.Provided that the cathode has been made properly, 1/ f noise is due to gridcurrentnoiseand,aswesawinChapter3,thisislargelydowntomanufacturingcleanliness,making it sample dependent. However, the clean room conditionsneeded to manufacture semiconductors mean that manufacturers of low-noiseBipolar JunctionTransistors (BJTs) are able to provide graphs that showhow

noise varieswith frequency.The lower the 1/ f corner frequency, the better itwillbe.

ConnectingDevicesinParalleltoReducenoise

High- g m valves are so expensive that we might choose to increase g m byconnectinganumberofdevicesinparallel,sincethenoisefallsbyafactorof√n. The MAT02/LM394 supermatch transistor is an extreme example of thistechnique, as it contains a pair of composite transistors each made of 100individual devices to give a 20 dB improvement. Paralleling 100 E88CCs isimpractical,butaworthwhile,ifsomewhatmodest,improvementof4.5 dBcanbe gained by using three devices in parallel. Note that the input capacitancetrebles,outlawinginputtransformers,movingmagnetcartridges,andevensomemoving coil cartridges. (The high output moving coil Sumiko ‘Blue PointSpecial’specifiesmaximumloadcapacitanceas200 pF.)Unfortunately,thepreviousexamplesdemonstrateanimportantpoint.Althoughwemayimprovenoisebyabetterchoiceofinputvalve,orvalves,wepaydearlyfor quite small improvements, since obtaining a high g m is expensive andinvariablycurrenthungry.Tominimisenoise, it isalwaysbetter topresent theinputstagewithahealthysignal,ratherthanhopetoamplifyaweakonecleanly.

ValveNoiseSummary

Despiteallthepreviouscaveats,qualificationsandprovisos,wecanmakesomeuseful generalisations thatwill avoid unnecessary calculationswhen designingforlownoise:• Pentodes are significantly noisier than triodes, and JFETs can be evenquieter.•Valvesamplevariationcanbelarge.(1/fnoiseislargelydeterminedbythecleanlinessoftheroominwhichthevalvewasassembled,soalthoughagivenmanufacturer tends to be consistent, there can be differences betweenmanufacturers–ormoreaccurately,theirassemblyrooms.)•To render the noise ofRL insignificant, theremust be no feedback at thecathode,sincethisreducestheshuntingeffectofra.Thisisalsotrueforaμ-follower, even though omittingC k has no discernible effect on gain. Thecascodehasra≈∞,sothenoisefromRLmustbeconsidered.

•Maximisegmforlownoise,eitherwithasingleexcellentdevice,orwitha

numberoflesserdevicesinparallel.•Maximisedgminvariablyraisestheinputcapacitanceoftheinputstageandmayprecludeusingamoving-coilstep-uptransformer.•Excessnoisedominates infilmresistorspassingDC.Wirewoundandbulkfoilresistorsdonotproduceexcessnoise.•Avery large (typically100 timesnormal) couplingcapacitor allows r a toshuntthenoisegeneratedbythegrid-leakresistorofthefollowingstage,butDCcouplingwouldbeevenbetter.

Together,thesenoiseandinputcapacitanceconsiderationsallbuteliminatetheECC83,6SL7GT,andotherhigh-μ,low-gmvalvesfromtheinputstageofanRIAAstage.

NoiseAdvantageduetoRIAAEqualisation

NumericalintegrationofRIAAequalisation(3,180 μs,318 μsand75 μs)from20 Hz to 20 kHz using thirtieth octave bands gives a noise equivalentbandwidth of 94 Hz, which reduces noise by 22.3 dB, but because theequalisation imposesagainof19.9 dBreferred to1 kHz, thefinaladvantagedue to equalisation referred to the 1 kHz sensitivity is a meagre 3.4 dB(unchanged if the 3.18 μs time constant is implemented). The significance ofthis 3.4 dB figure is that if the input referred noise and input sensitivity isknown,afullpost-RIAAsignal-to-noiseratiomaybepredicted.

StrayCapacitances

Wenowknowthatourinputvalveis likelytobeahigh-gmvalvesuchasanE88CC,orbetter,andifweassumearequiredinputsensitivityof2.5 mVRMSat1 kHz5 cm/s,thisislikelytoresultinasignalof≈65 mVRMSleavingthefirststage, requiring split equalisation and necessitating three stages. The secondstagecanbesimilartothefirst,butthethirdprobablyneedstobeafollowerforreasonsthatwillbecomeapparentshortly.WecannowdrawacircuitdiagramforourexampleRIAAstage(seeFigure7.35).

Figure7.35ExamplesplitequalisationRIAAstage.

The75 μshighfrequencylossisformedbythecombinationofR4,R5andC3,whereas the 3,180 μs, 318 μs pairing is formed byR 8 ,R 9 andC 5 . Thecalculationofthesecomponentsissimple,butwemustremembertoaccountforhiddencomponentssuchastheoutputresistanceoftheprecedingvalveandtheMillerinputcapacitanceofthefollowingvalveinparallelwithstrays.

CalculationofComponentValuesfor75 μs

We first note that the first and second gain stages are identical, so anycalculationappliedtoonealsoappliestotheother.FortheDCconditionschosenforourcommoncathodetriodeinputstage,ra=6 kΩ;thisisinparallelwiththe100 kΩanodeloadresistor,sorout=5.66 kΩ.Thegainofthesecondstageis29,andCag=1.4 pF,sotheMillercapacitancewillbe30×1.4 pF=42 pF. Inaddition to this, thecathode, theheatersand thescreenareatearthpotential,andareinparallelwiththiscapacitance.Cg−k+h+s=3.3 pF, and we ought to allow a few pF for external strays. A total inputcapacitanceof50 pFwouldbeaboutright.Tocalculatethecapacitanceneededforthe75 μstimeconstant,weneedtofindthetotalThéveninresistancethatthecapacitorseesinparallel(seeFigure7.36).

Figure7.36Determining75μsRIAAvalues.

Forthemoment,wewillignoreC1,butthiswillbeaccountedforlater.C3seesthe grid-leak resistorR 5 in parallelwith the series combination of the outputresistanceof theprecedingvalveandR4 .As isusual,wewillmake thegrid-leakaslargeaspermissible,soR5=1 MΩ.We are now free to choose the value of R 4 . We need r out to be a smallproportion of R 4 , otherwise variations in r awill upset the accuracy of theequalisation, but too large a value ofR 4would form an unnecessarily lossypotentialdividerincombinationwithR5.Athighfrequency,thecapacitorC3isashortcircuit,andsotheadditionalACloadontheinputvalvewillbeR4.200kΩisagoodvalueforR4,andithasthebonusofbeingavailablebothin0.1%E96 series and 1% E24 series (very few E24 values are common to the E96series).IncombinationwithR5,thisgivesanacceptablelossof1.6 dBwhilstnotbeinganundulyonerousloadfortheinputstage.Thecapacitornowsees200 kΩ+ 5.66 kΩinparallelwith1 MΩ,whichgivesa total resistanceof170.58 kΩ.Dividing thisvalue into75 μsgives the totalvalueofcapacitancerequired,440 pF.Butthisnetworkisloadedbythesecondstagewhichalreadyhas50 pFofinputcapacitancefromgridtoground,sotheactualcapacitance thatwe need is 440 pF−50 pF=390 pF, so a 390 pF 1%capacitorwouldbefine.We ignored theeffectof thecouplingcapacitorC 1 , but thismusthave someeffect on the Thévenin resistance seen by the capacitor. We could use asufficientlylargevaluetomakeitsreactancenegligiblecomparedtothe200 kΩseries resistor, but amore elegantmethod is tomove its position slightly (seeFigure7.37).

Figure7.37Movingthecouplingcapacitortoreduceinteraction.

The capacitor now only has to be negligible compared to 1 MΩ. 75 μscorrespondstoa−3 dBpointof≈2 kHz,soitisatthisfrequencythatthevaluesofothercomponentsarecritical.At2 kHz,a100 nFcapacitorhasareactanceof ≈800 Ω, which is less than 0.1% of 1 MΩ. If we had not moved thecapacitor, we would have needed a value >470 nF simply to avoidcompromisingRIAAaccuracy.Conversely, there is little point in using a very large coupling capacitor in anefforttoreducenoiseatLFs,sincethe200 kΩseriesresistanceofR4swampsthe output resistance of the input valve andnullifies its shunting effect on thegrid-leakofthesecondvalve.

180 μs,318 μsEqualisationandtheProblemofInteraction

The second stage is direct coupled to a cathode follower in order to eliminateinteraction between any coupling capacitor and the 3,180 μs, 318 μs pairing.3,180 μscorrespondstof−3 dB=50 Hz,whichisfartooclosetothetypical1.6Hzcut-offresultingfrom100 nFto1 MΩ,sotheywouldinteractsignificantly.Theotherreasonforusingacathodefollowerisitslowinputcapacitance,whichcauses an additional high frequency roll-off when placed in parallel with the3,180 μs,318 μspairing.Inthe75 μsnetwork,wewereabletoincorporatethevalue of stray capacitance into our calculations, but in this instance it is notpossible, so it is essential that any stray capacitance is so small that it can beignored.Thefullequationfortheinputcapacitanceofacathodefolloweris:

Toagoodapproximation,Av=μ/(μ+1),soforanE88CC(μ≈32),Av=0.97,Cag=1.4 pFandCgk=3.3 pF.TheCgktermisthusentirelynegligibleat0.1pF,sotheinputcapacitanceisvirtuallyindependentofgainat≈8 pF,includingahealthyallowanceforstraystoground.

3180 μsand318 μsEqualisationTheequationsthatgovernthe3,180 μs,318 μspairingaredelightfullysimple,CR=318×10−6 , and theupper resistor=9R ,whilst the lossat1 kHz for thisnetworkis19.05 dB(seeFigure7.38).

Figure7.38Implementingthe3180μs,318μsRIAApairing.

We should now check whether our worst case 8 pF shunt capacitance issufficiently small not to cause a problem. To do this, we need to employ aslightlycircularargument.We first say that it will not cause any interaction. If this is true, then thefrequencyatwhichthecut-offoccurswillbesohighthatCinthenetworkisashort circuit. If it is a short circuit,we can replace itwith a short circuit, andcalculate thenewThéveninoutputresistanceof thenetwork.Sincetheratiooftheresistorsis9:1,thepotentialdividermusthavealossof10:1,andtheoutputresistance is therefore one-tenth of the upper resistor. If we assume that ourupperresistorwillagainbe200 kΩ(neglectingroutofthepreviousstage),theThéveninresistancethatthestraycapacitanceseesathighfrequencyis20 kΩ;combinedwith8 pF,thisgivesanahighfrequencycut-offof1 MHz.Asaruleofthumb,oncetheratiooftwointeractivetimeconstantsis≥100:1,theresponseerrorcausedbyinteractionis inverselyproportional to thatratio,soaratioof100:1causesanerrorof≈0.1 dB.In our example, the ratio of 1 MHz to the nearest time constant of 318 μs(500.5 Hz)is2,000:1,sowecansafelyignoreinteractionandgoontocalculate

accuratelythevaluesforthe3,180 μs,318 μspairing.Ifweweredrivingthenetworkfromasourceofzeroresistance,idealvaluesfortheresistorswouldbe180 kΩand20 kΩ(perfect9:1ratio),sincebothofthesearemembersoftheE24series,andthecapacitorcouldthenbe16 nFwithonly0.6%designerror.Unfortunately,oursourcehasappreciableoutput resistance,sowewillchoose200 kΩastheupperresistorandmustacceptwhatevervaluesthisgeneratesforthelowertwocomponents.Thesecondstageisidenticaltotheinputstage,sooutputresistanceis5.66 kΩ,makingatotalupperresistanceof205.66 kΩ.Thelowerresistorwillthereforebe22.85 kΩ,andthecapacitor13.92 nF.22.85 kΩcanbemadeoutofa23k20.1%resistorinparallelwitha1M51%.13.92 nFcanbeinconvenientlymadeoutofapairof6n8sinparallelwitha330 pF,or10ninparallelwith3n9and20pF. We can now draw a full diagram of the example RIAA stage withcomponentvalues(seeFigure7.39).

Figure7.39Finalcircuitwithcomponentvalues.

AwkwardValuesandTolerances

Equalisation networks and filters invariably generate awkward componentvalues, andmuchmanoeuvring is required tonudge themonto theE24 series.Sadly, this is usually wasted effort, since, although 0.1% resistors are readilyavailable, capacitors are only readily available in 1%, and often only in E6values. Therefore, for best accuracy, we measure the value of the largestcapacitors on a precision component bridge (or perhaps a digital multimeterhaving an accurate capacitance range), and add an additional capacitor toachievetherequiredvalue.Forthe13.92 nFcapacitorneededearlier,wemightmeasurethe6n8capacitors,andfindthattheywereactually6.74 nF,sowewouldactuallyneeda430 pF,ratherthan330 pF.Thisisnotaproblem,butsupposewehadchosenthemoreobvious10 nF//3n9option,butwhenthe10 nF1%capacitorwasmeasured,it

wasfoundtobe10.1 nF.Wecanhardlyfileabitofftheend!Closetolerancecomponentsareexpensive,buttheyarenotalwaysnecessary.Ifwe combine a close tolerance component with a looser tolerance component,thentheresultingcomponentwillstillbeclosetolerance,providedthattheratioof the values is greater than the ratio of the tolerances. Clearly, the closetolerance component must be the main component, whilst the trimmingcomponent can be looser tolerance. As an example, if we need a 22.85 kΩresistor to a close tolerance,we could choose 23k2 0.1%, and parallel itwith1M5 1%. 1.5 MΩ/23.2 kΩ=65:1, and is greater than the 10:1 ratio of thetolerances, so this combination will be fine. Similarly, for the 13.92 nFcapacitor needed earlier, the ratio of the main component to the trimmingcomponent is16:1, soevena430 pF10%wouldbe fine.Wecouldprobablyonlybuya1%component,sothereisnoneedtomeasureit.Just because we have adjusted component values on test to meet our exactrequiredvaluedoesnotmeanthatwenowhavezerotolerancecomponents.Realcomponentsdriftwithtimeandtemperature,sothevalueswillchange.Whatwehave done is to remove the initial error so that the practical value equals thecalculated value, which places us in a better starting position for overalltoleranceduetodrift.

TheEC8010RIAAStageInvestigatingtheexamplestageintroducedthetwomainproblemsofnoiseandachieving accurate RIAA in the face of real-world gain stages, but gave onlypassing consideration to distortion. This single-ended split equalisation RIAAstageusesμ-followerstominimisedistortionandtransformercouplingfromthemoving-coilcartridgetotheinputstagetominimisenoiseandinterference.

TheInputStage

Theoverridingrequirementoftheinputstageisthatitshouldproducelownoise,requiringhighgm,soTable7.5sortsvalvegroupsbygm.

Table7.5ComparisonofTriodegmType Achievablegm(mA/V)

E810F(triodeconnected),EC8020 ≈503A/167M,437A ≈42D3a ≈34EC8010,5842,417A ≈20EC86,PC86,EC88,PC88 ≈11ECC88/6DJ8,E88CC/6922 ≈8

Thevalues given in the table are somewhat lower thanmanufacturers’ quotedvaluesbecausetheyreflectusablevalues thatcanbeachievedinarealdesign.Asaveryroughruleofthumb,valvesdesignedforhighgmtypicallyachieveamutualconductanceofbetweenonetoone-and-a-halftimestheiranodecurrent.In other words, the E810F requires I a ≈35 mA to achieve g m ≈50 mA/V,makingitexpensivetouse,sothechoicenarrowedtothegm≈20family.Havingchosenthevalvefamily,wemustchooseIa.Sincegm∝Ia,wesetIaashighas ispractical, so theauthorchose tooperate thevalveat I a≈15 mAbecausethiscurrentattainsmostoftheachievablegm.WenextneedtochooseVgk .ManydesignshavesetVgk<1 V,butwhen theauthor investigated thedistortionspectrumofa5842whilstsweepingVgk ,hefoundthatifVgk<1.3V,tinychangesinbiascompletelychangedthedistortionspectrum.OnceVgk>1.5 V, the higher harmonics subsided and became stable, so the valve wasbiassedbyacheapredLED(settingVgk≈1.7 V),whichsetVa=126 VforIa=15 mA.ThevalueoftheanodeloadRLcannowbechosen.Theoretically,ahighvalueofRLincreasesself-noise( ),butasthisismostlyattenuatedbythe

potential divider formed by r a andR L , changing the value over an extremerangeonlychangesthefinalS/Nratioby≈1 dB.ThefactorthatdeterminesRListheavailableHTvoltage.TohaveasufficientlylargeHTdroppingresistortoallowadequateHTsmoothing,weshouldkeep the first stageHT<300 V,andsince126 Visdroppedacrossthevalve,174 VisavailableforRL,soOhm’slawdeterminesthatRL≤11.6 kΩ.RLdissipatessignificantpowerinthisstage,andbecauseawirewoundtypeisnecessarytoeliminateexcessnoise,thenearestE6valueof10 kΩwaschosen.(WirewoundresistorsarecommonlyavailableinE6valuesonly.)WenowknowRL,andthecurrentthroughit,sowecandeterminethepreciseHTvoltage.Theresistordrops150 V,andVa=126 V,soweneed276 VofHTfortheinputstage(seeFigure7.40).

Figure7.40EC8010inputstagewithLEDbias.

Oncethedesignoftheinputstagehadbeenset,itcouldbetestedfordistortion.The circuit was tested at an output of +18 dBu, which lifted the distortionharmonics clear of the noise floor but was well below clipping. Twenty-sixsamplesweretestedfromtheEC8010,5842,417Afamily,andtheywereveryconsistentbothfortotalTHD+Nandfortheindividuallevelsoftheirharmonics,soatypicalexampleisshown(seeFigure7.41).

Figure7.41TypicaldistortionspectraofEC8010/5842/417Afamilyat+18dBu.

The distortion is dominated by second harmonic at −44 dB (0.65%), and thefourthharmonicis54 dBbelowthisatanentirelynegligible−98 dB.Becausedistortionforatriodeisproportionaltolevel,wecanpredictthedistortionattheproposedoperatinglevel.Thenominalinputsensitivityisrequiredtobe2.5 mVRMSfor5 cm/s,andweconvertthistodBu:

Butweknowthatprogrammepeakswillbe12 dBhigherthanthis,sothepeaksreach−50 dBu+12 dB=−38 dBu.UsinganEC8010,thestagehadameasuredgain of 32 dB, so programme peaks at the output of the stage reach −38dBu+32 dB=−6 dBu.Wetesteddistortionat+18 dBu,whichis24 dBhigherthan −6 dBu, so the distortion at −6 dBu will be 24 dB better than thatmeasured at +18 dBu. Thus, the distortion at −6 dBuwill be −44 dB − 24dB=−68 dB=0.04%, which is perfectly satisfactory. If we like impressivenumbers, we could instead quote the distortion at the nominal 5 cm/s level,whichreducesitto0.01%.We should next check the input capacitance of the stage. For the EC8010,SiemensspecifiesCag=1.4 pF,butthiswillbemultipliedby(1+Av)togiveaMillercapacitanceof57 pF.Cin=7 pF,sothetotalinputcapacitanceis64 pF.Sincetheauthoralreadyhadthestagesetuponthebench,itwaseasytocheckthisvalue.Addingaresistorinserieswiththeoscillatoroutputproducesalow-passfilterinconjunctionwithC input .The resistorvalue isnotcritical, so longas its exact

value is precisely known. The filter f −3 dB point can be found by adjustingoscillatorfrequencyuntiltheamplitudeattheoutputoftheteststagedropsby3dBoritsphase(relativetoinput)changesto135°(180°−45°).Usingan18-kΩresistor,f−3 dB=46.9 kHz.

Thisisalongwayawayfromtheexpectedvalue.SinceweknowthegainAvofthestage,CagcanbedeterminedusingtheMillerequationinreverse:

C in is the capacitance from grid to all other electrodes, as specified by themanufacturer,plusasmallallowanceforstrays–perhaps2–5 pF,dependingontestcircuitlayout.SincethemanufacturerclaimsCag=1.4 pF,thevalueof4.6 pFcameasquiteasurprise,butadirectmeasurementofCagonthecomponentbridgegaveavalueof ≈4.8 pF. All bridges have trouble measuring small capacitances, and theMarconiTF2700usedforthismeasurementwasnoexception.Nevertheless,themanufacturer’s claimedvalue forC ag is clearlyhopelesslyoptimistic at audiofrequencies.

OptimisingtheInputTransformer

Unfortunately,190 pFisalargeshuntcapacitancefortheinputtransformerandinitial squarewave testswith the Sowter 8055were very disappointing, but aZobelnetworkacross the transformersecondarygreatly improvedmatters.Therequired value of Zobel capacitance depends on cartridge DC resistance, asshowninTable7.6.

Table7.6ZobelCapacitanceforSowter8055Moving-CoilInputTransformerwhenLoadedwith190 pF//6k8CartridgeRDC 4 Ω 6 Ω 8 Ω 10 ΩCZobel 1.5 nF 1 nF 910 pF 680 pF

Alternatively, the Jensen JT-346-AX transformer can be used, but it is a littlenoisier(higherDCwindingresistance).TheJensentransformerwasdesignedfor3 Ωor5 Ωcartridgeswhen set to1:12 step-up ratio, and themanufacturer’sdata sheet gives appropriate Zobel values (assuming zero load capacitance).Experimentationrevealedthat680 pFand2k4wereoptimumZobelvaluesfor11 Ωsourceresistanceand190 pFloadcapacitance.

Ultimately, the choice between transformers will probably be determined byyour country of residence because buying transformers abroad is expensive.Thus,UKreaderswillprobablyoptfortheSowter,andNorthAmericanreaderstheJensen,whereasEuropeanreaderswillprobablyinvestigateLundahl.

TheSecondStage

This stage has the highest amplitude signals and therefore can be expected toproduce themostdistortion.Asexpected,when tested,gain stageswith activeloads such as the μ -follower and β -follower produced significantly lowerdistortionthanasimplecommoncathodetriodeamplifier,withthefurtherbonusofareducedoutputresistance.Theμ-followerprovedtobeanexcellenttestbedfordeterminingtheirreducibledistortionofavalve.ThehugeexpansionofInternettradingmeansthatthereisnowaworldmarketforNewOldStock(NOS)valves,andalmostanyvalvethatwasevermadeisavailablesomewhere.Thesecondstageneededavalvewithμ≈16,soanylikelycandidatewastested–togetherwithsomeunlikelyones(fulldetailsinChapter3).Surprisingly,givenitsgoodreputation,the76didnotmeasureparticularlywell.Althoughitproducedthelowestsecondharmonicdistortionofall,itsdistortionwas not proportional to level, and the higher-order harmonics were at acomparativelyhigh level.Since single-endeddesign reliesondistortion fallingwithlevel,thisvalvewasreluctantlyeliminated.One triodewas significantly better than all others. It might be packaged as asingleoradualtriode,anditmighthaveanOctaloraLoctalbase,witha6.3 Vora12.6 Vheater,butinternallythevalveisthesame.Perhapsunsurprisingly,this valve is the 6SN7, 12SN7, 7N7, 14N7 or 6J5. The selection was furtherwhittled down by the discovery that the metal envelope variants producedmeasurablyhigherdistortion,probablyduetooutgassingfromthehotenvelopecausingincreasedgridioncurrent.FurthertestsrevealedthattheblackenedglassvariantssuchastheCV1988(UKmilitary 6SN7) consistently produced the lowest distortion, but that the farcheaper Pinnacle 6J5GT was very good, and selected examples equalled theCV1988.Themanufacturers claimausefully reducedC ag (3 pFcompared to3.9 pF)fortheLoctals,butthemainreasonforchoosingaLoctalwouldbetoavoid the leakage of a phenolic base that potentially increases noise. Any ofthese variations on the theme would be suitable, and the final choice wouldprobably be decided by more prosaic matters such as heater supplies,convenienceofsingleversusdualtriodes,availabilityofvalvebasesorwhether

youhaveany.Theμ-followerandβ-followerwereextensivelytested,andtheβ-followerwasverygood,but theμ -followerhad theslightadvantage that it ismore flexibleaboutHTvoltage,and theauthorwanted toeaseregulatordesignbyoperatingthesecondandthirdstagesatthesameHTvoltage.ForthePinnacle6J5GTμ-follower,typicaldistortionat+28 dBuwas0.25%or−52 dB.Using thisvalve,programmepeaksat theoutputof the second stagereach+12 dBu,whichis16 dBlower,sothedistortioncanbeexpectedtobe−52 dB−16 dB=−68 dB=0.04%,whichisthesameastheinputstage.Oncedistortionduetothelowervalveinaμ-followerhasbeenminimised,thechoiceofuppervalveslightlyaffectsdistortion.Variousvalvesweretried,suchastriode-strappedD3a,6C45πandPinnacle6J5GT.Thedifferenceindistortionbetween the various typeswas small, but the Pinnacle 6J5GTwasmarginallybetterat8 mAthantheothervalves,soitwaschosen.Having found C ag of the EC8010 to be higher than expected, the Pinnacle6J5GTwasalsotested.TwodifferentmeasurementmethodsgaveCag≈5.4 pF,slightlyhigherthanthegenericvalueof4 pF.

TheOutputStage

Thethirdstagehasverysimilaroutputlevelrequirementstothesecondstage,soanother μ -follower was indicated. However, far less gain (and inputcapacitance)isrequired,soa6J5GTisnotsuitable.Thereareveryfewlow-μsmall triodes available – the 6BX7, 6AH4 ( μ =8) and 12B4-A ( μ =6) areobviouschoices.Thesevalvesweredesignedfor television fieldscanorseriesregulatoruse,solinearityisnotguaranteed.Theauthorhadconsiderablequalmsaboutthedecision,buteventuallydecidedtoselectfromhisstockof12B4-Astofindapairoflowdistortionsamplesfortheoutputstage.All of these low-μvalves require significant−V gk to set optimumoperatingconditions, soLEDbias becomes less practical, andbattery bias is required ifbiasshift istobeavoidedafteroverload.Again,aPinnacle6J5GTwaschosenfortheuppervalve.Ifthe12B4-Acannotbeselectedforlowdistortion,onepossiblealternativeistouse anNOS 37 ( μ=9) for both the second stage and the output stage. Eventhough a test of nine samples indicated that this valve produces double thedistortionof aPinnacle 6J5GT, its distortionwas farmore consistent betweensamplesthanthe12B4-A,sofinalperformancecouldbebetterthanifapairofunselected12B4-Ashadtobeused.

RefiningValveChoicebyHeaters

RefiningValveChoicebyHeaters

Ifthe12B4-Ahasitsheatersstrappedinparallelfor6.3 V(Ih=0.6 A),astereopairrequiresIh=1.2 A.IfanSN7/N7issharedbetweenthestereochannelsforthesecondstage,itrequiresIh=0.6 A.TogetherwiththeEC8010(Ih=0.28A), a total of 2.08 A is then required from the 6.3 V regulator. This isachievable, but a little awkward, and a pair of series 300 mA heater chainswouldbemoreconvenient.ShuntingtheEC8010bya315 Ωresistanceallowsittobeusedina300 mAchain;the300 mA6J5GTisdirectlysuitable,andthe12B4 Acanbeusedasa12 V300 mAheater,sothefinalline-upisEC8010,Pinnacle6J5GTand12B4 A.Apartfromtherelaxedrequirementsoftheheaterregulator,aseriesheaterchainhas other advantages, which are detailed in Chapter 4 , not least of which isreducedsensitivitytoRFnoise.

ChoosingtheImplementationofRIAAEqualisation

TheEC8010firststagehasagainof38,resultinginanoutputofonly95 mVRMS at 1 kHz 5 cm/s, which is well below the 200 mV RMS decision pointbetween split and ‘all in one go’ equalisation. Consideration of the secondstage’snoiserequirementsif‘allinonego’equalisationweretobeappliedtoa95 mVRMSsignalwillquicklyreinforcethisdecision.WeknowthatwewillusesplitpassiveRIAAequalisationandthetopologyofindividualgainstages.Wemustnowchooseimpedancesfortheequalisersthatgive the best balance between distortion due to loading or grid current andequalisationerrorsduetostraycapacitancesandnon-zerosourceresistances.

GridCurrentDistortionandRIAAEqualiserSeriesResistances

Allvalvessourcesomegridcurrent.Whenavalveisfedfromanon-zerosourceimpedance, its grid current develops a voltage across that impedance.Unfortunately,thisvoltage(whichisinserieswiththewantedsignal)isusuallydistorted,soitaddsdistortiontothewantedsignal.PassiveRIAAstagesmust includeseries resistance toformtheirequalisers,sothis provides a mechanism for grid current to introduce additional distortion.Sadly, reducing series resistance in order to reduce grid current distortion hassnags:•Atfrequencieswhenanequaliserprovidesmaximumattenuation,thedrivingstagemustdrivealoadequaltotheseriesresistance.Reducingastage’sload

resistance steepens its loadline and increases distortion. Stages including acathode follower, such as the proposed μ -followers, are more tolerant ofloading,butcautionisstillneeded.• The required capacitances for the RIAA equalisers become rather large.Fortunately, 1% polypropylene capacitors are now available, but theirrestrictedrangeofvaluesandvoltageratingsmeansthatacertainamountofjugglingisnecessary.

From the input stage to the second stage, a 20 kΩ series resistorwould havebeen ideal from the point of view of grid current distortion, but this loadingwouldhave reduced thegainand increased thedistortionof theEC8010 inputstage. On test, 47 kΩ series resistance was a suitable compromise thatminimised distortion due to the two effects. Happily, the 6J5GT/6J5GT μ -follower second stage could comfortably drive 20 kΩ, making grid currentdistortionduetothethirdstage12B4-A/6J5GTμ-followerinvisible.

3180 μs,318 μsPairingErrorsduetoMillerCapacitance

Inour exampleRIAAstage,weargued that theonly logical third stagewas acathode followerbecause it allowedDCcouplingwhicheliminated interactionanderrorstothe3,180 μs,318 μspairing,anditslowinputcapacitanceavoidedhigh frequency loss. If we could tolerate interaction, and had a means ofpredictingandsolvingtheproblem,thenthiswouldallowalittlemorefreedomofdesignchoice.Ifwewanttoachievelevelsfromvinylcomparabletothosefromdigitalsources,wemustincreasethegainoftheRIAAstage.IncreasingtheμofthevalveattheinputorsecondstagecausesMillercapacitanceproblems,sotheonlypracticalway of substantially increasing gain (without increasing the number of valvesproducingdistortion) is to substitute a commoncathode amplifier for the finalcathodefollower,whichimmediatelyintroducestwonewproblems:•ThefinalstagemusthaveitsinputACcoupled,causinginteractionbetweenthenew lowfrequency roll-off introducedby thecouplingcapacitorand the3,180 μstimeconstant,producinglowfrequencyresponseerrors.• Because the new final stage has a gain >1, Miller capacitance becomessignificant,and theequalisationnetworkwillbe loadedbya far larger straycapacitancethanbefore,causinghighfrequencyresponseerrors.

The75 μsProblem

Whenever possible, extended foil polystyrene capacitors are desirable forequalisationnetworkssincethisformofconstructionsignificantlyreducesESRand series inductance. Unfortunately, commercially available types have avoltage ratingofonly63 VDC , so the inter-stagecouplingcapacitorbetweenthe first and second stages has been forced to revert to its more traditionalposition,ensuringinteractionwiththe75 μsequalisation.Additionally, thegrid-leak resistorhasbeenmovedso that it isno longernearthegridbutdischargesthegridviatheseriesresistoroftheRIAAnetwork,thuseliminating the potential divider that caused 1.6 dB loss in the basic pre-amplifier.To theauthor’sknowledge, thefirstuseof thiscunning trickwas inArthurLoesch’stransformerlessRIAAMCstage[9](seeFigure7.42).

Figure7.42Modificationto75 μsimplementationthateliminatesunnecessaryloss.

TheComputerAidedDesign(CAD)Solution

Thevarious interactionproblemscanbesolvedby iterativeCADACanalysis.Westartbycalculatingvaluesinthenormalway(assumingnointeraction),andthenuseCADtopredicttheeffectsofinteractiononfrequencyresponseusingasweep between 2 Hz and 200 kHz. Once a problem is revealed, we adjustindividual component values to seek improvement. Although this soundslaborious,itcanactuallybequitequick,providedthatwethinkabouthow,andwhere,wemakeouradjustments.We have five variables thatmust be juggled to produce the correct result, sosome simplification is needed.We could best start by analysing a design thatdoes not have interaction and gently modifying it, gradually introducinginteractionsuntilwereachourfinaldesign.Alternatively,the3,180 μs,318 μspairing ismost affected by interaction, sowe could change these components

firstthendeterminetheremainingvalues.

3180 μs,318 μsPairingManipulation

•The shelving loss at frequencies<20 Hzcausedby adding the inter-stagecouplingcapacitorcanbecuredbyreducingthevalueoftheupperresistorinthepotentialdivider.• A mid-range shelved response (where frequencies above 1 kHz are at aconstant, but different, level to those below 250 Hz) can be cured bychanging the lower resistor value in the potential divider. If the higherfrequencies are at too high a level, this is because the potential divider hasinsufficient attenuation, so the lower resistormust be reduced in value, andviceversa.•Apeakintheresponsecentrednear500 Hzcanbecuredbyincreasingthecapacitorvalue,whereasadipcanbecuredbyreducingcapacitorvalue.Thisresultisnotquitesoeasilydeduced,butalargercapacitorwouldincreasethetime constant, lowering the frequency at which the potential divider takeseffectsothatattenuationbeginsearlierthanitshould,resultinginadipinthefinalresponse.

The last two adjustments are highly interactive, and an increase in oneimmediately requiresaproportionatedecrease (haveacalculatorhandy) in theother tomaintain thecorrect timeconstant. It isusuallyeasiest tooptimise theresistorfirst.Themodelshouldbetesteddownto2 Hz,andthelowfrequencyroll-off adjusted to emulate a simple 6 dB/octave filter, then optimised forminimumamplitudedeviationfrom20 Hzto20 kHz.

75 μs/3.18 μsManipulation

AlthoughRIAArecordequalisation isspecifiedwithonly three timeconstants(3,180 μs,318 μsand75 μs),thiswouldimplya6 dB/octaverisingresponseat the fragile cuttinghead.Wright [10]pointedout that at the timeof cutting,RIAApre-emphasiscannotcontinueindefinitelyandthatafinaltimeconstantof≈3.18 μs is commonly added to prevent excessive amplitude at ultrasonicfrequenciesfromdamagingthe(probablyNeuman)cuttinghead.Unfortunately,thevalueof this timeconstantvariesbetweencuttingheadmanufacturers,andthe less common Ortofon heads use a time constant nearer to 3.5 μs.Nevertheless, it seems reasonable to accept that an electrical 3.18 μs timeconstant has been deliberately added at the cutting stage in addition to the

inevitable mechanical losses within the cutting heads themselves. The newreplayequationistherefore:

where

This is an even more unpleasant equation than the original RIAA equation.Briefly, the effect is that instead of tending towards a 6 dB/octave low-passfilter, it tends towards ≈27.5 dB attenuation that is constant with frequency.Withintheaudioband,thenewequalisercorrectsa0.64 dBlossat20 kHz.The justification for adding a3.18 μs time constant to the replay equalisationhas little todowith amplitude response, butmore todowithgroupdelay andtransientresponse.Uncorrected,the3.18 μstimeconstantchangesthephaseoffrequenciesabove5 kHzsothattheynolongerarriveatthesametimeaslowerfrequencies (unequalgroupdelay), and thisdistorts the transient response.Wecannot compensate for the cutter, and we probably don't have the data tocompensate for the cartridge response, butwe can compensate for the hidden3.18 μstimeconstant.However,Yanigerconvincinglyargues inhis ‘HisMaster’sNoise’ [11]articlethat as moving coil cartridges typically have a fierce ultrasonic tip massresonance (whichwillcertainlycompensate for themissing timeconstant)andthatmoving-magnetcartridgesdon’t,onlyanRIAAstage intendedformovingmagnetcartridgesshouldincludethe3.18 μstimeconstant.Eitherway,thefinaltime constant of 3.18 μs is physically easily included by adding a resistor inserieswiththecapacitorproducingthe75 μstimeconstant(seeFigure7.43).

Figure7.43FinaldesignofEC8010μ-followerRIAApre-amplifier.

Sadly, setting the exact value of the resistor is considerably more difficultbecause there are so many other high frequency roll-offs within the pre-amplifier,usuallydominatedbytheoutputstageloadingofthe3,180-μs,318-μs

pairing. Usually, only the additional resistor needs adjustment, but minoradjustmentsofthe75 μscapacitorarelikely.Themodelshouldbetesteduptoat least300 kHz, and finallyadjusted foroptimumgroupdelay, thencheckedfordeviationsbetween20 Hzand20 kHz. Itmaybeevennecessary tomakeminorchangestothe3,180 μs,318 μspairing.

PracticalRIAAConsiderations

Settingtheprecisepracticalvalueofcapacitanceforthe75 μs,3.18 μspairingisawkward,soanAdjustOnTesttrimmer(AOT)isincluded.TherearevariousalternativesforsettingtheAOTtrimmer:•Setthevanesalmosthalfopen(≈17 pF),andassumecorrectvaluesfortheothercapacitors.•Measuretheother75 μs,3.18 μscapacitorsonabridge,andsetthetrimmertogiveapredictedtotalcapacitanceof1.35 nF,orconnectthemallinparallelandadjustthetrimmertogive1.35 nF.• Measure RIAA frequency response accuracy (with a 3.18 μs capableinstrument),andsetthetrimmerforcorrectresponse.

Notethatthecapacitanceofallcapacitorsfallswithfrequency,it’sjustthatthedefectsofthebetterdielectricsarelessvisible,soalthoughthebridgemethodsareindirect,theyarelikelytobethemostaccurateprovidedthatthecapacitorsarepolypropyleneorbetter.

RIAADirectMeasurementProblems

Given a well-equipped laboratory, direct measurement of RIAA equalisationerrorsseemssimple.Unfortunately,RIAAequalisationrangesfrom≈+20 dBat0 Hzto≈−25 dBat>50 kHz,makingprecisemeasurementquitedifficult.IfaconstantlevelisappliedtotheRIAAstage,itslevelmustbechosensoastoavoid overload and the measuring amplifier must accommodate the ≈45 dBrange without any error. Conversely, setting the output level to be constantrequiresthattheoscillatorcansetexactlevelsovera≈45 dBrangethatcanbemeasuredprecisely.Dependingonthetestequipment,thisiseitheraconversionproblem between the analogue and digital domains, or an analogue attenuatorproblem.Eitherway,guaranteeingattenuatorerror≤0.02 dBandsimultaneouslyaflatfrequencyresponseovera45 dBrangeisnottrivialandcostsmoney.A popular alternative is to feed the RIAA stage via a passive RIAA pre-emphasis network and measure the combined frequency response. A

theoretically ideal perfect RIAA pre-emphasis network would have an outputthatroseindefinitelyatarateof6 dB/octavefrom≈5 kHz,butpracticalpassivenetworksmusthaveafinaltimeconstant–evenifitisn’t3.18 μs.RIAA pre-emphasis networks are quite tricky to design, and even a perfectlydesignedandconstructedRIAApre-emphasisnetworkhasproblemsbecauseitissensitivetosourceandloadimpedances,whicharegenerallyconsideredtobeconstant during its design. Sadly, the carefully optimised real-world loadingrequiredbyamovingmagnetcartridgeoramovingcoiltransformerdisturbstheload impedance, andan incorrectoscillator source resistancewouldcompoundtheproblem.RIAApre-emphasisnetworksshouldusepolystyrenecapacitorstoavoidtheslightfrequencydependenceofpolypropylenecapacitance(seeFigure7.44).

Figure7.44Deviationfrom1kHzcapacitanceagainstfrequencyforpolystyreneandpolypropylenecapacitors.

Summing up, keepingmeasurement errors belowRIAA stage design errors isdifficult.

ProductionTolerancesandComponentSelection

Oncewehaveoptimisedcomponentvalues,wecantesttheeffectsoferrorsdueto component tolerances. There is little point in specifying close tolerancecomponents in one position if others with looser tolerances are able to upsetperformance.Thecomputerpredictedthe20 Hzto20 kHzfrequencyresponse10,000times,each time with random changes in all component values within their

manufacturer’stolerance.ThistechniqueisknownasMonteCarloanalysis,andprovided that sufficient runs areused, it predicts a likelyworst case spreadoffrequency response. The predicted error spread for the EC8010 pre-amplifierwas ±0.25 dB using the specified standard component values and withoutdeliberatepre-selection toobtainoptimumvaluesother thansetting the75 μs,3.18 μstrimmercapacitortoitsnominalvalueof17 pF.AlthoughRIAAerrorsareawkwardtomeasure,theproblemcanbeside-steppedbypre-selecting capacitors using a component bridge,whilst a 4½digitDVMmight even allow selection of 0.1% resistors. Even without component pre-selection, the errorwithnewvalves is likely tobewellwithin±0.25 dB, andpre-selectioncouldfurtherreduceerrors.

RIAAEqualisationErrorsduetoValveTolerances

Even when a design deliberately sets out to minimise the effects of valvetolerances, the valves still dominateRIAA errors because passive componentscannowbesoprecise.Unfortunately, r out of the input stage is a significant proportion of the seriesresistancethatdeterminesthe75 μs,3.18 μspairing.Despitethis,thecomputerpredictedanHFshelflossofonly0.15 dBduetogmoftheEC8010fallingto⅔ofitsnominalvalue.Asgmfalls,rarises,whichreducesgainandMillercapacitance.Inthisdesign,the valves expected to affect RIAA accuracy due to changes in Millercapacitance are the second and final valves, but as they are operated as μ -followers,changesinradonotaffectgain(RL≈∞),sothismechanismisnotsignificant.Becauseroutfortheμ-followerissuchasmallproportionoftheresistancethatdetermines theRIAA time constants, a tired valve in the upper stage of aμ -followerdoesnotsignificantlyaffectRIAAaccuracy.Thispre-amplifier’sweaknessisitssensitivitytovariationsofCaginthelower6J5GTof thesecondμ-follower. IfC agrisesby50%,anHFshelving lossof0.32 dBispredicted,whereasifitfallsby50%,anHFshelvingboostof0.34dBispredicted.Happily,thepre-amplifierisimmuneto±50%variationsinCagfor the 12B4-A because the 20 kΩ series resistor chosen for low distortionforceslowimpedancesinthe3,180 μs,318 μspairing.Some pre-amplifiers using passive equalisation with high- μ valves, such asECC83, have been found to sound audibly different with different makes ofvalve,givingrisetothebeliefthataSiemensECC83isbetter(orworse)thana

Mullard,whenitwasactuallydifferingraandCgkcausingclearerrorsinRIAAequalisation.

TheBalancedHybridRIAAStageThe Denon DL103 moving-coil cartridge offers excellent performance for itsprice,sothechallengewastoequaliseandamplifyitssignaltothedigital2-VRMSstandardwithasimilarprice/performanceratio.

NoStep-UpTransformers

TheDL103 is an idiosyncratic cartridge touse–perhapsexplaining itsmixedreviews. Its lowcompliancemeans that it needs a veryhighmass armhavingbearings that will not rattle, and its abnormally high coil resistance incombination with step-up transformer leakage inductance forms a significantlow-passfilter,whichmeansthatitsuffershighfrequencylossunlesspartneredwithstep-uptransformerseachcostingmorethanthecartridge.Havingrejectedstep-uptransformers,wenowhavetheproblemofamplifying0.3 mVRMSat1kHzat5 cm/sfroma40 Ωsourcewithnegligiblehumandnoise.Ifweranatriode-connectedE810Fatfulltilt,wecouldobtaingm=50 mA/V,resultinginan equivalent noise resistance of 50 Ω – comparable with the source. ButE810Fs are expensive, andwewould need 35 mAper channel of evenmoreexpensiveanodecurrent.Weneedacheaperformoflow-noiseamplification.

SemiconductorstotheRescue

The way to obtain the required g m and therefore low noise is to use asemiconductorinputdevice.Wecouldmakeanentiresemiconductorgainstage,thencouple it to avalve stage,but thatwouldbewastefulof components andinvolveunnecessaryACcoupling.Amoreelegantsolutionistomakeahybridcascodewiththesemiconductorasthelowerdeviceandthevalvetheupper(seeFigure7.45).

Figure7.45HybridFET/triodecascode.

Thegainofacascodeis:

To aworking approximation (neglecting semiconductor output resistance), thesemiconductor sees as its load the triode’s anode loadRLdividedby (μ+1),which implies that we can adjust the balance of the cascode’s gain structurebetweenupperandlowerdevicesbychangingμ.Ahighvalueofμputsmoreofthegaininthevalve,whereasalowvalueshiftsittowardsthesemiconductor.Unfortunately,high-μvalves suchas theECC83and7F7probablycan’tpassenough current for the semiconductor to achieve the noise performance werequire.Althoughwecoulddriveadditionalcurrentfromelsewhere,thiswouldbe tantamount to injecting noise directly into the input stage, and no designerlikesdoingthat.Allofthesemiconductor’srequiredcurrentmustthereforecomethroughthevalve,andthatmeansweneedtheLoctalN7(atthesesignallevels,we can’t tolerate the leakage currents in the phenolic base of anSN7). Ifweassume that we will need ≈3 mA and that the *N7 has r a ≈6 kΩ and cantoleratea33 kΩload,wenowknowthatoursemiconductorseesaloadof:

This is an acceptable load and suggests that it is worth continuing with thedesign.

MillerCapacitance

MillerCapacitance

AtypicalLSK170CJFETcanachievegm≈15 mA/VatIds=3 mA,sotoafirstapproximation,thecascodegainwillbe:

Moresignificantly,thegaintothevalve’scathodewillbe:

This is a much higher value than normal within a cascode and is a directconsequence of deliberately choosing a semiconductor having high g m . Ineffect, minimising noise by maximising semiconductor g m always results inhighgaintothevalve’scathode,andthismeansthatthesemiconductor’sMillercapacitance(thecapacitanceseenlookingintoitsinput)mustrise:

Worse, the capacitance of the depletion region at a reverse biassedsemiconductorjunctionisvoltagedependent:

IfwewanttoreducethesignaldependencyofourMillercapacitance,weneedareasonably large DC voltage (10 V or more) across the semiconductor.IncreasingVreversereducestheproblemofCreverseintwoways:

•AhighVreversereducesCreverse(makingitlessofaproblem).

•SignalswingbecomesasmallerproportionofVreverse,reducingmodulationofCreverse.

YouwillundoubtedlyhaveseenFET/triodecascodeswhere thevalve’sgrid isgrounded,resulting inonlyavoltor twoacross theFET, implyinga largeandsignal-dependentMillercapacitanceattheFET’sgate.Thismightnotbeideal,but it isdonebecause thedesigner is terrifiedof injectingnoise into the inputstagebyliftingthevalve’sgridfromground.

DCStabilisationandConsequentGainReduction

Assoonaswe includeR s to addDC feedback to stabiliseDCconditions,wehavealsoaddedACfeedbackandreducedcascodegain.Ifweneedtodrop100mV whilst passing 3 mA, R s =33 Ω, and we can calculate the effect oncascodegainifthisresistorisleftunbypassed:

Usingthefeedbackequation,thecascodegainbecomes:

Remembering thatwewant toamplifya0.3 mVRMSsignal, this translates to100 mV RMS at the output of the cascode, which is satisfactory. We wouldnormallyfretabouttheeffectonraofleavingsuchacapacitorunbypassed,butthecascodealreadyhasnear-infiniteracomparedtoitsRL,somakingithigherdoesn’t make matters any worse. Nevertheless, we will have to address thecascode'shighraproblemlater.

JFETNoise

The LSK170C is specified as producing 0.9 nV/√Hz at 1 kHz, so we canquicklyestimatethetheoreticalsignal-to-noiseratioofourcascode.WestartbyfindingtheequivalentnoiseoftheLSK170Covertheaudiobandwidth:

Weknowthatourcartridgeproduces0.3 mVRMS,sowedividetheonebytheothertoobtainoursignal-to-noiseratio:

ButwesawearlierthatRIAAequalisationconfersa3.4-dBnoiseadvantage,sothefinalsignal-to-noiseratiois69 dB.Thisquickcalculationhasneglectedthenoise generated by the cartridge’s 40 Ω winding resistance, but it’s usefulbecause Tim de Paravacini’s rule of thumb is that the practical limit for anyRIAAstage’ssignal-to-noiseratiois≈68 dBref.5 cm/s.Thus,thecalculationsuggests that our hybrid cascode input stage can’t be too far away from thepracticallimit.Unfortunately,wehavealsoneglected1/fnoise,andJFETstendtohavea1/fnoise corner somewhere between 10 Hz and 100 Hz – justwhereRIAAhasplentyofgain.Inshort,1/fnoiseisnotnegligibleinthisapplicationandtendstodisqualify JFETs from being used to amplifymoving coil cartridges – a low-noiseBJTisneeded.

BJTNoise

AswesawinChapter3,allamplifyingdeviceshaveavoltagenoisesourceandacurrentnoisesource.Unlesswe’reconsideringcapacitormicrophonecapsulesor other capacitive sources,we can neglect current noise in FETs and valves,hence the simple 0.9 nV/√Hz JFET noise calculation. Sadly, bipolar junctiontransistors are not so simple, andwemust calculate then sumboth sources ofnoise.The SSM2210 is AnalogDevices’ version of theMAT02/LM394 supermatchtransistor and has v n ≈0.8 nV/√Hz and i n ≈2 pA/√Hz at 3 mA, but moresignificantlyits1/fnoisecorneris≈1.5 Hz–belowtheaudiobandandmuchlowerthananycontemporaryJFET.Wecalculatethevoltagenoiseasbeforeandobtainafigureof113 nVRMS,butwemustalsocalculatethenoisecurrent:

WethenuseOhm’slawtofindthevoltagethisdevelopsacrossthe40 Ωsourceresistanceofthecartridge:

Thisnoisevoltageisuncorrelatedwiththetransistor’snoisevoltage,sowemustaddnoisepowers:

In this particular instance, adding the noise due to the current source barelychangedthefinalnoise,butahighersourceresistancesuchasamovingmagnetcartridge would make a significant difference, biassing the noise argumentfirmlyinfavouroftheJFET.Wedividethe114 nVRMSnoiseintoour0.3 mVRMSsignaltofindoursignal-to-noiseratioasbefore,resultinginafigureof70 dBonceweincludethe3.4dBRIAAadvantage.Thiscalculatedvalueof70 dBdoesn’tviolatethe68 dBrule of thumbbecausewehave neglected all other noise sources in theRIAAstage.Nevertheless,this70 dBfigureisfarmorelikelytobecrediblethantheJFET’s71 dBbecauseoftheSSM2210’slow1/fcornerfrequency.Irritatingly,theSSM2210isnowobsoleteandhasbeenreplacedbytheelectricallyidenticalSSM2212thatisn’tavailableineight-pinDIP.SurfaceMountDevices(SMDs)canbe solderedbyhand,butyouneedavery fine tip and<0.5 mmdiametersilver-loadedsolder.

ChoosingbetweentheBJTandJFET:Equalisation,Distortionand

HTPower

TheBJThasfarhighergmthantheJFET:

Therefore,cascodegainwillbemuchhigher:

Thisimpliesthattherewillbe≈1 VRMSleavingthefirststage,ratherthanthe100 mVRMScalculated for the JFETversion, so the immediate implication isthat the JFET requires split equalisation over three stages, whereas the BJTversionmustuse‘allinonego’equalisationandmightonlyneedtwostages.Sofar,wehavenotconsidereddistortion,butcascodesarenotespeciallylinearbecausethelowerdevicefacesthesteeploadlineof theresistancelookingintothe valve’s cathode.Moreover, the BJT versionwill suffer 10 times asmuchdistortionsimplybecausewithafixedinputsignal,10timesthegaintranslatesinto10timestheoutputvoltage.Steep loadlines tend to increase second harmonic distortion, which can becancelledbypush–pullaction.Thus,onewaytodealwiththegreaterdistortionoftheBJTversionwouldbetoconfigureapairofcascodesasadifferentialpair.Notonlywouldthishalvethevoltageoneachcascode(halvingthedistortion),but it would also cancel the predominant second harmonic distortion. TheSSM2210 comprises two NPN transistors having the defect h fematched to‘about0.5%’[12],makingitparticularlysuitablefordifferentialpairs.Thus, the decision between JFET or BJTwill be determined not somuch bymarginal noise considerations but by single-ended versus balancedconsiderations.The EC8010 RIAA stage demonstrated that it is possible to obtain very lowdistortioninasingle-endedtopology,butthatonepartofthepriceisahighHTvoltage (390 V) because the μ -follower is a series amplifier. 100 V of thevoltagedropisduetothe10 kΩ5 Wresistors,andaβ-followercouldavoidthat drop, bringing the HT down from ≈400 V to ≈300 V. Turning to thebalanced topology, it’sveryeasy tonotonlydouble thecomponentcount,butalsodoubletheHTpowerrequirement–andthat’sexpensive.Ifabalancedtopologyistobechosen,itmustusethesameHTpower(orless)asanequivalent single-endeddesignandhaveanotheradvantage to justify thepotentially higher component count. Having become accustomed to hum-freebalancedworkingfrommovingcoilcartridges,theauthorwasnotkeentoreturntothehumproblemsassociatedwithunbalancedworking.

ReconcilingtheBalancedDecisionwithPracticalities

HavingmadethedecisiontoadoptabalancedtopologyandthereforechoosetheSSM2210BJTinputdevice,thedesignneedstobemadepractical.TheEC8010RIAAstagerequires26 WfromitsHT,andalmosthalfofthatpowerisduetotheneedtosink15 mAthrougheachEC8010inputstageinordertosecurelownoise.Conversely,theSSM2210producesitslowestvoltagenoiseatIc=3 mA,andbecausedifferentialpairsare inherently lowdistortion, there isnoneed tosquanderHTvoltageacrossseriesamplifiers.Thus,onedesignaimshouldbetoreduceHTvoltageandkeepthecurrentdown,minimisingHTpower.WehavealreadyseenthatthehighergainoftheBJT/triodecascoderequires‘allinonego’equalisation,soanotherdesignaimshouldbetoonlyneedtwogainstages.Consideringthesecondstageinparticular,althoughthedifferentialpaircancelseven harmonic distortion, it would be better to minimise distortion beforecancellation,andthatimpliesmaximisingitsratioofRLtora.Butweneedtobe able to drive a cable or sound card, so a unity gain cable driver is alsorequired.Wearenowabletodrawablockdiagram(seeFigure7.46).

Figure7.46BlockdiagramofbalancedhybridRIAAstage.

ImplicationsoftheBlockDiagram

In our implementation, the emitters of the SSM2210 are tied together and itsbasesaretiedtoground,sobothitstransistorshavethesameVBE,forcingtheirbase currents to be the same, and if their defect h FE is matched, then theircollectorcurrentsmustalsobematched.Ifthetriodesdrawnogridcurrent,thenIk=Ia,andallthetransistors’collectorcurrentmustflowthroughthetriodes’anode loads, so if theanode loadsarematched, thematchedcollectorcurrentsmustresultinmatchedanodevoltages.The significance of the previous argument is that the block diagram usefullyshows us that the ‘all in one go’ equalisation can be implemented beforeACcouplingtothesecondgainstage,minimisinginteractionbetweenthe3,180 μs

and318 μstimeconstantsandtheACcouplingtimeconstant,andalsoenablingtheuseoflow-voltageclosetolerancecapacitorsfortheRIAAnetwork.However, thediagramalso showsus that theMiller capacitanceof the secondgainstageisacrosstheRIAAnetwork,sothismustbetakenintoaccountduringcalculation.Moresignificantly,itshouldbeminimised(tominimiseerrorswhenitvaries),suggestingthatE88CC(Cag=1.4 pF)wouldbeabetterchoicethan*N7(Cag=3 pF).Another requirement highlighted by the block diagram is thatwe need doubletheusualnumberofcouplingcapacitors,sotheyhadbetternotbeexpensive.SincetheSSM2210basesoftheBJT/triodecascodedifferentialpairmustbeat0V(toavoidcouplingcapacitors tothecartridge), theemittersmustbeat−0.7V, necessitating a negative supply for the tail’sCCS.Given that a subsidiarysupplyisalreadyrequired,theidealCCSisacascodeBJTdesign,whichwouldworkwellfroma−15 Vregulatedsupply.AnidenticalCCSwilldoverynicelyforthesecondgainstage’stail.

TheUnity-GainCableDrivers

Unity-gain cable-driving ability immediately implies low distortion followerswith constant current loads: either cathode followers or source followers.Further,weneedACcouplingsomewherebetweenthesecondgainstageandtheoutputterminals.ThealternativesarepresentedinTable7.7.

Table7.7ComparisonofFollowerAlternativesACcouplingbeforefollowers ACcouplingafterfollowers

Cathodefollowers

HighVak(andthereforePa)orsubsidiarysupplyneeded.Needsbiasservotoforcecathodesto0 V

Easybiassing,idealVak,butelevatedheatersandlargecouplingcapacitorsneeded

Sourcefollowers Asabove,butsubsidiarysupplycouldbemuchlowervoltage Asabove,butnoheatersupply

As Table 7.7 shows, the advantage of AC coupling before the followers is asmaller coupling capacitor, but this is won at considerable expense.Traditionally, the expense would have been considered worthwhile because a2.2-μF capacitor would have been large, expensive and polyethyleneterephthalate. However, low voltage metallised polypropylene capacitors arenow readily available, and a batch of 2.2 μF 400 V Vishay MKP1840smeasured sowell (lowD , lowESR, constancy ofCwith f and high ratio ofimaginary-to-real capacitance) that the author hadnohesitation in choosing toACcoupleafterthefollowers.From the point of viewof sensitivity to induced interference, the ideal sourceresistance is zero because it equalises the (opposing) interference voltages

developed by equal induced interference currents in each cable leg, enablingthem tobenulled, irrespectiveofwhether thesource isbalancedornot.Thus,the increased source impedance (≈1.5 kΩ as opposed to ≈100 Ω) at linefrequency(50 Hzor60 Hz)dueto theseriesreactanceofa2.2 μFcapacitordegradeshumrejectionby≈24 dB(1,500 Ω/100 Ω)inanunbalancedsystem.For a balanced system, any degradation is due to imbalance impedance, notabsolute,soifwetaketheextremeofone2.2 μFcouplingcapacitorbeing+5%andtheother−5%,wehaveanimbalancereactanceofonly76 Ω,implyingthatAC coupling at the output of the followers will not degrade interferencesuppression. Note that this argument assumes low output resistance from thefollowersatallfrequencies.Sourcefollowershaveveryslightlybetterdistortionthancathodefollowers,buttheirmain advantage is the avoidanceof elevatedheaters, so the author chosesourcefollowers.

DecidingtheHTVoltage

TheAnalogDevicesdatasheettellsusthatweneedtooperatetheSSM2210at3mA to minimise voltage noise, and this single requirement pretty welldetermines the rest of the entire design. We already know that we need tominimisevalveMillercapacitance,soweprefer theE88CCover the7N7,andwe know that for the E88CC, V ak ≈90 V is an operating point with goodlinearity.IfwesetRL=33 kΩ,then3 mAwilldrop99 Vacrossit,andwewillneedanHTvoltageof≈195 V(189 VplusanallowanceforVgk).195 VisaverysignificantvoltagebecauseitiscomfortablywithintheboundsofthestatisticalregulatorintroducedinChapter5.Thisisimportantbecauseacascode’shighrameansthatithasnorejectionofpowersupplynoise.Choosinga BJT lower device rather than a JFET increased the gain, and therefore thesignal at the anode, reducing the effectofpower supplynoise, but thebiggestimprovement (>40 dB) came from choosing a differential topology. Thecombination of a simple, extremely quiet HT supply and gain stages havinggood common-mode rejection ratio (CMRR) enables all the stages to share acommonsupply,greatlysimplifyingthedesign.Wenowhaveenoughinformationtobeabletodrawafullcircuitdiagram(seeFigure7.47).

Figure7.47CircuitdiagramofbalancedhybridRIAAstage.

InputStageBJTMillerCapacitance

Itwasmentionedearlierthatthesemiconductorinahybridcascodesufferslargeandsignal-dependentMillercapacitanceunlessthevalve’sgridiselevated,butthat doing so risks injecting noise directly into the input stage. There are tworeasonswhywecouldsafelyelevatethedifferentialpair’sgrids:•Anyinjectednoisewouldbecommonmodeandrejectedbythedifferentialpair’sCMRRof>40 dB.• The statistical regulator produces very low noise and hum, minimisinginjectednoise.

Havingdeemeditsafetoelevatethegrids,wemustdecidewhetherweneedto,andifso,byhowmuch.Lookingupintothecathode,wesee:

At3 mA,thetransistorhasgm=105 mA/V,sothegaintothecathodeis≈130.AgoodfittothepublishedSSM2210curvesofCcbagainstVcbcanbeobtainedusing:

Notethatthisequationhasnophysicalsignificance–itjustprovidesagoodfit.KnowingCcbandgaintothecathode,wecancalculateMillercapacitance.FromtheE88CCcurves,ifVa=90 VandIa=3 mA,Vgk≈−2.6 V,soifthegridisnot elevated, V cb =2.6 V, resulting in C in =2,760 pF. Both halves of thedifferentialpairhave thiscapacitance toground,but thecartridge isconnectedbetweenthebases,soitseesthesetwocapacitancesinseries,resultingin1,380pF seen by the cartridge. In combinationwith theDL103’smeasured 62 μHcoilinductance,thisresultsinaresonantfrequencyof540 kHz–wellabovetheaudioband,andcertainlynotlowenoughtopeaktheaudibleresponse.Knowingthatwewillusethestatisticalregulator,wecouldconvenientlyelevatethevalves’gridsin5.6 Vsteps.Ifweelevatethemto11.2 V(twoZenerdrops),V cb rises to 13.8 V and the cartridge sees 830 pF, which is 60% of theunelevatedvalue,andausefulbutnotcompellingreduction.

VCEandBJTLinearity

We know that if we don’t elevate the triodes’ grids, the collectors of theSSM2210willbeheldat+2.6 V.Sincetheirbasesareat0 V,theiremittersareat −0.7 V, and V CE =3.3 V. Small-signal transistors such as the SSM2210achieve constant current output characteristics at IC=3 mAonceVCE>100mV,and1.3 kΩisacomparativelyshallowloadline,soweshouldexpecttobeable to swing 2 V pk–pkwithout clipping at each collector. The gain of theE88CCsectionofthecascodewouldtranslatethisto100 Vpk–pkateachanode,or71 VRMSbetween theanodes,37 dBhigher than thenominal levelat thispoint.Inshort,VCE=3.3 Visperfectlyadequate,there’snoneedtoincreaseit,andwecanjustifiablyleavethetriodes’gridsat0 V.In practice, the E88CC draws grid current before the SSM2210 runs out ofcollectorswing,furtherreinforcingthepreviousargument.Nevertheless,ontest,with the triodes’ grids held at 0 V, the stage managed a very creditablemaximum output of 85.61 V RMS between the anodes at 3.2% pure thirdharmonicdistortion,justbeforegridcurrentintroducedevenharmonicdistortion(seeFigure7.48).

Figure7.48Maximumoutputswingofdifferentialhybridcascodestage.

Backingoffto1%distortionallowed48.17 VRMSbetweentheanodeswithaninputof13.76 mVRMS,correspondingtoa33 dBoverloadmarginandagainof3,500.

InputResistanceandBiasCurrent

TheindividualamplitudeagainstfrequencyresponsegraphthatcomeswitheachDL103 shows that it was tested into a load of 1 kΩ, so this is the inputresistanceweshouldaimfor.Thismakessensefromnoiseconsiderationsasthepotentialdividerformedbyasourceresistanceof40 Ωandloadresistanceof1kΩcausesanalmostnegligibleS/Ndegradationof0.34 dB,whereasthe100 Ωorgreater recommended loadresistance in theDL103pamphletwouldcausearuinous2.9 dBdegradationat100 Ω.UnlikeavalveorJFET,aBJTdrawsasignificantbiascurrentduetoitsforwardbiassedPNjunction,anditssmall-signalinputresistancehieloadsthecartridge.TheSSM2210datasheetincludesagraphofhieagainstIC,andatIC=3 mA,hie=4.4 kΩ.WeneedaDCpathto0 Vfromeachbasetoallowbasebiascurrentto flow, so this resistancewill be in parallelwithh ie .Note that because thetransistors arematched and the cartridge is connected between their bases, nocurrentflowsthroughthecartridge.Ifwewantthecartridgetosee1 kΩ:

Butthisisthetotalresistanceformedbythetwobasebiasresistorsinseries,soeachoneneedstobehalfthisvalueat565 Ω,andtheE24standardvalueof560Ωwillbefine.Butthebasebiascurrentflowsthroughtheseresistors,andalthoughtheirexactvalueisnotcritical,theyshouldbematchedtoavoidgeneratinganoffsetvoltagethat would bemultiplied by the (×3,500) gain of the amplifier. Thus, 562 Ω0.1%toleranceisabetterchoice.

InputStageNoise

Althoughnotexplicitlystated,thepreviousnoisecalculationsassumedasingle-ended input stagewith a single source of voltage and current noise, but eachtransistorinthedifferentialpairisanoisesource.Wesawearlier thatwithasourceresistanceof40 Ω, thecurrentnoisesourcewasnegligibleincomparisontothevoltagesource,soweneedonlyconsiderthetwo voltage noise sources which are in series and equal. The signal voltageremains the same, and we add noise powers, resulting in the differential pairhaving a signal-to-noise ratio 3 dB worse than the equivalent single-endedstage. This is a deliberate design choice; we have bought a >40 dB humreductionduetothedifferentialpair’sCMRRat theexpenseofa3 dBrise inrandomnoise.Toenabledirectcomparisonoftheoryandmeasurement,noisewasmeasuredattheoutputoftheinputstagebeforeRIAA.Withtheinputterminatedbya43 Ωresistor (to simulate 40 ΩDL103 source resistance plus 3 Ω arm and cableresistance), noisewasmeasured at −61.5 dBu ± 0.5 dB (22 Hz to 22 kHzbandwidth,RMSrectifier).Referredtothe1 VRMSsignalat thispoint, thisisequivalent to−63.7 dB, andadding the3.4 dBRIAAadvantage,wehaveanentirely respectableS/N ratioof67 dB.Given that the single-endedS/N ratiousing the BJT was predicted to be 70 dB, and that this was expected to bedegradedby3 dBbythedifferentialpairto67 dB,theagreementisexcellent,confirming that practical semiconductor noise matches manufacturers’ datasheets sufficiently well to enable reliable noise predictions over the audiobandwidth.Summarising,whilst the noise performancemight not be quite at the practicallimit, it is satisfyingly close, and a >40 dB rejection of hum pick-up on thecablingfromthecartridgeshouldrenderanyreasonableturntableentirelyhum-free, so the author considers this to be a very worthwhile trade. Note thatmagnetic fields coupled directly into cartridge coils from adjacent motors ortransformersaredifferentialmodeandthereforecannotberejected.

RIAACalculations

TheequationsweneedaretheLipshitzequationswesawearlier:

Aswith split equalisation, beforewe can apply these equations,wemust firstdetermineoursourceresistance,loadresistanceandloadcapacitance.Wewilltreattheproblemassingle-ended,andasvaluesaredetermined,convertthemtobalancedvalues.Toafirstapproximation, theoutputresistanceofacascodeisequal to its loadresistance.Strictly,weneedtodeterminethetriode’sra:

Thus,wefirstneedtofindRk,whichforthishybridcascodeisthesmall-signalresistance seen looking into theSSM2210's collector,1/h oe .Fortunately, theSSM2210datasheetgivesagraphofsmall-signaloutputconductance(hoe)intermsofμA/VagainstIC,andatIC=3 mA,sowesimplyinvertthevaluefromthegraphandfindthatthesmall-signalresistanceseenlookingintothecollectorisapproximately18 kΩat3 mA.Atthechosenoperatingpoint,μ≈30,so:

In parallelwith the 33 kΩ load resistance, this becomes31.13 kΩ.Note thatunlikethesplitequalisationexamplesseenearlier,itisRLthatdominatesoutputresistance.The input resistance of the following stage is equal to its grid-leak resistance,whichwegenerallyarbitrarilysetto1 MΩ,buttheauthorfoundthat1M2gavemoreconvenientcapacitorvalues.Notethatalthough1M2exceedstheMullarddatasheet’sRgk(max)valueof1 MΩ,thisispermissiblebecauseanodecurrentrunawayispreventedbythedifferentialpair’sCCS.ThereseemednoreasontochoosedifferentDCconditionsforthesecondstage,sowithRL=33 kΩandIa=3 mA,A=25.FromtheMullardE88CCdatasheet,Cag=1.4 pF,so:

ThisisinparallelwithCin=3.3 pF,makingaround40 pF.

ThefourLipshitzequationsallowus tostartanywhere,butagoodplace isbysetting thecapacitanceacross the inputof thesecondstage.Remembering thatwe are quite restricted in capacitor values, the author chose 1 nF//150 pFbetween the two grids, which is equivalent to 2,300 pF from each grid toground.The40 pFinputcapacitanceofeachvalveisinparallelwiththis,sothefinal value for the purposes of calculation is 2,340 pF. InLipshitz’s notation,thisisC1,so:

But this is the value of capacitance that would be needed for an unbalancednetwork,andwewantbalanced,sowedivideby2togive3.411 nF.UsingthebalancedvalueofC1,wefindthebalancedvalueofR2directly:

Finally,weneedR1:

ThecalculatedvalueofR1istheeffectiveseriesresistanceseenineachlegbytheequalisationnetwork,whichhas the1M2grid-leak inparallel, sowemustaccountforthis:

But this pure series resistance includes the 31.13 kΩ output resistance of theprecedingstage,sotheactualseriesresistorweneedineachlegis:

Thus,wehavecalculatedallthecomponentvaluesforourRIAAnetwork,andifwewereabletoDCcoupletothesecondstage, thesearethevalueswewoulduse. However, we know that we need to AC couple to the 1M2 grid-leakresistors,and thismusthaveaslighteffect.Thesolution,asalways, is todropour calculatedRIAAequaliser values, coupling capacitance, source resistance,load resistance and load capacitance into a CAD package together with theRIAAequationanditerativelyadjustthemuntilwegetaflatresponse.Theauthorhadsome56 nF500 VSovietPTFEcapacitors thathewanted touse,butyoumightnothaveany,soTable7.8alsoshowsvaluescalculatedfor100 nFcouplingcapacitors.

Table7.8PracticalRIAAEqualiserComponentValues

Table7.8PracticalRIAAEqualiserComponentValues100 nF 56 nF

R1 412 k0.1%+750 Ω 412 k0.1%+5 k11%

R2 93k10.1%+160 ΩC1 3n31%+110 pF1%C2 1 nF1%+150 pF1%

Ascanbeseen,onlyR1changedsignificantlywiththeinclusionofthecouplingcapacitor.

TheSourceFollowers

TheauthorchoseFQP1N50Pbecausehehadpreviouslyboughtlotsofthemandbecause earlier tests showed that they produced lower distortion than 6C45πcathodefollowers.Wedon’texpecttodrive20 mcables,so6 mAofquiescentcurrentperfollowerwillbefine.

TheConstantCurrentSinks

TheCCSs for thedifferential pairs’ tails are standard, usingBC549C (the ‘C’varianthasaguaranteedhfe>420)tomaximisetheiroutputresistance.ThesourcefollowerCCSsmustdissipate0.6 Wwith100 Vacrossthem,andintheabsenceofCRTvideodrivertransistors(loweroutputcapacitance),MJE340will have to do for the outer device.TheseCCSs are identical to those in theBulwer-Lyttonpoweramplifier,andshare theLEDreferencechainnotsimplyfor economy, but also because it renders any noise due to the reference chaincommonmode, which can therefore be rejected by the next stage. Given thevoltageatthefollowers’sources,theCCSscouldhavereturnedtheircurrentto0V,ratherthan−15 V.However,notonlywouldthishavedirtiedthe0 V,butthe14 mArequiredbytheLEDswouldhavebeensuppliedbytheHT,greatlyincreasingrequiredHTpower.Wecannowdrawafullcircuitdiagramwithcomponentvalues(seeFigure7.49).

Figure7.49CircuitdiagramofbalancedhybridRIAAstagewithcomponentvalues.

Theoutputcouplingcapacitorshave1M2resistorstogroundnotbecausesuchaprecisevalue isrequired,butbecause it isconvenient touse thesamevalueastheseconddifferentialpair’sgrid-leakresistors.

TheHTSupply

Westatedearlier thatweneeded195 V,andwefind thatweneed48 mAofcurrent, so we have achieved our design aim of using significantly less HTpowerthantheEC8010RIAAstage.Wecanuseasinglestatisticalregulatortopowerallthestagesbecause(beingbalanced)eachstagedrawsnegligiblesignalcurrentfromtheHTsupply,minimisingthesignalvoltagedevelopedacrossitsoutput impedance. To minimise interference entering the RIAA stage, thestatistical regulator shouldbewithin theRIAAstage,not in thepowersupply.Further, for optimum LF RF rejection, the 10 μF 400 V polypropylenecapacitor across the Zener chain should have a Kelvin connection (thesecapacitorsareavailablefromSuppressionDevicesofClitheroe,UK)(seeFigure7.50).

Figure7.50FourwireKelvinconnectedcapacitor.

TotalGainandChannelBalance

Asconfigured,theRIAAstagehas5.1 dBgaininhandtomatchthe4 VRMSbalanced digital standard from 0.3 mV RMS , and this is to allow for low-amplituderecordings.Cartridgesdonotalwaysproducematchedoutputsevenwhenperfectlyaligned.If required, thecurrentprogrammingresistor ineach inputstage’sCCScanbefinelyadjustedtocorrectchannelbalance.Thisworksbecausegm=35·ICandA=gm ·RL , soachange inICdirectlychangesgain. Ifsuchanadjustment isimplemented, use fixed resistors rather than a trimmer potentiometer to avoidcontactnoisedegradingtheRIAAstage’sS/Nratio.

Summary

ThebalancedhybridRIAAstageproducesalmostthreetimesasmuchdistortionas theEC8010RIAA stage and it is third harmonic rather than second, but itcostsratherlessthanathirdofthepriceandhasacomparableS/Nratio.Nothingbeatsawell-balancedtransformerforrejectingcableinterference−100dB rejection is commonly achieved. Conversely, achieving >40 dB CMRRfrom a practical differential pair over the 20 Hz to 20 kHz audio bandwidthrequires attention to construction detail, and the rejection only holds for smallinterference voltages. In short, the balanced hybridRIAA stage cannot rescuepoor screening or earthing strategy, but it can put the final polish on goodpracticeandallowstheDL103togiveofitsbest.

TheBulwer-LyttonpoweramplifierinChapter6includedavolumecontrolbutneeded nomore because it used its associated Digital to Analogue Converter(DACs’)digitalinputselectortoselectbetweencomputerserver,CDplayerandbroadcast receiver/recorder. However, we may need rather more analogueflexibility,sointhischapterwewillinvestigatethehotch-potchoffunctionsthathavebeentraditionallyallocatedtheterm‘pre-amplifier’.

[1]Radiolympiaview.WirelessWorld1949;November:438.[2]Self,D,Smallsignalaudiodesign.(2010)Focal;48–51.[3]JamesEJ.Simpletonecontrolcircuit.Bassandtreble,cutandlift.Wireless

World1949;February:48–50.[4]BaxandallPJ.Negative-feedbacktonecontrol.WirelessWorld1952;

October:402–5.[5]Self,D,Smallsignalaudiodesign.(2010)Focal;pp.259–67.[6]Lipshitz,SP,OnRIAAequalizationnetworks,JAudioEngSoc27(June(6)

)(1979)458–P481.[7]Terman,FE,Electronicandradioengineering.4thed.(1955)McGraw-Hill

;438.[8]VanderZiel,A,Noise:sources,characterization,measurement.(1970

)Prentice-Hall.[9]Fewstonesunturned.AnarticlebyHerbertReichertfeaturingArthur

Loesch’sRIAAMCstage.SoundPracticesEarly1993;23–28.[10]WrightA.Thetubepre-ampcookbook.2nded;1997.[11]YanigerS.Hismaster’snoise:athoroughlymoderntubephonopreamp.

Availableatthe‘Articles’sectionofdiyAudio.com[12]AudiodualmatchedNPNtransistorSSM2210.Analogdevicesdatasheet;

2003.

References

RecommendedFurtherReading•Self,D,Smallsignalaudiodesign.(2010)FocalOxford;Evenifyouthink

‘solidstate’ispronounced‘squalidstate’youoweittoyourselftoownthisbook.Youmightnotagreewithalltheauthor’sviewsbuthedoesn’tshirkfromprovidingsupportingevidence,andashe’sworkedonbothsidesofthedesignfence(recordingandreproduction),youhavetotakehisopinionsseriously.

•WrightA.Thetubepre-ampcookbook.2nded;1997.Thisself-publishedworklackstheproductionqualityofaprofessionalpublication,butatleastyouknowallthemoneyisgoingtotheauthor.YoumightnotagreewithAllen’sdogmaticapproachbuthisdesignshavestoodthetestoftimeandareignoredatyourperil.

•Vogel,B,Thesoundofsilence.(2008)SpringerBerlin;Thisentirebookisabouthowtodesignlow-noiseRIAAstages,eitherwithvalvesorsolidstate.Itsstrengthisitsthoroughmathematicaltreatmentoftheproblemsillustratedbycopiousworkedexamples.Sadly,it’sexpensiveandEnglishisnottheauthor’smothertongue.

•Gayford,M,Microphoneengineeringhandbook.(1994)FocalOxford;ThetwohardestanalogueaudiochallengesaremicrophoneamplifiersandRIAAstagesbecausebothrequirelownoiseandwidedynamicrange,sothereismuchtobelearnedfromstudyingmicrophonesandtheiramplifiers.Bewarnedthatthisexpensivebookisfarmoreaboutmicrophonesthantheiramplifiers,butitdoesgivevaluableinsights.

AppendixValveDataObtaining detailed valve data used to be extremely difficult, and the authorconsideredhimself to be very fortunate in having a large collectionof printedMullardvalvedatasheets.Fortunately,therearenowmanyexcellentsourcesofscannedvalvedatasheets,andfullmanufacturers’datasheetscannowbefoundatvarioussites,butthedefinitivesitehastobe:http://tubedata.org.Frank’ssiteisaservicetotheworld,andtheauthorwouldbelostwithoutit.Sadly,websiteaddresseschangerapidly(intermsofbooklifetimes),butmanyvalvevendorsprovideupdatedlinkstousefulsites.Keepsearching.

EuropeanPro-ElectronValveCodesThe Pro-Electron system of valve codes gives significant information about avalve.

HeaterType(1stLetter) ValveType(2nd,andSubsequentLetters) BaseType(1stDigitofSerialNumber)A 4 V Small-signaldiode 1 Use2nddigitB 180 mA Doublesmall-signaldiode 2 B8BC 200 mA Small-signaltriode 3 OctalD 0.5–1.5 V Powertriode 4 B8AE 6.3 V Small-signaltetrode 5 B9DF 13 V Small-signalpentode 8 B9AG 5 V 9 B7GH 150 mA HexodeorheptodeK 2 V HeptodeoroctodeL PowertetrodeorpentodeM FluorescentindicatorN ThyratronP 300 mAQ NonodeX Gas-filledrectifierY Half-waverectifierZ Full-waverectifier

Asanexample,theECC88hasa6.3 Vheater,withtwosmall-signaltriodesonaB9Abase.EuropeanmanufacturerssuchasMullard/PhilipsreversedtheorderofdigitsandlettersaftertheheaterlettertosignifyaSpecialQualitytype,suchas E88CC, so although this is a superior version of ECC88 and a plug-inreplacement, its heater is specified as 365 mA, although onlyMullard/Philips/Amperexadheredtothis,andmostmanufacturersactuallyused

300 mA heaters. Brimar specified 365 mA, but the author tested 10 BrimarECC88/6DJ8s, and found that they were all 300 mA. Sadly, coding reversalusuallyimpliesentirelydifferentvalves(EL81≠E81L,EF80≠E80F).ItwouldbenicetosaythatthePro-Electroncodingsystemwasrigidlyobserved,butit’sratherlikeFrenchverbs–therearesomeirregulartypes,andthe6.3 Vheater,dual triodeECC99valveactuallyusesaB9Abaserather than theB7Gimpliedbyitscode.Itwascommonforasinglecompany tousedifferentbrandnames indifferentmarkets. Thus, Osram or Marconi-Osram was used for the BritishCommonwealthmarket andGEC for the rest of theworld, yet the valves andtheirtypenumberswereidentical.STCwastheBritisharmofWesternElectric,but useddifferent typenumbers for industrial valves, so theWE437Abecamethe3A/167M,andthebrand‘Brimar’(BritishmadefortheAmericanmarket)wasusedforconsumervalves.The EF86 was a popular small-signal pentode and many companies madeequivalents. Mullard’s Special Quality plug-in equivalent was the M8195,whereas GEC’s very quiet plug-in equivalent used the British militarydesignation CV4085 (CV=Common Valve – common across the militaryservices). Although Telefunkenmade a long-life plug-in equivalent (EF806s),they alsomade long-life electrical equivalents with different pin-outs: EF804,EF804s.Since the valves in any piece of equipment were consumable items, claimingthataparticularvalvehadnoequivalentsensuredthatthemanufacturerhadalsocornered the replacement market. Thus, most manufacturers used proprietarycodes in an attempt to disguise their valves, and some deliberately inventedproprietary bases (such as the notorious Mazda octal) to prevent electricalequivalentsbeinginserted.Thesignificanceof thismarketmanipulationis thatlesser-knownequivalentsshouldbecheaperthanthemoregenericcode.Ediswan/Mazdaapplied theirproprietarycode inastartlinglyHumptyDumptyfashion(“When Iuseaword, itmeans justwhat Ichoose it tomean–neithermorenorless”),sometimestheyconformedtotheircode,sometimestheydidn’t.

HeaterType1stNumber ValveType1standSubsequentLetters6 6.3 V C Frequencychanger10 100 mA D Small-signaldiode20 200 mA F Small-signalpentode30 300 mA K Thyratron

L TriodeM FluorescentindicatorP Pentodeorbeamtetrode

Half-waverectifier

U Half-waverectifier

UU Full-waverectifier

Thus, the Mazda 6F13 is a small-signal pentode with a 6.3 V heater, and a6/30L2isasmall-signaltriodehavinga6.3 V300 mAheater,butyouwouldneed the data sheet or an inspired guess to realise that it is actually a doubletriode.

AmericanValveCodesLike the Pro-Electron system, the American RETMA number/letter systemsought to introduce some logic to consumer valve codes. Unfortunately, thisutopian ideal was soon overturned, and a non-systematic four digit industrialcodewas used in tandem.Nevertheless, the number/letter system offers somecluesastoavalve’sinternals.

1stDigit Letters 2ndDigitApproximateheatervoltage(however,7or14meansLoctalbase)

Purelyrandom–relatestoindividualvalvedesign

Numberofelectrodes(includingheaterandmetalenvelope)

Example:6SN7hasa6.3 Vheaterandsevenelectrodes(twoindividualtriodesplus one heater adds up to seven). Unfortunately, this codingwas not alwaysstrictlyobeyed–the6BQ5isactuallyapentode(directequivalenttoEL84).Inaddition,thefollowingAmericanOctalsuffixeswerealsoused:Suffix Meaning Comment

None Metalenvelope Introducedin1935,althoughtheenvelopeprovidesausefulscreen,envelopeoutgassingandtheconsequentgridgascurrentworsensnoiseanddistortionperformance.

G Glass EarlyvalvestendedtousetheST14(ShoulderedTube)envelopethatlookslikeasoftdrinkbottle.GT Glass,tubular Laterglassenvelopeswereofashorter,tubularconstruction.GT/G Interchangeable UsablewithequipmentspecifiedforeitherGorGT.

Asuffixfollowinganobliquesignifiedadevelopmentofabasictype,andtheywerestatedtobereverse-compatiblewiththeoriginaltype.Thus,forthe6SN7:

6SN7GT 6SN7GTA 6SN7GTBPa(max)pertriode 3.5 Wa 5 WPa(max)total 5 W 7.5 WVa(max) 300 450Controlledwarm-uptime – – YesaDependsondateofmanufactureandmanufacturer.Earlyvalvestendtobe2.5 W,laterones3.5 W.

Theincreasedvoltageratingwasusuallyachievedbyadditionalperforationsinthe supporting micas to lengthen leakage paths between anode and grid. Theincreasedpowerratingwasusuallyachievedbychangingtheanodefromsingletodoublesutureswhichincreasedtheradiatingareaandallowedbettercooling.For many valves, the ‘B’ suffix indicates controlled warm-up time. Ideally,

seriesheaterchainsshouldbedrivenbyconstantcurrentsources,butinpracticethey were more likely to be connected directly across the mains supply (aconstantvoltagesource)viaeitheratappedresistororvaristor.Sincemost valveswere intended for use in radios, capacitances and screeningwere important. As an alternative to the metal envelope, early octal glassenvelope valves added a pressedmetal ring (often connected to pin 1) aroundtheir base that acted as a crude guard to reduce capacitances to othercomponents.TheLoctalandB9Gguardringsaddedaflangeunderthebasethatencircledvalvepinsandwasthereforemuchmoreeffectivebecauseit reducedinter-electrodeleakageandcapacitance.

PinConnectionsUnlikeICs,valvesarenumbered,viewedfromunderneathcountingclockwise.

ThermionicEmissionThe Richardson/Dushmann equation for emitted cathode current (A) per unitarea(m2)is:

where

,butseenoteΦ=workfunctionofthecathodesurface(≈4.55 eVfortungsten)

k=Boltzmann'sconstant(≈1.381×10−23 J/K)T=absolutetemperature(°C+273.16)e=baseofnaturallogarithms(≈2.718)

me=electronrestmass(≈9.109×10−31 kg)

qe=electroniccharge(≈1.602×10−19 C)

h=Planck'sconstant(≈6.626×10−34 J s).

NB:Although the theoretical value forA≈1.202×10 6, Spangenberg [1] notedthat the experimental valuewas typically half this value, butVanderZiel [2]explainedthisdiscrepancybypointingoutthattheproblemlaynotinadeviation

fromthetheoreticalvalueof“A”,butinthetemperaturecoefficientoftheworkfunction “Φ” and recommended using the theoretical equation for “ A” as ameansofdeterminingthetruevalueof“Φ”atthetemperatureofinterest.

StandardComponentValuesThe following series of components covers one decade; other values areobtainedbymultiplyingordividingbyfactorsof10.E61 1.5 2.2 3.3 4.7 6.8E121 1.2 1.5 1.8 2.2 2.7 3.3 3.9 4.7 5.6 6.8 8.2E241 1.1 1.2 1.3 1.5 1.6 1.8 2 2.2 2.4 2.7 33.3 3.6 3.9 4.3 4.7 5.1 5.6 6.2 6.8 7.5 8.2 9.1E961 1.02 1.05 1.07 1.1 1.13 1.15 1.18 1.21 1.24 1.27 1.31.33 1.37 1.4 1.43 1.47 1.5 1.54 1.58 1.62 1.65 1.69 1.741.78 1.82 1.87 1.91 1.96 2 2.05 2.1 2.15 2.21 2.26 2.322.37 2.43 2.49 2.55 2.61 2.67 2.74 2.8 2.87 2.94 3.01 3.093.16 3.24 3.32 3.4 3.48 3.57 3.65 3.74 3.83 3.92 4.02 4.124.22 4.32 4.42 4.53 4.64 4.75 4.87 4.99 5.11 5.23 5.36 5.495.62 5.76 5.9 6.04 6.19 6.34 6.49 6.65 6.81 6.98 7.15 7.327.5 7.68 7.87 8.06 8.25 8.45 8.66 8.87 9.09 9.31 9.53 9.76E96valuesinboldarecommontotheE24series.

ResCalc

Wefrequentlyneedavaluethatisnotastandardvalue.Theproblemistofindthebestcombinationoftwostandardvaluesthatwouldgivetherequiredvaluewithminimumerror.Doan Internet search (orgodirectly toPeteMillett’s orDuncanMunro’ssite),andyouwillfindthatMarkLovellandtheauthorwroteapieceoffreewarecalledResCalcthatsolvestheproblem.Chooseyouravailableresistorseries, tellResCalc therequiredvalue,anditgivesyouthequestiontotheanswer.Evennicer,itdisplaystheresistorwiththecorrectcolourcode.

ResistorColourCodeMost resistors are marked with their value in the form of a colour codeconsistingoffourorsixconcentricbandsofpaintonthebodyofthecomponentwhicharereadfromlefttoright(seeFigure1).

Figure1Resistorcolourcodes.

Four-BandResistors

Thefirsttwobandsdenotethetwosignificantdigitsofthevalue.Thethirdbandisthemultiplier,whosevalueis10x,wherexisthevalueoftheband.Goldusedasamultipliermeans10−1=0.1,andsilvermeans10−2=0.01.Thefourthbandis thetolerance,whichwillusuallybe1%(brown)orperhaps2%(red).Onveryoldequipment (orcarbonresistors),youwill seegold (5%)andsilver(10%);theuseofthesecoloursastolerancesdatesfromthedayswhen5%wasconsideredtobeclosetolerance.Ifthereisnofourthband,thetoleranceis20%.

Six-BandResistors

The first three bands denote the significant digits, and the fourth band is themultiplier.The fifth band is the tolerance; note that six-band resistors imply greaterprecisionandso5%,orworse,tolerancewillnotbeseen.

Examples

Yellow,violet,yellow,red=470 kΩ2%Yellow,violet,black,orange,brown,red=470 kΩ1%50 ppmRed,red,red,red=2.2 kΩ2%

Red,red,black,brown,brown,red=2.2 kΩ1%50 ppmBrown,black,black,red=10 Ω2%Brown,black,black,gold,brown,red=10 Ω1%50 ppm

Note that because the six-band resistors have an extra significant digit, theirmultiplier is always one level lower than for the same value in a four-bandcomponent.Sometimes itcanbedifficult todecidewhichendof theresistor iswhich,andthevaluemakessenseeitherwayround:Brown,orange, yellow, red=130 kΩ,2%,but read theotherway round=24kΩ1%

If in doubt, measure the resistor with a digital multimeter; it is far easier tochangethecomponentnow,thanwhenithasbeensolderedintoplace.

PlasticCapacitorCodingThefirstofthethreelettersreferstotheplates:F=foilM=metallised

Thesecondletter‘K’isforKunststoff–Germanforplastic.Thelastletterdenotesthedielectric:S=PS,polystyreneP=PP,polypropyleneC=PC,polycarbonateT=PETP,polyethyleneterephthalateN=PEN,polyethylenenaphthalateI=PPS,polyphenylenesulphide

Thus, FKP is foil polypropylene, whilst MKT is metallised polyethyleneterephthalate.Many small (and particularly ceramic) capacitors use pF as their base units.SomecolourfulEuropeancapacitorsused the resistor colour code todesignatevalue,butitisnowmorecommontouseathree-digitcodewherebythefirsttwosignificant digits are followed by a multiplier signifying the number of zerosafterthefirsttwodigits.Thus,103=10,000 pF=10 nF.

Cable

Cable

CoaxialCableCapacitanceAudio coaxial cable has a typical capacitance of ≈120 pF/m, but RF coaxialcable tends to have a lower capacitance (perhaps ≈70 pF/m) dictated by therequiredcharacteristic impedance.Thecapacitanceperunit lengthofacoaxialcapacitoris:

where

ε0=permittivityoffreespace(≈8.854×10−12 F/m)

εr=relativepermittivity(comparedtofreespace)

d=innerdiameterD=outerdiameter.

Unfortunately, the logarithmic relationship implies that low-capacitance cablerequires a very small inner diameter. Oscilloscope probe leads need lowcapacitance and solve the resulting fragility problem using a steel core platedwith copper then silver (to reduce resistance) and have a capacitance of <2pF/m.Thecable ismadeby theSurprenant companyand fits all the standardminiaturecoaxconnectorssuchasSMA,SMB,MCX.

AmericanWireGauge(AWG)

The author found the following equation in a post by psychokids at diyAudioandcannotresistrepeatingit:

whereD=diameterininchesn=AWGnumber.

Quitewhatwasinthemindoftheoriginatorofthisequationisunknown,butitworks.

SquareWaveSagandLowFrequencyf−3 dBA square wave with LF sag is a decaying exponential, whose instantaneousvoltageatanytime‘t’maybefoundusing:

Rearranging,andsolvingforτ:

where‘t’isthetimeallowedforthedecayacrossthebartop,butforasquarewavewithequalpositiveandnegativedurations,itishalfoftheperiodictimeT:

ButTisthereciprocaloffrequency:

So:

Substituting:

Fromthefrequencydomain,aCRfilterhasa−3 dBcut-offfrequency:

ButCR=τandτ=L/R,soauniversalequation,validforbothCRandLR,is:

Rearranging:

Wenowhavetwoformulaeforτ,whichcanbeequatedas:

Solvingfortheratiof/f–3 dB:

Sag is the percentage of peak-to-peak level by which the horizontal bar hassaggedinlevel.10%sagiseasilymeasuredonanoscilloscope,andmeansthatthelevelhasfallenfrom100%to90%,so:

Applying10%sagtothef/f–3 dBformula:

So,10%sagmeans that theapplied squarewave frequency is30 timeshigherthanf–3dB

SagObservedUsingaSquareWaveofFrequency“f”(%) f/f−3 dB10 305 601 300

Playing78sYouhavejustinheritedacollectionof78sthatappeartobeinsuperbcondition,some of them are original recordings of legendary performers, and you aredesperatetoplaythem.Therearefourmainproblems.

CorrectSpeed

Although colloquially known as ‘78s’, referring to their speed, very early 78swere recorded on rather crude lathes and the actual recorded speed wassomewhatvariable.Thefirstrequirementforreplayisthereforeaturntablethatwillnotonly rotateat78 rpm,butalsohasvarispeed, so theGarrard301and401, and Thorens TD124 are obvious contenders. The BBC modified theTechnics SP10 direct drive turntable to give varispeed, added a pick-uparm/cartridge plus elaborate electronics, and called the whole confection anRP2/10(ReProducer2,version10).Oddly,thedisco-orientedTechnicsSL1200(production terminated 2010) was capable of playing 78s – provoking thestartlingthoughtofnightclubsbeltingoutAlmaCoganat110 dB(A)froma78.

GrooveSize

The 78 has a coarse groove, and was traditionally played with a crude steel‘needle’. TheLP stylus of amodern cartridge is far too small, so a dedicatedlarge-diameterstylusisrequired.Traditionally,onlybroadcastcartridgesliketheShure SC35 and Ortofon OM Pro were offered with 78 styli by theirmanufacturers, but the situation has now changed. Vinyl has recovered tobecome a niche market, and the cartridge manufacturers must respond to thedemandsofthatniche,withtheresultthatalmostallmanufacturersnowoffera

monocartridge,eitherformonovinyl,orwitha larger tipfor78s.Gradogoesonestep furtherandoffersamono78cartridgewith fourdifferent size tips toallow quick determination of the best compromise betweenworn grooves andsurfacedamageforagivenrecord.Afinalalternativecouldbetoaskaspecialistre-tippingconcerntofit78tiptoyourcartridge.Because different 78s are likely to need a different size tip, moving magnetcartridges are more suitable for playing 78s because removable styli are thenorm(AudioTechnicaOC9notwithstanding).Evenso,theLyraHelikonMonomovingcoilcartridgecouldpresumablybefittedwitha78tip,andifyouhadanarm with a replaceable headshell or arm assembly, different cartridges couldhavedifferent tips.Youwouldneedanawful lotofpriceless78s to justify theexpense, and probably only a national library that needed to transcribe rarerecordingscouldaffordit.Incidentally, the78 is theonly recordingmedium that is provably robust overdecades.Magnetic tapewent throughastickypatchin the1970swithunstablebinders.‘Perfectsoundforever’turnedoutnottobetrueiftheCDinquestionhadbeenpressedatBlackburn.TheUKplanthadbeenconvertedfrompressingLaservision video discs to CDs, and used silver rather than aluminium as thereflective coating,whichwasn’t a problem, but they then had a problemwithimperfect lacquer sealing at the periphery. Even that wouldn’t have been toobad,except that thepaper linershadanunusuallyhigh sulphurcontent,whichpromptlyreactedwiththesilvertoproduceyellowsilversulphide,whichisn’tsoreflective, and causes data errors. ‘Laser rot’ was nonsense. Any recordingformatbasedonvideotape(CDswereoriginallymasteredonU-matic)becomesunplayable not just because the medium deteriorates, but because workingmachinesareunavailable.Two-inchquadruplexvideotapeisonly50yearsold,andwasincommonuseforalmost30years,yettherearenowveryfewofeventhefinalgenerationmachinesinworkingorder.Asaspecies,wearebecomingincreasinglysloppyaboutsafeguardingourdata.TheRosettastonemighthavebeendifficulttoread,butatleastthatwaslargelyalinguisticproblem,ratherthandeteriorationofthemedium.

Pick-UpArmMechanics

Playing a 78 drives considerable vibration into the pick-up arm, and loosebearingscauserattlesandmistracking.Atamoresubtlelevel,astylustraversingan imperfection, or speck of dust, produces amechanical impulse and excitesarmresonances,whichgreatlymagnifiesthesubjectivenuisance.Paradoxically,theinferiormediumneedsagoodarmtoreplayitadequately–soamodernarm

such as the gimballed Rega RB251 arm and its derivatives seem a minimumrequirement,althoughunipivotscanbeevenbetteratrejectingclicksandbangs.

Equalisation

AnalogueDiscIt took some time before themanufacturers of 78s andLPs standardised theirequalisation. The following table gives the electrical time constants used bymajor organisations, and therefore an indication of the likely equalisationrequired[3].(AlltimeconstantsarespecifiedaccordingtoLipshitz'snotation[4]).

TimeConstants(μs)t3 t4 t5

78

‘Standard’ – 636 –Decca‘ffrr’/European – 636 25AES – 400 63.6Pre-1954DG – 450 50BBC – 450 25International – 450 50

LP

Pre-1954DG 1590 450 50Pre-1954Decca 1590 318 50Columbia/EMI 1590 318 100European 2230 318 50NAB 3180 318 100RCANewOrthophonic 3180 318 75RIAA 3180 318 75

Errors in t4 and t5 cause sharppeaksand troughs in thecriticalmid-band,anddespitepopularbelief,cannotpossiblybecorrectedbytonecontrolsorgraphicequalisers.Ifonly the later78s (whenan international standardhadbeen fixed) are tobeplayedinadditiontomodernLPs,thent4needonlybeswitchablebetween318μsand450 μs,andt5between75 μsand50 μs.LangfordSmith [5] stated that theDecca (London)LP recordingcharacteristichadthefollowingresponse(January1951):Frequency 30 Hz 50 Hz 100 Hz 300 Hz 1 kHz 10 kHz 15 kHzLevel −17.5 dB −14 dB −9 dB −3 dB 0 dB +14 dB +16 dB

Lipshitztimeconstantsthatproducearesponsepassingwithin±0.1 dBofthesepointsare:τ3=9.6 ms

τ4=735 μs

τ5=110 μs

τ6=10.2 μs.

ModernAnalogue‘Microgroove’τ2(μs) τ3(μs) τ4(μs) τ5(μs)

RIAA – 3180 318 75IEC 7950 3180 318 75

Notethatthe7,950-μsIECtimeconstantisreplayonly,andisa20-Hzhigh-passfilter intended to remove rumble produced by turntables; see Chapter 7 fordetailsonwhytoignoreit.The RIAA record equalisation implies a 6 dB/octave rising response withfrequency. If a 3.18-μs time constant is added to the head power amplifier toprotect the fragile cutting head from ultrasonic energy, the Lipshitz replayequationbecomes:

wheres=jω,ω=2πfτ3=3180 μs

τ4=318 μs

τ5=75 μs

τ6=3.18 μs.

Thus:

Alternatively, the followingequation [6] (modified to include3.18 μs) canbeused:

Thefirst(fundamental)equationrequiresconsiderablemanipulation,butallowsphase tobe found,whereas the second is far easier to compute if onlygain isrequired.Thetwoequationsproduceexactlythesamegainresults.

Notethatincludingthe3.18-μstimeconstantchangestheextremeHFresponsefrom a 6 dB/octave low-pass filter to a final attenuation of 27.5 dB that isconstantwithfrequency.

CD

0 μs,15 μs

Thisequalisationwasusedona fewveryearlyCDs.Asub-code flag told theplayer toapply theequalisation that is commonly implementeddigitally in theoversamplingfilterwithnumericalprecision,butthatrathernegatestheintendednoise advantage of pre-emphasis after the Digital to Aalogue Convertor, sopreciselyimplementedanalogueequalisationwouldtheoreticallybebetter.

SourcingComponents:BargainsandDealingDirectly

NewPartsThemainstreamelectronicsdistributorsstockgeneralelectroniccomponents,butdo not necessarily stock specialist audio components such as largepolypropylene capacitors. It is well worth shopping around for specialistcomponents,assomestockistshaveimaginativepricingpolicies.Ifyouandyourfriendsareabletoclubtogethertogeneratealargeorderitcanbeworthapproachingmanufacturersdirectly;afterall,theworsttheycandoistolaughatyou.Transformersandcapacitorsarecottageindustrycomponents,sotheycanoftenbemadespecially toorder,andtheauthorhashad transformersmade by Sowter Transformers and capacitors by SuppressionDevices. If youchoosetofollowthiscourse,specifyinproperengineeringtermsascompletelyas possible what you need, and remember that every additional complicationaddstothefinishedprice.CompaniesatHi-Fishowsoftengivea‘show’discountontheirgoods,soitmaybeworthtimingyourordertocoincidewithashow.Theymayevenbepreparedtonegotiateafurtherdiscountonthelastdayoftheshow.

New/Second-HandParts

Electronicssurplusshopsareexcellentplacesforpickingupbargains,providedthatyouknowwhattolookfor.Itisagoodideatotakeadigitalmultimeter(forspotting open-circuit transformers), ESRmeter (for spotting faulty electrolyticcapacitors),tapemeasureandcalculatorwithyou.Ifyoucanafford(modern)orcarry (old) a specialist resistance meter that applies a high voltage (known

generically as a ‘Megger’ in theUK, but ‘hi-pot tester’ in theUSA), you canleavetheDVMathomeandalsospotfailedinsulation(rathercommon).Amateurradioandvintageaudiofairsareoftenfruitfulsourcesofcomponents,butbear inmind thatmostof thestandsareoccupiedby traderswhocirculatefromonefairtoanother,sotheyareunlikelytooffermanygoodsat‘giveaway’prices. Nevertheless, bargains can be had, and otherwise awkward-to-sourcecomponents can be found. In addition to components, there are usuallymanylargeritemsonsale–theauthorwasdelightedtopickupascruffyGarrard401for£30,buttherearealsoboatanchors.(‘Boatanchor’isthecharmingamateurradiotermforequipmentwhosemainattributeismass.)Whenlargecompaniesclosedownasiteorlaboratory,theyoftenauctionequipment,andthiscanbeasourceofcarefullymaintainedtestequipment.Itisyourresponsibilitytochecktheconditionofwhatyoubuy,andyouhavenocomebackafterwards.Don'tgetcarried away at the auction, and remember that taxwill be added to your bidprice.Beware of the second-hand test equipment that has not come from an entirelaboratory being closed down. Many large companies undertake a rollingreplacementof testequipment,but rather thanupgradinganentire laboratory’soscilloscopes at once (very expensive), one or twomight be bought per year.There are now older oscilloscopes which the accountants think are surplus(probably because the engineers claimed they were worn out). However, realengineersfeelthatthere’snosuchthingastoomuchtestequipment,sotheyhidethegoodkitandonlyreleasethefaultystuff.Thus,theequipmenttheyintendtoreleaseisthestuffthat:•worksexactlyasthemanufacturerintended,butishorrible;•hasadefinitefaultthatnobodyinthatlaboratorycould/wouldfix;• and worst, has a nasty little intermittent fault/feature that means nobodytrustsitanymore.

Incaseyouthinkthatthismeansthatsecond-handequipmentisinvariablydoomand gloom, there is the recent possibility that some fool will decide to ‘clearvaluablespace’byemptyingaroom‘fullof junkI’veneverseenanyoneuse’.Sadly, the only time such fools display efficiency is when they empty storerooms of irreplaceable (but rarely used) equipment, which is then sold forpeanuts; these clearances tend to be handled bywell-established industrial re-sellersratherthaneBay.Nevertheless,eBaycanbeausefulsource,andmanysellersareentirelyhonestintheirdescriptions.However,thefollowingdescriptions(andtheirtranslations)

maybehelpful:

“Idon’thaveanyelectronicsknowledgeandhaven’tbeenabletotestit,butI’msureit’sexcellent.”

Translation:“Iamanunprincipledcheattryingtoduckresponsibilityforthefactthatthejunkyou’rebiddingfordoesn’twork.”

“Rare.”

Translation:“Ididn’tseeanyothersforsaleattheinstantIplacedthisitem.”

“Excellentcondition.”

Translation:“Notvisiblybroken.”

“Goodconditionforitsage.”

Translation:“Ruined.”Anhonestandknowledgeablesellerwillhaveuploadedsufficientphotographs(correctly lit and in focus) to enable you to accurately gauge the condition oftheiritemandwillbehappytoanswer(sensible)questions.Theverybestsellermayrequireyoutoprovethatyouunderstandwhatyou’rebuyingandthatyouwilllookafterit.If you are not careful, Internet purchases can cost more than you thought.Carriage isalwaysextra (andsomeeBaysellers inflatepostage to reduce theirauctionfees).Ifitisaforeignpurchase,onceitarrivesinyourcountry,itwillbeliable for import duty, and you may need to insure against unreliable postalsystems.This all adds to costs, sodoyour sumsbeforebidding.Nevertheless,theInternetisanextremelyusefulworldwidesourceforotherwiseunobtainableitems.Evenwithin your own country, second-hand goods can be expensive, becausesome sellers have wildly inflated ideas about the value of their goods, sobargainsareoftenbest found throughyourcircleof friends,whoareawareofyour hobby. If you buy second-hand equipment from private advertisements,remember to add the cost of your return journey to inspect the goods, pluswhatever cost is required to refurbish. Just like buying a second-handvehicle,alwaysbepreparedtowalkawayfromadeal.

References

[1]Spangenberg,K,Vacuumtubes.1sted(1948)McGraw-Hill;p.31.[2]vanderZiel,A,Solidstatephysicalelectronics.2nded(

1968)Prentice-Hall;p.140.[3]QC11owner'smanual.AcousticalManufacturingCompany;

1953–1967.[4]Lipshitz,SP,JuneOnRIAAequalisationnetworks.(1977)JAES;

456-81.[5]Smith,L,Radiodesigners’handbook.4thed(1953)Iliffe;p.730.[6]DigestofHi-Fi.PartFour:Recordreplay.Hi-FiAnswers;August

1990.

0-9,andSymbols1/fnoise 6065μs/3.18-μsmanipulation 623–6246SN7valvefamily:distortionharmonics 202t, 204t7N7valvefamily,distortionharmonics 204t12SN7valvefamily,distortionharmonics 204t75-μs:

componentvalues 608–610de-emphasisnetwork 31f

78s,playing 656–657180μs:

equalisation 610, 611–614pairingerrors/manipulation 621, 622–623

300pFair-spacedcapacitors576f

317ICvoltageregulator235–236, 386–390317T:

asaconstantcurrentregulator 431fvoltagedropatswitch-on 431f

318μs:equalisation 610, 611–614pairingerrors/manipulation 621, 622–623

334Zconstantcurrentsink 521417Atriode 86f, 87f

Aabbreviations(measurementunits) 19–20

ACsee alternatingcurrent

ACloadline 120, 122activecrossovers 501–503, 559–561activedevices 41activeloads:cathodefollowers 113–114aircoredinductors 273–275airdielectic,metalplatecapacitors 253, 253fairspacedcapacitors 576f‘allinonego’equalisation 596–597Alpssteppedattenuator 554alternatingcurrent(AC) 21–41

balance 136, 446fcapacitors 25–27circuitanalysis 21–41filters 27–30inductors 25–27power 33–34randomnoise 40–41reactance 25–27resonance 31–33

RMS33–34sinewaves 21–24squarewaves 34–35timeconstants 30–31transformers 24–25

aluminiumelectrolyticcapacitors 258–266Americanvalvecodes 649–650AmericanWireGauge(AWG) 654America,RecordingIndustryAssociationof see RIAA

Ampere:definition 3amplificationfactor:definition 73amplifierstability:voltageregulators 398–399amplitude:sinewaves 22–23analoguediscsignal 585–591

balancedworking 589–591digital/vinyllevelcomparison 585–586equalisation 657–658humloops 589mechanicalproblems 587–588moving-coilcartridgeDCresistance 588–589phonoplugs 591pick-uparmwiring 588–591replayrumble 586RIAAstandard 586turntables 591, 656unbalancedinterfaces 589vinyl/digitalcomparison 585–586 seealso vinylrecords

analoguemicrogrooveequalisation 658–659analogue-to-digitalconversion 163–164anodes 319–321

anodecurves 516f, 613fanoderesistance 72, 75–76anodestoppers 469commoncathodetriodeamplifier 65, 65f, 66, 66fcurvebunching 178–179graphiteanodes 321heatdissipation 319–320maximumanodedissipation 69micawafers 326outgassing 319, 324, 324foverheating 324, 324fsecondaryemissionratio 320–321

arcs:transformers 293–294Arpeggioloudspeaker 187fattenuators:

Alps-steppedattenuator 554switchedattenuators 554–558

auctions:equipmentbuying 660

audiocircuit:Bulwer-Lyttonamplifier 542CrystalPalaceamplifier 529f

audionpatent 296audiosignalinterference 409audiotestlevelandfrequency 200audiotransformers 292–294 seealso inputtransformers; outputtransformers; transformersautomaticvoltageregulator(AVR) 305AWG(AmericanWireGauge) 654Ayrton-Perrywinding 247

Bbafflestepcompensation 501, 541–542balance:

Bulwer-Lyttonamplifier 536–540poweramplifiers 540–541pre-amplifiers 568–572

volumecontrols565

balancedhybridRIAAstage 628–645biascurrent 639–640BJTlinearity 638–639BJTnoise 632–633blockdiagram 634–635cathodefollowers 636tchannelbalance 645constantcurrentsinks 643DCstabilisation 631distortion 633–634equalisation 633–634

componentvalues 643tgainreduction 631HTpower 633–634HTsupply 643–645HTvoltage 636–637inputresistance 639–640inputstage

BJTMillercapacitance 637–638noise 640

JFETnoise 631–632low-noiseamplification 629Millercapacitance 630–631, 637–638practicalconsiderations 634RIAAcalculations 641–642semiconductor 629–630sourcefollowers 636t, 642–643totalgain 645

unity-gaincabledrivers 635–636VCE 638–639

balancedworking:analoguediscsignal 589–591bandgapreferences 44, 45bandwidth:definition 40bass:loudspeakers 438–439batteries 4–5, 76–77Baxandall:

feedbackanddistortiongraph 219–220, 219f, 220ftonecontrol 579, 580f, 581t, 583, 583f, 584f

BC549NPNtransistorcurves 131fBC558BPNPtransistorcurves 50fbeadcapacitors 387–388, 388fbeamtetrodes:

beamformingplates 89pentodes 87–94suppressorgrids 87–88

beamtriodes 85–86ß-follower 128–129B/Hcurve:inductors 273, 274fbias:

balancedhybridRIAAstage 639–640biascurrent 62, 639–640Bulwer-Lyttonamplifier 536–539cascodes 101fcathodefollowers 105–107, 106fdifferentialpair 524fgridbias 68f, 77, 190–191poweramplifiers 478fScrapboxChallengeamplifier 483–484, 493voltageregulators 384–386

binarynumbersystem 166tbins 167–168bipolarelectrolyticcapacitors 266, 266fbipolarjunctiontransistors(BJTs) 45–52, 147t

commonemitteramplifier 47–49Darlingtonpair 52, 52fDCconditions 49

emitterfollower 51generalobservations 52–53inputandoutputresistances 49–51linearity 638–639noise 632–633

‘blackbox’network 15, 15fbleederresistors 413fblocking 208–209, 593Blumleindistributedloadoutputstage 446fbridgerectifiers 334brightemitters:cathodes 299broadbandresponse:LCfilters 369–375Brownianmotion 81, 301Bulwer-Lyttonscalableparallelpush-pullamplifier 531–545

audiocircuit 542background 531–533bafflestepcompensation 541–542balance 536–540balancedinputs 540–541cathodefollowers

FETsourcefollowercomparison 533–536outputvalves 533

circuitry 542coupling 536–539distortion 532, 532t, 533gain 539–540globalnegativefeedback 545outputstagebias 536–539

volumecontrol541–542, 543t

bunchingofanodecurves 178–179burstingpimple:capacitors 264fbypasscapacitors 79–81, 271–272

Ccablecapacitance 653–654cabledrivers 572–579

air-spacedcapacitor 576fcathodefollowervalvechoice 574gainadding 577–578passiveRIAAde-emphasisnetwork 575fpolarityinversion 578–579practicalconsiderations 575–577quiescentcurrentdetermination 572–573

CAD(computeraideddesign) 622cancellation:distortionreduction 180–188canpotentials 414–415capacitance/capacitors 25–27, 249–251

addingplates 250airdielectric,metalplatecapacitors 253, 253fair-spacedcapacitors 576falternatingcurrent 25–27aluminiumelectrolyticcapacitors 258–266bipolarelectrolyticcapacitors 266, 266fburstingpimple 264fbypasscapacitors 79–81, 271–272capacitancevalue 269–270capacitancevariationwithfrequency 267, 268fceramiccapacitors 257choiceof 269–272coupling 207–219dielectrics 250–251, 267teffectiveseriesresistance 251, 270electrolyticcapacitors 258–266, 261f, 262f, 263f, 264fequivalentcircuits 252f, 254fheat 270HTcapacitors 413–415imaginarycapacitance 267–269impedanceagainstfrequency 259finputcapacitance,pre-amplifiers 599–605insulation/leakageresistance 251leakagecurrent 261f, 262–264, 262f, 263f, 270

maximumripplecurrent 251metallisedpapercapacitors 256–257metallisedplasticfilmcapacitors 256metalplatecapacitors 253microphony 270–271muscovitemicacapacitors 257noise 262foperatingvoltage 265outputcapacitance 152f, 402–403, 402foutputcouplingcapacitors 83parallelplatecapacitors 249–250, 250fplasticcapacitorcoding 653plasticfilm,foilplatecapacitors 253–256polypropylenecapacitors 263fpolystyrenecapacitors 255, 255fpolytetrafluoroethylenecapacitors 255–256relativepermittivity 251resonantfrequency 260–261, 260fself-capacitance 277–279silveredmicacapacitors 257speed-upcapacitor 382–384straycapacitances 608symbols 26ftantalumbeadcapacitors 387–388, 388ftantalumelectrolyticcapacitors 266types 251–269unit 25–26value 269–270variationwithfrequency 268fvoltagerating 269 seealso Millercapacitance

capsulemicrophones 103carbonresistors:distortion 222cartridges:

channelbalance 645mechanicalproblems 587–588Millercapacitancereduction 603fmoving-coilcartridges 588–589, 628, 629outputlevel 656–657sensitivity 593

unequalisedenvelopedmusicoutput 573f seealso analoguediscsignal; vinylrecords

cascodes 94–102bias 99, 101fcathodebiasresistor 99cathodefollowerbias 101fconstantcurrentsource 402fdistortion 172–173gain 98, 630Millercapacitance 98ra 97–98, 98fself-bias 100, 100fsemiconductorconstantcurrentsink 139–142, 144–145, 146ftriodemutualcharacteristics 97fuppervalve,operatingpoint 96fvalves 95, 96f, 99f, 101–102

cathodebias:cathodebiasresistor 99, 188–190commoncathodetriodeamplifier 76–78light-emittingdiodes 194frechargeablebattery 191, 191f

cathodebypasscapacitors 484–485cathodecoupledamplifier 130–133cathodecoupledphasesplitter 455–456, 459fcathodedecouplingcapacitor 79–81cathodefollowers 103–107, 179f

activeload 113–114balancedhybridRIAAstage 636tbias 105–107, 106fBulwer-Lyttonamplifier 533cabledrivers 574cascodes 101fdifferentialpair 454fdirect-coupling 513fdistortioncancellation 181fFETsourcefollowercomparison 533–536fixed-bias 104f, 105finputresistance 105–106

linearity 107loadline 104output

resistance 101stage 448fvalves 533

RL 107, 108fseriesfeedback 562fvalvechoice 574Whitecathodefollower 114–118 seealso μ-follower

cathodejunctionsignal 136cathoderaytube(CRT) 197–198, 335cathodes 299–302

brightemitters 299Brownianmotion 301controlgrids 314–315currenthoggingandheaterpower 309–311directvsindirectheating 303–305distortion 317–318dullemitters 300electromagneticproblem 304electrostaticproblem 304frame-gridvalves 316gridcurrent 315gridemission 315–316heater/cathodeinsulation 305–306heaterfilament 306fheatersandtheirsupplies 307–309heatervoltageandcurrent 311–313, 313findirectlyheatedcathodes 304–305ionbombardment 301ionisationnoise 322micawafers 326Miller-Larsoneffect 302–303oxide-coatedcathodes 300, 300fpoisoning 301–302, 326rejuvenation 301sputtering 315

standbymode 301–302Stefan’slaw 299–300stripping 301–302temperatureconsiderations 307thermalproblems 303, 315thoriatedtungstencathodes 299–300, 302–330variable-μgridsanddistortion 317–318 seealso commoncathodetriodeamplifier

Ccoretransformers 281–283, 282fCDs 585–586, 657, 659centre-tappedrectifiers 339ceramiccapacitors 257charge:definition 3chargeamplifiers 60–62, 102–103chargedobjects 2chassisbond:HFstability 469chokeinputpowersupplies 357–358

currentrating 359–361currentspikesandsnubbers 361–364intermediatemode 365–367mainstransformercurrentrating 361minimumloadcurrent 358–359

chokesuitability:hightension 487–488circuitanalysis 1–64

activedevices 41alternatingcurrent 21–41bipolarjunctiontransistors 45–52

commonemitteramplifier 47–49Darlingtonpair 52, 52fDCconditions 49emitterfollower 51generalobservations 52–53inputandoutputresistances 49–51

definitions 2–13electrons 2–13, 41feedback 53–56

equation 53–54mathematicalsymbols 1–2operationalamplifier 56–62

chargeamplifier 60–62DCoffsets 62emitterfollower 59, 60fintegrator 60inverters 57–58, 57fnon-invertingamplifier 58–59offsetcurrent 62virtualearthadder 57–58voltagefollower 58–59

potentialdividers 14–21silicondiodes 42–45symbols 1–2

circuits:definition 4equivalentcircuits 14–15Nortonequivalentcircuit 18–19, 18fseriesresonantcircuits 32fsimplecircuit 4–5Théveninequivalentcircuit 15–18, 72f

Class*1amplifiers 443Class*2amplifiers 443ClassA1loading 461–462ClassA2amplifiers 175–177, 177fClassAamplifiers 436–438, 441, 442fClassBamplifiers 441, 442f, 463–464ClassBloading 462–463ClassCamplifiers 441–443, 442fclipping 174fCMRR(common-moderejectionratio) 136–138coaxialcablecapacitance 653–654Cockcroft,J.D. 355collector-to-basecapacitance 141fcolourcodes:resistors 651–653commoncathodetestamplifiercircuit 170fcommoncathodetriodeamplifier 65–86

ACconditions 78–79ACparameters 73–76anodecharacteristics 65, 65f, 66, 66fbeamtriode 85–86

cathodebias 76–78cathodedecouplingcapacitor 79–81asaconstantcurrentsink 109–113distortion

cancellation 181fharmonics 170t

dynamicparameters 73–76gain 73, 74–75, 74fgridbiasusingbattery 68fgrid-leakresistor,valuechoice 81–82guided-gridtriode 85–86loadline 67–68, 67fMillercapacitance 83–85open-loopdistortion 221foperatingpoint 68–72outputcouplingcapacitor,valuechoice 83outputresistancereduction 85safeoperatingarea 70f

commonemitteramplifier 47–49, 51stabilisedamplifier 48f, 49

common-modeinterference 408–412heaters

audiosignalinterference 409history 408–409

mainstransformers 409, 410–411, 411fpost-transformerfiltering 411–412

common-moderejectionratio(CMRR) 136–138compactdiscs see CDscomponents 239–332

buying 660–662capacitors 249–251magneticcomponents 272newparts 660–662resistors 239–248second-handparts 660–662sourcing 660–662standardcomponentvalues 651

compositecurves 507compositeZener see Zenerdiodes

compression:power 501computeraideddesign(CAD) 622concertinaphasesplitter 460, 464f

gain 460–461outputresistance

equalloadingofterminals 461–462oneoutputonlyloaded 462–463

condensermicrophones 103conductionangle:

poweramplifiers 441–442ripplecurrent 346–350

conductors:resistance 245constantcurrentsinks see sinks,constantcurrentcontactcapacitance:pre-amplifiers 549–550contactresistance:pre-amplifiers 550controlgrids 314–315controlgrid-stoppers 468, 469copperlosses:transformers 284copperoxiderectifiers 342–343coulomb:definition 3coupling 207–219

blocking 208–209Bulwer-Lyttonamplifier 536–539couplingcapacitors 69, 207–219, 593fDC-couplingandlevelshifting 211–213electromagneticheadphoneamplifier 213–216levelshiftingandDCcoupling 211–213low-frequencystepnetworks 210–211Nortonlevelshifter 212–213, 212f, 216–219overload 208–209Théveninlevelshifter 213transformers 210

CRcircuits 36fCRhigh-passfilter 28fCRnetworks 35–39crossovers,active 501–503, 559–561crosstalk 549–550, 570f, 571fCRT see cathoderaytubeCrystalPalaceamplifier 505–531

13E1conditions507–510

334Zconstantcurrentsink521audiocircuit 529fcascodeconstantcurrentsink 518–521circuitry 512–513, 529fconstantcurrentsinks 512–513, 518–521designer’sobservations 525differentialpair 514–515, 516f, 517distortion 510driverstage 510–512globalnegativefeedback 527–531, 529f, 530f, 531fGM70triode 527gridcurrentagainstloadresistance 509fHFstability 522, 523fHTregulators 522–524, 524fHTsupply 513–514, 517Ikmeasurement 527negativefeedback 527–531, 529f, 530f, 531fnegativeHTsupply 514operatingpoints 520foutputresistance 511outputstage

conductionangle 511–512current 514–515, 516f

overloadrecovery 512positiveHTsupply 513–514powersupply 512–513, 524–525, 526fregulatordesign 530fstabilisation 515–517, 518–521stereovsmass 524symmetryandnegativeHTsupply 514thermalstability 521valvematching 517–518

Va(max)andpositiveHTsupply 513–514Vg2ratings 525–527Zobelnetwork 509f

CSS see sources,constantcurrentcurrent 3

atanode 8fconventional/electronflow 41currentgaindefect 46, 46f, 52hogging 309–311Kirchhoff’slaw 7–8spikes 361–364 seealso alternatingcurrent

currentsinks see sinkscurvebunching:anodes 178–179cut-offfrequency:filters 29–30

DDarlingtonpair 52, 52fdB(decibel)scale 20–21DCbalanceadjustment 445fDC-bias 188–196

cathoderesistorbias 188–190constantcurrentsinkbias 195–196diodecathodebias 191–195gridbias 190–191rechargeablebatterycathodebias 191

DC-coupledClassAelectromagneticheadphoneamplifier 213–216DC-coupledpowercathodefollower 177fDCcoupling 211–213DCmagnetisation 283–284DCoffsets 62DCreferencenoise 230–236DCstabilisation 631decibel(dB)scale 20–21degaussing 199deLee,Forest 296denarynumbersystem 166tDenonDL103moving-coilcartridge 628, 629dielectrics:

capacitors 250–251, 267tdielectricabsorption 254

differentialpair 133–139ACbalance 136bias 524fcathodejunctionsignal 136common-moderejectionratio 136–138CrystalPalaceamplifier 514–515, 516f, 517distortioncancellation 182–183driverstage 454fgain 135HTsupply 517linearity 517outputresistance 135–136outputstagecurrent 514–515, 516f

phasesplitters 455powersupplyrejectionratio 138–139signalatcathodejunction 136

digitalactivecrossovers 559–561digitalmeasurement 163–166

Moirépatternings 164numbersystems 165, 166tNyquistcriterion 164precision 165–166quantisation 165sampling 164scaling 164–165

digitaloscilloscopes 162digitalrecordings 585–586 seealso CDsdiodecathodebias 191–195diodes 43, 193–194

ACrectification 42fchoiceof 334–340conduction 43definition 42forwarddrop 192tlight-emittingdiodes 44Schottkydiodes 43sloperesistance 192t seealso Zenerdiodes

distortion 54balancedhybridRIAAstage 633–634Bulwer-Lyttonamplifier 532, 532t, 533cancellation 180–188

common-cathodeamplifier/cathodefollower 181fpush-pulldistortion 184WesternElectricharmonicequaliser 184–185, 186–188

carbonresistors 222cascodes 172–173cathodes 317–318clipping 174fcommon-cathodeamplifier/cathodefollower 181fCrystalPalaceamplifier 510DC-biasproblems 188–196

cathoderesistorbias 188–190

constantcurrentsinkbias 195–196diodecathodebias 191–195gridbias 190–191rechargeablebatterycathodebias 191, 191f

differentialpair 182–183distortionresidual 160, 161EC8010RIAAstage 615, 616, 616fgridcurrentdistortion 173–177, 620–621

atcontactpotential 173ClassA2amplifiers 175–177

volumecontrols174–175waveforms 174f

intermodulationdistortion 157lineardistortion 155, 156lowdistortiondesign 169μ-follower 124f, 125f, 172fnegativefeedback 219–222non-lineardistortion 156–157, 195fnulling 182fparameterrestriction 177–180pentodes 90–91, 90f, 582fpush-pulldistortion 184ScrapboxChallengeamplifier 482–483, 498tshunt-regulatedpush-pullamplifier 128, 129fsignalamplitude 169–173slewingdistortion 39, 584, 585fsoftclipping 174ftestcircuits 183ftransfercharacteristics 156ftypes 155–156valvechoice 196–207

audiotestlevelandfrequency 200conclusions 206–207convention 205distortion-weightedresults 206, 207telectrondeflection 198–199

envelopecarbonization 198interpretation 203–205low-distortionvalves 196–198, 199medium-μvalves 205–206tests 199–202

WesternElectricharmonicequaliser 184–185, 186–188distortionmeasurement 155–163

alternativerectifiers 162author’smethod 168–169choiceofmeasurement 158–159harmonicdistortion 159, 170t, 182f, 184t

6SN7valvefamily 202tsummationandrectifiers 160–161weightingofharmonics 159–160

interpretation 157–158measurementchoice 158–159noiseandTHD+N 162–163non-lineardistortion 156–157, 195frectifiers 162RMSmeasurement 161spectrumanalysers 163testequipment 171f

DN2540:outputcapacitance 152fDN2540:constantcurrentsinkdesign 149–153dominantpoleslugging 465–467driverstage:

CrystalPalaceamplifier 510–512differentialpair 454fpoweramplifiers 452–453ScrapboxChallengeamplifier 491–493

dualtriodes:asdrivers 452tseries-passregulatorvalves 481t

dullemitters:cathodes 300Dushmanequation 650dynamic/ACparameters 73–76dynamicrange 155–238

definition 155

E

E55Lpentode90feBay 661, 662EC8010RIAAstage 614–628

5μs/3.18μsmanipulation 623–62475μsproblem 621180μspairingerrors/manipulation 621, 622–623318μspairingerrors/manipulation 621, 622–623componentselection 627–628computeraideddesignsolution 622directmeasurementproblems 624–627distortion 615, 616, 616fgridcurrentdistortion 620–621heaters 619–620inputstage 614–617inputtransformer 617–618Millercapacitance 621outputstage 619powersupply 426–433, 432fpracticalconsiderations 624productiontolerances 627–628RIAAequalisation 620–621, 628secondstage 618–619valvechoice 619–620valvetolerances 628Zobelcapacitance 617t

ECC88/6DJ8valve 95eddycurrentlosses 280EF86pentode 91–94, 605effectiveseriesresistance(ESR) 251, 270efficiency:definition 441E/Icoretransformers 281, 281felectrolyticcapacitors 258–266, 261f, 262f, 263f, 264felectromagneticheadphoneamplifier 213–216electro-mechanicalswitches 550–551

electrometres 226–229electro-motiveforce(EMF) 3, 4electrons 2–13

deflection 198–199emission 296–297flow 41, 81, 82ionisation 81velocity 297–298

electrostaticscreens 284–285EMF see electro-motiveforceemitterfollower 51, 59, 60fendcaps:resistors 242–243envelopecarbonization 198envelopetemperature 324–326equalisation:

180-μsequalisation 610318-μsequalisation 610, 611–614‘allinonego’equalisation 596–597analoguediscs 657–658analoguemicrogroove 658–659awkwardtolerances/values 612–614balancedhybridRIAAstage 633–634CDs 659componentvalues 643timplementation 594–596networks 611–614noiseadvantage 607replaygainagainstfrequency 595fsplitRIAAequalisation 597–599vinylrecords 657–659 seealso EC8010RIAAstage

equipment:newparts 660–662second-handparts 660–662sourcing 660–662

equivalentcircuits 14–15capacitors 252finductors 277f

equivalentresistance see outputresistanceEseriesresistors 239, 240

ESR see effectiveseriesresistanceEuropeanPro-Electronvalvecodes 647–649excessnoise 40–41EZ81rectifier 502f

FFarad 19–20, 25–26fastfouriertransform(FFT) 166–169

periodicityassumption 167windowing 167–168

feedback:circuitanalysis 53–56feedbackequation 53–54, 461–462

limitations 54feedbackfactor 56, 219f, 220f, 461–462inputandoutputimpedances 55–56inputstage 471foutputimpedance 55–56ScrapboxChallengeamplifier 494, 499tshuntfeedback 560fterminology 55–56transformers 285–286 seealso negativefeedback; positivefeedback

ferritedustcore:transformers 280FETs(field-effecttransistors) 147–148FETsourcefollowers 533–536

FFTsee fastfouriertransform

field-effecttransistors(FETs) 147–148filmresistors 241–244filters 27–30

alternatingcurrent 27–30high-passfilters 27–28, 28fLCfilters 369–376, 372f, 373f, 373tmains 425–426pass-bandvalue 29stop-bandfrequency 29

Fleming,JohnAmbrose 295, 296flickernoise 40–41floatingparaphasephasesplitter 458–460, 461ffoilplatecapacitors 253–256

ß-follower 128–129force 3, 4Forest,Leede 296forwardvoltagedrop 43, 44t, 192tframe-gridvalves 316freeware:ResCalc 651frequency 22, 34full-waverectification 334, 335f, 340fundamentalfrequency 34fundamentalseriesregulators 379–381, 379ffuses 415–416

Ggain:

balancedhybridRIAAstage 631, 645Bulwer-Lyttonamplifier 539–540cabledrivers 577–578cascodes 98, 630commoncathodetriodeamplifier 73, 74–75, 74fconcertinaphasesplitter 460–461CrystalPalaceamplifier 511differentialpair 135pentodes 91, 92fpoweramplifiers 465–466, 493pre-amplifiers 577–578ScrapboxChallengeamplifier 493

gappedcores:inductors 275–277, 277fgasamplification 340–341gasrectifiers 340–341gasreferences:

noise 232voltageregulators 392f, 393, 395

GETItransistor 45fgetters 323–324Gillespie,A.B. 228–229glassenvelopes 328–329glassreinforcedplastic(GRP)boards 329–330globalnegativefeedback see negativefeedbackGM70triode 527gold-platedpins 329graphiteanodes 321Greinachervoltagemultiplier 356f, 357gridbias 68f, 77, 190–191gridcurrent 229, 315

againstloadresistance 509fdistortion 173–177, 620–621electrometres 226–229noise 226, 228f, 229

gridemission 315–316

grid-leakresistors 77, 81–82, 563–565, 601fgrids,control 314–315gridstoppers 468, 469GRP(glassreinforcedplastic)boards 329–330guarding 570fguided-gridtriodes 85–86guitaramplifiers 293–294

Hhalf-waverectification 340hardvacuumvalverectifiers 336, 336t, 337harmonicequaliser 184–185, 186–188, 187fharmonics 34–35

againstfeedbackfactor 219f, 220fdistortionmeasurement 159, 170t, 182f, 184t

6SN7valvefamily202tsummationandrectifiers 160–161weightingofharmonics 159–160

poweramplifiers 445headphoneamplifier,DCcoupledClassAelectromagnetic 213–216heat:

anodes 319–320capacitors 270dissipation,anodes 319–320resistors 240–241, 248

heaters:history 408–409power 305–306, 309–311rectificationandsmoothing 423–424, 429–430, 432–433regulation 424–425, 431valvechoice 619–620voltage 311–313, 313f, 405–407

Hedgecascodedifferentialpair 513fHenry:unit 25–26HFsinewavetest 39HFstability:CrystalPalaceamplifier 522, 523fhigh-passfilters 27–28, 28fhightension(HT)supplies:

balancedhybridRIAAstage 643–645capacitorcanpotentials 414–415chokesuitability 487–488CrystalPalaceamplifier 513–514, 517, 522–524, 523f, 524fdifferentialpair 517

HTpower,balancedhybridRIAAstage 633–634HTvoltage 485, 636–637

ratings 413–414, 413f, 414frectificationandsmoothing 420–423, 429–430, 485–486regulation 388–390, 418–419, 428–429

CrystalPalaceamplifier 524, 524fScrapboxChallengeamplifier 485–490

smoothing 485transformers 486–487

humcancellation 394humloops 589hysteresisloss:transformers 280

IIkmeasurement:CrystalPalaceamplifier 527imaginarycapacitance 267–269impedance:

definition 26 seealso outputresistance; resistanceindirectlyheatedcathodes 304–305indirectlyheatedrectifiers 336inductance/inductors 25–27, 273–279

air-coredinductors 273–275alternatingcurrent 25–27B/Hcurve 273, 274fequivalentcircuits 277fgappedcores

ACandDC 276–277, 277fAConly 275–276

impedanceagainstfrequency 278fLissajousfigure 279, 279fphaseagainstfrequency 278fpowersupplychokes 276–277, 277frelativepermeability 273self-capacitance 277–279symbols 26fThieleformulae 273–275, 275funit 25–26voltageregulators 384wirewoundresistors 245–248

inputcapacitance:pre-amplifiers 599–605inputimpedance:feedback 55–56inputresistance 49–51

balancedhybridRIAAstage 639–640bipolarjunctiontransistors 49–51cathodefollowers 105–106

inputselection:pre-amplifiers 548–551inputstage:

balancedhybridRIAAstage 637–638poweramplifiers 464, 471fpre-amplifiers 580f, 581f, 582f

inputtransformers 289–291, 617–618insulation/leakageresistance:capacitors 251integrators:operationalamplifiers 60intermodulationdistortion 157internet:equipmentbuying 661, 662inter-stagetransformers 291–292inter-windingcapacitance:mainstransformers 409, 410–411, 411finverters:operationalamplifiers 57–58, 57fionbombardment:cathodes 301ionisationnoise 322ironlosses:transformers 279–283

JJFETcascodeconstantcurrentsink 152f, 185fJFETnoise:balancedhybridRIAAstage 631–632JFETs 606Johnsonnoise 40Joule:definition 4JTBakerCompany 300

KKelvinconnection 374–375, 374f, 375f, 424Kirchhoff:

equations 208–209laws 7–9, 8f, 9f

Kovarpins 329

Llamps 4–5lasercutting:resistors 243, 244lawfaking:balancecontrol 568–572LCfilters:

amplitudeagainstfrequencyresponse 373fbroadbandresponse 369–375capacitorvaluesandparasiticcomponents 373tmodel 372fwide-bandresponse 375–376

leads:resistors 242leakagecurrent:

capacitors 261fvoltageregulators 405

leakageinductance:transformers 280–281leakageresistance:

capacitors 251pre-amplifiers 550

LEDs see light-emittingdiodeslevelshiftingandDCcoupling 211–213LF see low-frequencylight-emittingdiodes(LEDs) 44

cathodebias 191–193, 194fforwarddropagainstappliedcurrent 44fredLEDnoise 236

light-sensitiveresistors 565–567, 566tlineardistortion 155, 156linearity:

bipolarjunctiontransistors 638–639testcircuit 171f

linearpowersupplies 333, 334fLipshitzRIAAreplayequations 659Lissajousfigure:inductors 279, 279flisteningtests 497lithiumbatteries 76–77loadline:

ACloadline 120, 122cathodefollowers 104

commoncathodetriodeamplifier 67–68, 67fellipticalloadline 611fμ-follower 122fortransformer-coupledstage 437f

localfeedback 55logarithmiclaw:

deviationagainstrotation 570f

volumecontrols553, 563f

Loktalbase 326–328long-tailedpairs see differentialpairloopgain 465loudspeakers:

Arpeggioloudspeaker 187fefficiency 501impedancedeviationagainstfrequency 187freflexloudspeakers 438transformers 285–286treble 438–439

low-distortionvalves 196–198, 199low-frequency(LF):

LFinstability 467–468stabilitychecking 367stepnetworks 210–211

low-passfilters 29LPs see vinylrecordsLRnetworks:squarewavetransients 35–39

Mmagneticcomponents 272 seealso inductance/inductors; transformersmagneticcoredeterioration:transformers 294magneticscreeningcans:transformers 294, 295fmagnetisingcurrent:transformers 353–354, 355fmagnetostriction:transformers 285Maidahighvoltageregulator 389fmainsfiltering 425–426mainsfusing 415–416mainsswitching 416–417mainstransformers:inter-windingcapacitance 409, 410–411, 411fmainsvariation:stabilisationagainst 518–521mathematicalsymbols:circuitanalysis 1–2maximumanodedissipation 69maximumripplecurrent 251measurementunits 19–20medium-μvalves 201f, 205–206mercuryvapourrectifiers 340, 340t, 341, 341tmercury-wettedrelays 550meshanodes 319fmetalfilmresistors 241–244metallisedpapercapacitors 256–257metallisedplasticfilmcapacitors 256metalplatecapacitors 253micawafers 324–326microgrooveequalisation 658–659microphony 103, 270–271Millercapacitance 83–85

balancedhybridRIAAstage 630–631, 637–638cartridges 603fcascodes 98phasesplitters 463–464

Miller-Larsoneffect 302–303modulationnoise:resistors 243–244Moirépatterning 164MOSFETs 217, 218motorboating 399, 467–468

moving-coilcartridges 588–589, 617t, 628, 629μfollower 118–124

ACloadline 122circuits 128fclipping 124distortion 124f, 125f, 172fwithJFETconstantcurrentsource 131flimitations 123–124linearitytestcircuit 171fnoiseimmunity 121operatingconditionsoflowervalve 120faspre-amplifieroutputstage 555fvalvechoice 122–123

Mullard5-20amplifier 472–477MullardEF37 228–229multifilarwinding:transformers 283multipliersandunits 19–20muscovitemicacapacitors 257mutualconductance 75–76, 76f

definition 47pentodes 92, 93triodes 614t

NN-channelMOSFET 217, 218negativefeedback 53, 55

Bulwer-Lyttonamplifier 545CrystalPalaceamplifier 527–531, 529f, 530f, 531fDC-coupledheadphoneamplifier 215distortion 219–222ScrapboxChallengeamplifier 494, 499t seealso feedback

nickel-chromiumfilmresistors 242noise 222–223

1/fnoise 606amplifyingdevices 224–229

gridcurrentnoiseandPoisssondistribution 226BJTnoise 632–633capacitors 262fDCreferences 230–236

author’smeasurements 230–232compositeZener/317ICregulatorcomparison 235–236gasreferencenoise 232, 233tredLEDnoise 236semiconductorreferencenoisemeasurementsandstatisticalsummation 232–234Zenerreferencenoisevariationwithoperatingcurrent 234–235

definition 222–223electrometersandgridcurrent 226–229gasreferencevalvescomparison 233tinputstagenoise 640ionisationnoise 322JFETnoise 631–632Johnsonnoise 40modulationnoise 243–244paralleldeviceconnection 606–607pentodes 93, 94, 551fpre-amplifiers 550, 580f, 581f, 582f, 599–605randomnoise 40–41resistance/resistors 223–224, 243–244, 245–248, 604, 605andTHD+N 156–157thermalnoise 40

totalharmonicdistortion 162–163valves 605–606valvesockets 326voltage-referrednoise 233t

volumecontrolvalues562–563wirewoundresistors 245–248

non-inductivethickfilmpowerresistors 248non-invertingamplifier 58–59non-lineardistortion 156–157, 195fNortonequivalentcircuit 18–19, 18fNortonlevelshifter 212–213, 212f, 216–219NPNtransistors 45–46, 131fN-typeregions 42nulling 182fnumbersystems 165, 166tNyquistcriterion 164

Ooctave:definition 28–29offsetcurrentandvoltage 62Ohm’slaw 5–6op-amps see operationalamplifiersopen-loopdistortion 220f, 221foperatingpoint:

commoncathodetriodeamplifier 68–72CrystalPalaceamplifier 520fScrapboxChallengeamplifier 482–483, 492–493

operationalamplifiers(op-amps) 56–62chargeamplifier 60–62DCoffsets 62emitterfollower 59, 60fintegrator 60inverters 57–58, 57fnon-invertingamplifier 58–59offsetcurrent 62virtualearthadder 57–58voltagefollower 58–59

optimisedvalvevoltageregulators 393–394, 396foscilloscopeamplifiers 130–133oscilloscopes 162, 279OTL(outputtransformer-less)amplifiers 450, 451foutgassing 319, 324, 324foutputamplifiersoutputbiasservo 478foutputcapacitance:

DN2540 152fvoltageregulators 402–403, 402f

outputcouplingcapacitors 83outputcurrent:voltageregulators 394–397outputimpedance:feedback 55–56outputinductance:voltageregulators 384outputpower 500–504

activecrossovers 501–503compression 501

loudspeakerefficiency 501paralleloutputvalves 503–504ScrapboxChallengeamplifier 482–483transformerdesign 503–504Zobelnetworks 501–503

outputresistance 15–16, 49–51bipolarjunctiontransistors 49–51cathodefollowers 101commoncathodetriodeamplifier 85constantcurrentsink/source 108CrystalPalaceamplifier 511differentialpair 135–136ScrapboxChallengeamplifier 490–491, 493voltageregulators 397–399

outputstage:conductionangle 511–512current 514–515, 516fpoweramplifiers 435–441, 504–505

single-endedClassAoutputstage 436–438transformerimperfections 439–441

outputtransformer-less(OTL)amplifiers 450, 451foutputtransformers 285–286, 291

ClassBsignals 444fconnectionmodification 446–450imperfections 439–441poweramplifiers 443–450ScrapboxChallengeamplifier 483

outputvalves 506tBulwer-Lyttonamplifier 533ScrapboxChallengeamplifier 481, 488f

outputvoltage:equation 15–16overheating:anodes 324foverload 208–209, 512oxide-coatedcathodes 300, 300f

Ppairingerrors/manipulation:

180-μs 621, 622–623318-μs 621, 622–623

paperboards,syntheticresinbonded 329–330paralleldeviceconnection:noisereduction 606–607paralleloutputvalves 503–504parallelplatecapacitors 249–250, 250fparallelresonantcircuits 33fparameterrestriction:distortionreduction 177–180parasiticoscillation 468

anodestoppers 469ultra-linearoutputstages 469

partitionnoise:pentodes 93, 94pass-band:filters 29patents:audionpatent 296PCBmaterials 329–330P-channelMOSFET 217, 218peak 22pentodes:

6K7variable-μpentode,controlgrid 317fanodecharacteristics 92fBaxandalltonecontrol 581tbeamtetrodes 87–94asconstantcurrentsinks 111–113curves 89–91distortion

harmonicsagainstlevel 582fspectrum 90–91, 90f

driverstage 453tEF86pentode 91–94, 605gain 91, 92fgrids 318humcancellation 394mutualconductance 92, 93noise 93, 94, 551fpartitionnoise 93, 94 seealso tetrodes

period:definition 22

periodicityassumption 167perveance 76phase 22–23, 161fphasesplitters:

cathode-coupledphasesplitter 455–456, 459fClassBoutputstageMillercapacitance 463–464concertinaphasesplitter 460, 464f

gain 460–461outputresistance 461–463

differentialpair 455directcoupledtocathodefollowers 454fwithtriodeconstantcurrentsink 456f

floatingparaphasephasesplitter 458–460, 461fMillercapacitance 463–464phasesplitters 454–464Rk≈RLcompensatedsolution 455–458Rk<<RLhighfeedbacksolution 458–460Rk>>RLsolution 455Schmittphasesplitter 455–456see-sawphasesplitter 458–460

phonoplugs 591photoelectricemission 227–228pick-uparms 588–591, 657pinconnections 650pins:

glassenvelopes 328–329gold-platedpins 329

plasticcapacitorcoding 653plasticfilm,foilplatecapacitors 253–256platecapacitors 250PNPtransistors 50fPoissondistribution 226polarityinversion 23, 24, 578–579poleslugging:dominant 465–467polypropylenecapacitors 263fpolystyrenecapacitors 255, 255fpolytetrafluoroethylenecapacitors 255–256positivefeedback 53, 55 seealso feedback; negativefeedback

potentialdifference 3, 4potentialdividers 14–21, 214–215, 214f

decibelscale 20–21equivalentcircuits 14–15multipliers 19–20Nortonequivalentcircuit 18–19, 18fThéveninequivalentcircuit 15–18transformers 290units 19–20voltageregulators 379f, 398, 398f, 400f

potentials:summationwithinaloop 9fpotentiometers 553power 6–7

alternatingcurrent 33–34poweramplifiers 435–546

balancedinputs 540–541bias 478fBlumleindistributedloadoutputstage 446fBulwer-Lyttonscalableparallelpush-pullamplifier 531–545

audiocircuit 542background 531–533bafflestepcompensation 541–542balance 536–540cathodefollowers 533–536circuitry 542coupling 536–539distortion 532, 532t, 533gain 539–540globalnegativefeedback 545outputstagebias 536–539powersupplies 543–545

volumecontrol541–542, 543t

cathodefolloweroutputstage 448fcircuitry 450–452classesof 441–443conductionangle 441–442

CrystalPalaceamplifier 505–53113E1conditions 507–510334Zconstantcurrentsink 521audiocircuit 529fcascodeconstantcurrentsink 518–521circuitry 512–513, 529fconstantcurrentsinks 512–513designer’sobservations 525differentialpair 514–515, 516f, 517distortion 510driverstage 510–512gain 511globalnegativefeedback 527–531, 529f, 530f, 531fGM70triode 527gridcurrentagainstloadresistance 509fHFstability 522, 523fHTregulators 522–524, 524fHTsupply 517Ikmeasurement 527negativefeedback 527–531, 529f, 530f, 531fnegativeHTsupply 514outputresistance 511outputstageconductionangle 511–512outputstagecurrent 514–515, 516foverloadrecovery 512positiveHTsupply 513–514powersupply 512–513, 524–525, 526fregulatordesign 530fstabilisation 515–517, 518–521stereovsmass 524symmetryandnegativeHTsupply 514thermalstability 521valvematching 517–518Va(max)andpositiveHTsupply 513–514Vg2ratings 525–527Zobelnetwork 509f

designs 470–480driverstage 452–453, 454f

feedback 471fgain 465–466, 493globalfeedbackatinputstage 471fharmonicdistortion 445inputstage 464, 471floopgain 465, 466Mullard5-20amplifier 472–477non-zerosupplyresistance 489foutputbiasservo 478foutputpower 500–504

activecrossovers 501–503compression 501loudspeakerefficiency 501powercompression 501transformerdesign 503–504Zobelnetworks 501–503

outputstage 435–441, 504–505highoutputresistance 438–439single-endedClassAoutputstage 436–438transformerimperfections 439–441

outputtransformer-lessamplifier 450, 451foutputtransformers 439–441, 443–450phasesplitter 454–464push-pulloutputstage 443–450QuadIIamplifier 449, 449f, 477–480, 482fScrapboxChallengesingle-endedamplifier 480–499

bias 483–484cathodebypasscapacitor 484–485conclusions 498–499DCoperatingpoint 482–483designer’sobservations 497–498distortion 482–483, 498tdriverstage 491–493gain 493globalnegativefeedback 494, 499tHTchokesuitability 487–488HTrectification 485–486HTregulatoroption 488–490HTsmoothing 485

HTtransformers 486–487HTvoltage 485listeningtests 497operatingpoint 482–483, 492–493outputclass 482outputpower 482–483outputresistance 490–491outputtransformer 483outputvalves 481regulatoroption 496fteethingproblems 494–497valvebiasing 483–484

single-endeddesign 480stability 465–470

controlgrid-stoppers 468controlgridstoppers 469HFstabilityandchassisbond 469LFinstability 467–468motorboating 467–468parasiticoscillation 468, 469stabilitymargin 469–470

ultra-linearoutputstage 446fWilliamsonamplifier 470–472, 473f

powerrating:resistors 249powerresistors 244, 248powersupplies 333

blockdiagram 418fBulwer-Lyttonamplifier 543–545canpotentialsandundischargedHTcapacitors 414–415chokes 276–277, 277f, 376fcommon-modeinterference 408–412CrystalPalaceamplifier 512–513, 524–525, 526fdesign 417–426

heaterrectificationandsmoothing 423–424heaterregulation 424–425HTrectificationandsmoothing 420–423HTregulation 418–419mainsfiltering 425–426

differentialpair 138–139

EC8010RIAAstageadaptation 426–433heaterrectificationandsmoothing 432–433heaterregulation 431HTrectificationandsmoothing 429–430HTregulation 428–429referencevoltages 429

fuses 415–416HTcapacitorsandvoltageratings 413–414, 413f, 414fissues 412–417linearsupply 333, 334fmains

fusing 415–416switching 416–417

majorblocks 333–334powersupplyrejectionratio 121, 138–139

topologycomparison 138trectification 334–378smoothing 334–378switchers 333, 334fswitch-onsurge 415transformerregulation 412transistoramplifiers 351ftypes 333–334voltageregulators 378–407 seealso hightension(HT)supplies

pre-amplifiers 547–646analoguediscsignal 585–591

balancedworking 589–591digital/vinyllevelcomparison 585–586humloops 589mechanicalproblems 587–588moving-coilcartridgeDCresistance 588–589phonoplugs 591pick-uparmwiring 588–591replayrumble 586RIAAstandard 586turntables 591unbalancedinterfaces 589

balancecontrol 568–572cabledriver 572–579

air-spacedcapacitor 576fcathodefollowervalvechoice 574gainadding 577–578passiveRIAAde-emphasisnetwork 575fpolarityinversion 578–579practicalconsiderations 575–577quiescentcurrentdetermination 572–573valvechoice 574

gain 577–578inputselection 548–551

contactcapacitance 549–550contactresistance 550crosstalkbetweensources 549–550disparatelevelsbetweensources 548–549electro-mechanicalswitches 550–551leakageresistance 550noise 550relayswitching 550–551

limitedcontrolpre-amplifier 547RIAA

75μscomponentvalues 608–6103180μscomponentvalues 610, 611–614318μscomponentvalues 610, 611–614equalisation 594–599, 595f, 610, 611–614noise 599–607stagedesign 591–599stageexample 599–610

straycapacitances 608tonecontrol 579–585traditionalpre-amplifierwithfullcontrols 547vinyl/digitalcomparison 585–586

volumecontrols551–568

activecrossovers 559–561attenuationerroragainstattenuation 560fbalance 565controlvaluelimitations 552–553

digitalactivecrossovers 559–561disturbingchannelmatching 554–555grid-leakresistors 563–565light-sensitiveresistors 565–567, 566tlogarithmiclaw 553, 563fμ-follower 555fnoiseeffects 562–563potentiometers 553QBASICprograms 556, 557, 558quadrantfaders 554shuntfeedbackvsseriesfeedback 560fspreadsheets 558–559, 560fsteppedattenuators 564fswitchedattenuators 554–558transformervolumecontrols 567–568

volumecontrolplusunity-gainlinedriver548 seealso balancedhybridRIAAstage; EC8010RIAAstage

Pro-Electronvalvecodes,European 647–649PSSR(PowerSupplyRejectionRatio) 121, 138–139, 138tPSUD2software 367–369, 371, 420–423, 429–430PTFE(polytetrafluoroethylene)capacitors 255–256P-typeregions 42push-pullamplifier see shunt-regulatedpush-pullamplifierpush-pulldistortioncancellation 184

QQBASICprograms 556, 557, 558QuadIIamplifier 477–480, 482f, 449, 449fquadrantfaders 554quantisation 165quiescentcurrentdetermination 572–573

Rra,cascodes 97–98, 98frandomnoise 40–41RCfiltersectioning 376–378reactance:

alternatingcurrent 25–27inductorandcapacitoragainstfrequency 27f

rechargeablebatterycathodebias 191, 191fRecordingIndustryAssociationofAmerica see RIAArecords see vinylrecordsrectangularwindow:fastfouriertransform 167f, 168rectification/rectifiers 334–378

bridgerectifiers 334capacitoreffectonratings 337fcentre-tappedrectifiers 339chokeinputpowersupply 357–358

currentrating 359–361currentspikesandsnubbers 361–364intermediatemode 365–367mainstransformercurrentrating 361minimumloadcurrent 358–359

copperoxiderectifiers 342–343distortionmeasurement 160–161, 162EZ81rectifier 502ffull-waverectification 334, 335f, 340gasamplification 340–341gasrectifiers 340–341half-waverectification 340hard-vacuumvalverectifiers 336, 336t, 337heaterrectification 423–424, 432–433HTrectification 420–423, 429–430, 485–486hybridvalve/semiconductorrectifier 339findirectlyheatedrectifiers 336LCfilters

amplitudeagainstfrequencyresponse 373fbroadbandresponse 369–375capacitorvaluesandparasiticcomponents 373tmodel 372f

wide-bandresponse 375–376mercuryvapourrectifiers 340, 340t, 341, 341tproblematicrectifiers

copperoxiderectifiers 342–343gasrectifiers 340–341seleniumrectifiers 342, 342f

PSUD2software 367–369, 371RCfiltersectioning 376–378rectifier/diodechoice 334–340reservoircapacitors,choiceof 350–353reverserepetitivemaximum 338, 339, 339tRFinterference/spikes 343ripplecurrent 335–336, 346–350ripplevoltage 344–346, 344fseleniumrectifiers 342, 342fsinglereservoircapacitorapproach 343thermionicrectifiers 334–335transformers

back-to-backarrangementforHTsupplies 353–355choiceof 350–353coresaturation 350

valverectifiers 335–336, 336t, 337seriesresistance 348solidstateplug-inreplacement 338f

voltagemultipliers 355–357redLEDs:

forwarddropagainstappliedcurrent 44fnoise 236

referencevoltages 429reflexloudspeakers 438regulators see voltageregulatorsrelativepermeability 273relativepermittivity 251relayswitching 417, 550–551, 571freplaycurve:vinylequalisation 595–596, 596freplayrumble 586ResCalcfreeware 651reservoircapacitors 365–367

choiceof 350–353

rectification 343ripplecurrent 349fwaveforms 349f

resinbondedpaper,synthetic 329–330resistance:

conductors 245inputresistance 49–51noise 223–224Ohm’slaw 5–6outputresistance 49–51totalnetworkresistance 11, 11f, 12, 12f, 13–14, 13f

volumecontrols223–224

resistors 239–248Ayrton-Perrywinding 247bleederresistors 413fcarbonresistors 222choiceof 248–249colourcodes 651–653endcaps 242–243equivalentresistor 10–11, 11ffourbandresistors 652grid-leakresistors 601fheat 240–241, 248lasercutting 243, 244lawfakingresistors 568–572, 569tleads 242light-sensitiveresistors 565–567, 566tmetalfilmresistors 241–244modulationnoise 243–244noise 224–225, 243–244, 245–248, 604, 605non-inductivethickfilmpowerresistors 248powerrating 249powerresistors 244, 248preferredvalues 239–240series/parallelnetworks 9–13, 9fsixbandresistors 652

sputtering 242surfacemountresistors 564ftolerance 248tracking 243–244TypeAsteppedattenuator 561t, 563voltagerating 243, 249winding 247wirewoundresistors 244

ageing 244–245equivalentcircuits 247fnoiseandinductance 245–248

resonance:alternatingcurrent 31–33capacitors 260–261, 260f

reversebias 193–194reverserepetitivemaximum 338, 339, 339tRFinterference/spikes 343RIAA(RecordingIndustryAssociationofAmerica):

75μscomponentvalues 608–610180μsequalisation 610, 611–614‘allinonego’equalisation 596–597balancedhybridRIAAstage 641–642blocking 593equalisation

180μsequalisation 610, 611–614318μsequalisation 610, 611–614‘allinonego’equalisation 596–597awkwardtolerances/values 612–614implementation 594–596interactionproblem 610, 611–614noiseadvantage 607replaycurve 595–596, 596freplaygainagainstfrequency 595fsplitRIAAequalisation 597–599vinylrecords 586

inputstages 195JFETs 606noise

1/fnoise 606

inputstage 599–605noiseadvantageduetoequalisation 607paralleldeviceconnection 606–607resistornoise 604, 605valvenoise 605–606, 607

passiveRIAAde-emphasisnetwork 575fpre-amplifier 578f, 584f, 610fresistornoise 604, 605stages

design 591–599example 599–610noiseandinputcapacitance 599–605requirements 592–594

standard 586straycapacitances 608ultrasonicoverload 593, 594valvenoise 605–606, 607vinylrecordaudiotimeconstant 31 seealso balancedhybridRIAAstage; EC8010RIAAstage

Richardson/Dushmannequation 650ripplecurrent 349f

capacitors 251andconductionangle 346–350rectification 335–336waveform 347f

ripplereduction 382–384ripplevoltage 344–346, 344fRk≈RLcompensatedsolution:phasesplitters 455–458Rk<<RLhighfeedbacksolution 458–460Rk>>RLsolution 455RL,cathodefollowers 107, 108froutoptimisationbytransistortype,currentsinks 145–146RMS(RootoftheMeanoftheSquares) 33–34, 161R-Typevalve 296f

Ssag 39, 39tsampling:analogue-to-digitalconversion 164SanyoOS-CONelectrolyticcapacitor 264scaling:digitalmeasurement 164–165Schmittphasesplitter 455–456Schottkydiodes 43ScrapboxChallengesingle-endedamplifier 480–499

bias 483–484cathodebypasscapacitor 484–485conclusions 498–499DCoperatingpoint 482–483designer’sobservations 497–498distortion 482–483, 498tdriverstage

biassetting 493gain 493operatingpoint 492–493outputresistance 493requirements 491topology 491–492valvechoice 492

gain 493globalnegativefeedback 494, 499thightension

chokesuitability 487–488rectification 485–486regulatoroption 488–490, 496fsmoothing 485transformers 486–487voltage 485

listeningtests 497operatingpoint 482–483, 492–493output

class 482power 482–483resistance 490–491, 493transformer 483

valve 481, 488fteethingproblems 494–497valvebiasing 483–484

screengrids 86–87, 94, 318secondaryemissionkink 87secondaryemissionratio(SER) 320–321second-handequipment 660–662see-sawphasesplitter 458–460seleniumrectifiers 342, 342fself-bias:cascodes 100fself-capacitance 277–279semiconductorconstantcurrentsinks 139–153, 146f

designusingDN2540 149–153field-effecttransistors 147–148routoptimisationbytransistortype 145–146transistorsasactiveloadsforvalves 142–145

semiconductors 42–45balancedhybridRIAAstage 629–630referencenoisemeasurementsandstatisticalsummation 232–234

seriesfeedback 560f, 562fseries/parallelnetworks:resistors 9–13, 9fseriesregulators 378–379 seealso fundamentalseriesregulators; two-transistorseriesregulatorsseriesresonantcircuits 32fseriesswitching 571fSER(secondaryemissionratio) 320–321shuntfeedback 560fshunt-regulatedpush-pullamplifier(SRPP) 125–128, 443–450

circuits 128fdistortion 128, 129foperatingcurrent 127fTHDvsHTvoltage 129f

shuntregulators 378–379shuntswitching 571fsignalamplitude 169–173signalinterference 409silicondiodes 42–45

currentagainstforwardbiasvoltage 42f

silveredmicacapacitors 257silverpins 329sinewaves:

alternatingcurrent 21–24amplitude 22

single-endedClassAoutputstage 436–438sinks,constantcurrent:

334Zconstantcurrentsink 521balancedhybridRIAAstage 643bias 195–196commoncathodeamplifiers 109–113CrystalPalaceamplifier 512–513, 518–521definitions 107–109JFETcascode 152foperatingconditions 110fpentodes 111–113semiconductortype 139–153

designusingDN2540 149–153field-effecttransistors 147–148routoptimisationbytransistortype 145–146transistorsasactiveloadsforvalves 142–145

Skirrow,Peter 160slewingdistortion 39, 584, 585fsloperesistance 43, 44t, 192tsluggingthedominantpole 465–467Small,R. 438small-signalpentode(EF86) 91–94, 605smoothing 334–378

hightension 485singlereservoircapacitorapproach 343

SN7valvefamily:electricalalternatives 205theatervoltagesandcurrents 203t

snubbers 361–364, 502fsockets see valvesocketssoftclipping 174fsoftware:

PSUD2 367–369, 371, 420–423, 429–430

ResCalc 651sourcefollowers 636t, 642–643sources,constantcurrent:

cascodes 402fdefinitions 107–109μ-follower 131f

space-charge-limitedcondition:triodes 66spectrumanalysers 163speed-upcapacitors 382–384splitbobbintransformers 354–355, 410fsplitRIAAequalisation 597–599spreadsheets:

shuntfeedbackvsseriesfeedback 560f

volumecontrols558–559

sputtering 242squarewaves:

alternatingcurrent 34–35responseat10▒kHz 215fsag/low-frequencycut-offfrequencyrelationship 39tsquarewavesagandlowfrequency 654–656timeandfrequency 34ftransients 35–39

squegging 467SRBP(syntheticresinbondedpaper)boards 329–330SRRP see shunt-regulatedpush-pullamplifierstabilisedcommonemitteramplifier 48f, 49stability 465–470

controlgrid-stoppers 468, 469dominantpoleslugging 465–467HFstabilityandchassisbond 469LFinstability 467–468loopgain 465motorboating 467–468parasiticoscillation 468

anodestoppers 469ultra-linearoutputstages 469

sluggingthedominantpole 465–467squegging 467stabilitymargin 469–470

standardcomponentvalues 651statisticalregulators 399–402, 402f, 403, 403f, 404f, 418, 419f

heaterrectificationandsmoothing 420HTrectificationandsmoothing 420optimisation 404–405

Stefan’slaw 299–300step:definition 35stepnetworks 210–211steppedattenuators 561t, 563, 564fsteppedcurrentfeature:PSUD2software 367f, 368stereocrosstalk 397–398stop-bandfrequency:filters 29styli 656–657suppressorgrids 87–88surfacemountresistors 564fswitchedattenuators 554–555

design 555–558TypeA 555–556, 555f, 566tTypeB 555–556, 555fTypeC 555f, 556, 565

switcherpowersupplies 333, 334fswitches:

electro-mechanicalswitches 550–551leakageresistance 550mains 416–417

switch-onsurge 415symbols:circuitanalysis 1–2syntheticresinbondedpaper(SRBP)boards 329–330

Ttantalumbeadcapacitors 387–388, 388ftantalumelectrolyticcapacitors 266temperature see heattertiarywinding:transformers 25testcircuits 199–200

distortion 183flinearitytestcircuit 171fmedium-μvalve 201f

tetrodes 86–87anodecharacteristics 86–87, 88fgrids 318screengrids 86–87secondaryemissionkink 87 seealso beamtetrodes; pentodes

THD(totalharmonicdistortion) 90, 128, 158, 162–163thermalnoise 40thermalstability 521thermionicemission 650–651thermionicrectifiers 334–335thermionicvalves 295–299

electronsemission 296–297velocity 297–298

history 295–296transittime 298–299 seealso anodes; cathodes; commoncathodetriodeamplifier; controlgrids; pentodes; tetrodes; triodes; valvechoice/testing; valvesockets

Théveninequivalentcircuit 15–18, 72fThéveninlevelshifter 213thickfilmpowerresistors 248Thieleinductorformulae 273–275, 275fTHINGY(transistorisedheaterinsulationnoisegroundingyoke) 405–407thoriatedtungstencathodes 299–300, 302–330timeconstants 30–31tolerance:resistors 248tonecontrol 579–585toroidtransformers 282–283, 282f, 350totalharmonicdistortion(THD) 90, 128, 158, 162–163

totalnetworkresistance 11, 11f, 12, 12f, 13–14, 13ftotalparallelresistance:reciprocalof 10tracking:resistors 243–244transconductance see mutualconductancetransformers 279–291

abuses/uses 291–292, 293–294alternatingcurrent 24–25arcs 293–294audiotransformers 292–293back-to-backarrangementforHTsupplies 353–355bifilarwinding 283Ccores 281–283, 282fchoiceof 292–293, 350–353copperlosses 284coresaturation 350coupling 210damageprevention 294DCmagnetisation 283–284eddycurrentlosses 280E/Icores 281, 281felectrostaticscreens 284–285equivalentcircuits 287ffeedback 285–286guitaramplifiers 293–294high-frequencymodels 288–289, 289fHTtransformers 486–487hysteresisloss 280, 439, 440inputtransformers 289–291inter-stagetransformers 291–292ironlosses 279–283leakageinductance 280–281loudspeakers 285–286low-frequencymodels 287–288, 287fmagneticcoredeterioration 294magneticscreeningcans 294, 295fmagnetisingcurrent 353–354, 355fmagnetostriction 285mid-frequencymodels 288, 288fmodels 286–289

multifilarwinding 283potentialdividers 290splitbobbinisolatingtransformers 354–355splitchamber 283, 283fsymbols 24ftoroidalcorearrangement 282–283, 282fuses/abuses 291–292, 293–294voltageregulation 412

volumecontrol567–568windings 283–284Zobelnetwork 290, 290f, 291 seealso outputtransformers

transients:squarewaves 35–39transistoramplifiers 351f, 500transistorisedheaterinsulationnoisegroundingyoke(THINGY) 405–407transistors:

BC549NPNtransistor 131fBC558BPNPtransistor 50fGET1transistor 45f seealso bipolarjunctiontransistors;semiconductorconstantcurrentsinks

transittime:thermionicvalves 298–299triodes:

417Atriode 86f, 87faschargeamplifiers 102–103, 102fdriverstage 452tdualtriodes 452t, 481tGM70125Wtriode 527guided-gridtriodes 85–86noisefrom 225space-charge-limitedconditions 66transconductance 614t seealso commoncathodetriodeamplifier

tungstenfilaments 295, 302–330turntables 591, 656two-transistorseriesregulators 381–382, 381f, 496fTypeAsteppedattenuator 561t, 563TypeAswitchedattenuator 555–556, 555f, 558–559, 566tTypeBswitchedattenuator 555–556, 555f

TypeCswitchedattenuator 555f, 556, 565

Uultra-linearamplifiers 446f, 469ultrasoundoverload 593, 594unitsandmultipliers 19–20unity-gaincabledrivers 635–636US see American…

Vvacuumquality:valves 322valvebases:

leakageresistanceagainstfrequency 327fLoktalBase 326–328

valvechoice/testing:6SN7family 202t, 204t7N7valvefamily 204t12SN7valvefamily 204taudiotestlevelandfrequency 200conclusions 206–207convention 205distortion 196–207

distortion-weightedresults 206, 207tdriverstage 492electrondeflection 198–199envelopecarbonization 198heaters 619–620interpretation 203–205Loctalfamily 204tlow-distortionvalves 196–198, 199medium-μvalves 205–206μ-follower 122–123SN7family 203ttestcircuits 199–200testresults 200–202

valvedata 647–651Americanvalvecodes 649–650EuropeanPro-Electronvalvecodes 647–649pinconnections 650thermionicemission 650–651

valvenoise 322, 607valverectifiers 335–336, 336t, 337

seriesresistance 348solidstateplug-inreplacement 338f

valveregulators see voltageregulatorsvalvesockets:

leakageresistanceagainstfrequency 327f

lossesandnoise 326valves,thermionic 295–299

electronsemission 296–297velocity 297–298

history 295–296transittime 298–299 seealso anodes; cathodes; commoncathodetriodeamplifier; controlgrids; pentodes; tetrodes; triodes; valvechoice/testing

valvesupportcircuitry:bipolartransistors 147tvalvevoltageregulators see voltageregulatorsVa(max)andpositiveHTsupply 513–514variablebiasvoltageregulators 384–386variable-μvalves 317–318VCE:balancedhybridRIAAstage 638–639Vg2ratings 525–527vinylrecords:

cartridgeoutputlevel 656, 656–657cutcurve 595, 596, 596fdigitalcomparison 585–586equalisation 657–659groovesize 656–657old/worndiscs 594pick-uparmmechanics 657speedissues 656 seealso analoguediscsignal; EC8010RIAAstage; RIAA

virtualcathode 89virtualearthadder 57–58Volt:definition 4voltage:Kirchhoff’slaw 8–9 seealso Va(max); VCEvoltagecompliance 108voltagedrop,forward 43, 44t, 192tvoltagefolloweroperationalamplifiers 58–59voltagemultipliers 355–357voltagenoise 225voltagerating 525–527

capacitors 269, 413–414, 413f, 414fresistors 243, 249

voltagereferences 43–45voltage-referrednoise 233tvoltageregulators 378–407

317ICvoltageregulator 386–390amplifierstability 398–399automaticvoltageregulator 305compositeZenerbypassing 402–403CrystalPalaceamplifier 530ffundamentalseriesregulator 379–381, 379fgasreferences 392f, 393, 395heatersupplyelevation 405–407humcancellation 394increasingoutputcurrent 394–397leakagecurrent 405Maidahighvoltageregulator 389foptimisedvalvevoltageregulator 393–394, 396foutputcapacitance 402–403, 402foutputcurrent 394–397outputinductancecompensation 384pentodeinput 394potentialdividers 379f, 398, 398f, 400fpowersupplyoutputresistance 397–399seriesregulator 378–379shuntregulator 378–379speed-upcapacitor 382–384statisticalregulator 399–402, 402f, 403, 403f, 404f

optimisation 404–405stereocrosstalk 397–398THINGY 405–407transformers 412transistorisedheaterinsulationnoisegroundingyoke 405–407two-transistorseriesregulator 381–382, 381fvalvevoltageregulators 390–393variablebiasvoltageregulator 384–386voltagejumps 392Zenerdiodes 382, 401, 401f, 402–403, 404–405Zenersloperesistance 404f

volumecontrols

174–175, 175fattenuationerroragainstattenuation 560fbalance 565Bulwer-Lyttonamplifier 541–542, 543tcontrolvaluelimitations 552–553digitalactivecrossovers 559–561disturbingfrequencyresponse 552–553grid-leakresistors 563–565light-sensitiveresistors 565–567, 566tlogarithmiclaw 553, 563fnoise 223–224, 562–563potentiometers 553pre-amplifiers 551–568quadrantfaders 554shuntfeedbackvsseriesfeedback 560fspreadsheets 558–559, 560fsteppedattenuators 564fsurfacemountresistors 564fswitchedattenuators 554–558transformervolumecontrols 567–568

WWalton,E.T.S. 355watt:definition 6–7waveforms:

reservoircapacitors 349fripplecurrent 347f

weightingofharmonics 159–160WesternElectricharmonicequaliser 184–185, 186–188Whitecathodefollower 114–118

analysis 114–117asoutputstage 117–118

whitenoise 40, 162–163wide-bandresponse:LCfilters 375–376Williamsonamplifier 470–472, 473fwindings:

Ayrton-Perrywinding 247transformers 24–25, 283–284

windowing:fastfouriertransform 167–168periodicity 167f

wirewoundresistors 244–248work:definition 4

Index

ZZenerdiodes 43, 193–194

compositeZener/317ICregulatorcomparison 235–236voltageandappliedcurrentagainsttime 428fvoltageregulators 382, 401, 401f, 402–403, 404–405

Zenerreferencenoise 234–235Zenersloperesistance 404fZobelcapacitance 617tZobelnetworks 290, 290f, 291, 501–503, 509f