YAMAHJrTJiESousdREiNfoRCEMENTHANdbookSECONd EdmoxWRiTTEN FORYAMAI-IA ByGARy DAvis &RALpl-l JONESINSIDEDESIGN &ILLUSTRATIONBYGARYDAVIS &ASSOCIATESCOVERDESIGNBYLEESAVOlTPublished by.Halle,nardPulllishingC,rp,rali,n7777 W. Bluemound Road, P.O. Box 13819Milwaukee, WI 53213Copyright 1987, 1989 by Yamaha Corporation ofAmerica and Gary Davis & Associates.ISBN: 0-88188-900-8All Rights Reserved. Written Permission fromYamaha Corporation of America (P.O. Box 6600,Buena Park, CA90622) is required for reproductionin any form, except short excerpts may be reproducedor quoted forpurposes of critical review.First EditionSecond EditionFirst Printing:Second Printing:Third Printing:First Printing:Second Printing:December, 1987February, 1989April, 1989June, 1989February, 1990Printed in the U.S.A.PREfACEIn 1974, the people at Yamahaasked me to write some spec sheets fora dozen or so new guitar amplifiers andsmall mixers. As soon as that job wasdone, they showed me a new product.It was a console, one intended to be amajor departure- a leap into theheart of the professional sound rein-forcement market - fora companythen known primarily as a musical in-strument manufacturer (or a motor-cycle manufacturer, if you were not amusician). Yamaha said they wantedto firmly establish themselves as aleader, and they felt that a comprehen-sive instruction manual for the newconsole would help do the job.We hadonly aprototype board and somesketchy specs, but no detailed draw-ings or data, so I contacted engineerJohn Windt, and we measured the per-formance. Working with pencil andportable typewriter, I created the firstdraft ofthe PM-wOOOperating Man-ual.The PM-WOOconsole did putYamaha on the map, insofar as theprofessional sound reinforcementbusiness is concerned. The manual wasso popular that it had to be reprintedmany times (far exceeding the numberof consoles built). It became a standardtext in several college courses due to itsdetailed discussions of the basics ofsound reinforcement.During the ensuing decade, Yamahaasked me to write manuals for avariety of amps, signal processors,mixers and so forth, and to maintainthe same standard of excellence webegan with the PM-WOOmanual. Un-fortunately, it is very expensive toproduce and print 30 to 60 pages ofinstructions forevery product, and it isdifficult to justify - especially whenonly 8 to16 pages contain the "hardcore" operational data. For this reason,both Yamaha and I had pondered theconcept of a generalized guide forsound reinforcement, apart fromanyindividual operating manuals.Finally, 10 years after the PM-WOOmanual was published, Yamahadecided to move forward with thisproject. We anticipated a book of 96 to160 pages in length, and expected itwould take a year to complete. Thefirst edition of The Sound Reinforce-ment Handbook was comprised of 384pages, some 256 illustrations, and tookthree years to complete. The firstprinting of 10,000 copies sold out in ayear, and while we were completingthis second edition, another two runstotalling nearly 5,000 more copies hadto be printed. Clearly, the book hasbeen wellreceived, and we're grateful.The Sound Reinforcement Handbookis the largest project I have everundertaken. It would not have beenpossible without the support andpatience of the people at YamahaCorporation of America, and at theirparent company, Yamaha Corporationof Japan. All of uswere able to endurethe strain of gathering data, editing it,and producing this book for one reason:we had an important goalto achieve.That goal was to create ausefulreference for anyone who is interestedin learning the basics of sound rein-forcement. In this second edition, wehave improved many ofthe illustra-tions, and added entirely new topics,corrected a number of minor errors andtypos (perhaps created new ones). Wehave made the book much easier to useby completely reorganizing the chap-ters and creating an index.We had originally planned the firstedition for looseleafbinding, with theintent to publish updates periodically.The cost, however, would have beenprohibitive, and so this soft coverformat was adopted, with the prospectof a new edition when the need arises.We all hope you enjoy and learn fromthis one.Gary D. DavisSanta Monica, CaliforniaJune, 1989This hANdbookis dEdiCATEdTOThESOUNdREiNfORCEMENTiNdUSTRY,ANdTOAllThOSE proplr whohAVE WORkEdSOhARdTObRiNGbETTERSOUNdANdMusicTOTIlEWORLd. WEpARTicuLARLy wishTOAckNOwLEdGEThELATEDEANEJENSEN fORhisAdVANCEMENT ofSOUNd.AckNowLEdGEMENTSMy associate Ralph Jones made asubstantial contribution to the writingand illustrations that are in this hand-book. Ralph's background with MeyerSound Labs, and his formal musiceducation, served to balance theknowledge I have gleaned from myinvolvement with many other soundequipment manufacturers, and my ownphysics background. Many thanks,Ralph. And thanks also to your wife,Claudette, who helped with some of theearly deadlines.As I mentioned in the Preface, thepeople at Yamaha Corporation ofAmerica and of Japan (formerly Nip-pon-Gakki in Japan) have supportedthis project - both financially and withconsiderable assistance in terms ofsuggested contents, proof reading, andhelping to secure expert consultingassistance when that was required.They also deserve praise for giving mea free hand to write as much as wasrequired, to include all we wished(including a number of competitors'names, when that information seemedimportant), and to not make this asales presentation for any particularYamaha equipment. Special thanks goto John Gatts and Bob Davis foroverseeing the project at Yamaha, andto Craig Olsen for his help with theinitial outline. Nancy Mastroianni, askilled proof reader, was employed byYamaha to highlight my inconsistenthyphenation, dangling participles, andother typographical errors. SoundmanSteve Getson of Trenton, NJ, kindlyidentified many typos after the firstprinting. At our request, Brian WeissofWord'sworth also did extensive proofreading. Mind you, we exercised ourright of editorial license, so if some ofthe usage remains non-standard, itmay not be Brian's or Nancy's fault.Bob Davis, who collated all thecomments and edits at Yamaha forboth editions, was assisted byYamahaDistrict Manager Ray Bloom and by in-dependent consultant Rolly Brook.Without this valuable input, I wouldstill be choking on my left foot. Thanks,guys.I made many phone calls to engi-neer John Windt, whose extensiveknowledge of system grounding andsystem design added considerably tothis book. Thanks also to the lateDeane Jensen (of Jensen Transform-ers, Inc.), who provided very usefulinformation on transformer anddifferential balancing, mic splitting,and other aspects of circuit design.Lynn McCroskey and Alvis Wales ofSonics, Associates were very helpfulwith regard to interconnect of balancedand unbalanced circuitry, and theyalso made some useful suggestionsregarding the relatively minor directeffects of wind on sound propagation.Bill Swintek of Swintek WirelessMicrophones gave uspermission to useportions of data we wrote for himseveral years ago, and the people atlIMEsubmitted a major portion ofthedata dealing with wireless micro-phones and wireless intercom systems,which together make this portion of thebook far more accurate and completethan it otherwise would have been.Thanks to engineer Bob Ludwig forexplaining the pros and cons of consoleplacement. Thanks to Crown Interna-tional Corporation for sending photosand information on their PZM micro-phones.Composer/synthesist/consultantChristopher L. Stone of DragonsenseStudio was most helpful in guiding ourMIDI and SMPTE discussions, andspecial thanks go to Jim Cooper of J.L.Cooper Electronics for proof readingthe MIDI material and offeringvaluable corrections and suggestions.I also wish to thank Carolyn andDonDavis, whose Syn-Aud-Con semi-nar and whose book, Sound SystemEngineering,have significantly aug-mented my understanding of soundand acoustics.Last, but certainly not least, manythanks to Georgia Galey, my hard-working office manager who did somuch to help bring this book fromconcept to reality: typing some datainto the computer, proofing the typedand typeset copy, following uponphone calls, photocopying and thenecessary go-fer jobs - in other words,filling in wherever and whenever shecould. GDDPS: The answer to the unasked question:No. Bob Davis, Don Davis and Gary Davisarenot related to one another. They all justhappen toshare the same surname andwork in the same general industry.SOUNdREiNfoRCEMENT HANdbookTAbLE ofCONTENTSPage Section/Subsection & Title Page Section/Subsection & TitleSection1. Whatis a Sound System Section 5. Sound Outdoors1 1.1 The audiosignal43 5.1 The inverse square law1 1.1.1 Sound waves44 5.1.1 Inverse square law calculations2 1.1.2 The electrical representation of sound45 5.2 Effectsof environmental factors2 1.1.3 Phase45 5.2.1 Wind3 1.1.4 Adding sine waves46 5.2.2 Temperaturegradients4 1.2 The basic purpose of asound system46 5.2.3 Humidity4 1.3 A conceptual model of asound system47 5.3 Feedback control5 1.4 Inputtransducers47 5.3.1 Maximum gain (available gain before5 1.5 Output transducersfeedback)6 1.6 A practical model of asound system49 5.3.2 Using directional microphones andloudspeakersSection 2. Frequency ResponseSection 6. SoundIndoors9 2.1 A definition53 6.1 Boundaries10 2.1.1 Basicspecificationmethods54 6.1.1 Theabsorption coefficient11 2.1.2 Octaverelationships andmeasurements55 6.2 Standing waves12 2.2 Frequency response of practical audio devices56 6.2.1 Standing waves inaroom12 2.2.1 Electronic circuits and cables14 2.2.2 Microphones57 6.3 Reverberation58 6.4 Critical distance14 2.2.3 Loudspeakers60 6.4.1 Implicationsfor sound reinforcement15 2.3 Voiceand instrument ranges15 2.3.1 The speaking voiceSection 7. Block Diagrams15 2.3.2 Thesinging voiceand musical instruments16 2.3.3 Harmonics61 7.1 General discussion17 2.4 Effect of acoustical factors 63 7.2 Symbolicconventions66 7.3 Notational conventionsSection 3. The Decibel, SoundLevel,67 7.4 Analysisof simple block diagrams& RelatedItems70 7.5 Summation19 3.1 What isadecibel? Section 8. How toRead& Interpret19 3.1.1 Amathematical definition of the dBSpecifications21 3.1.2 Relative versusabsolutelevels22 3.2 Relating thedecibeltoelectrical signal levels 71 8.1 General discussion22 3.2.1 dBm 71 8.1.1 Why specs are notalways what they seem22 3.2.2 dBu71 8.1.2 Examplesof specs that should bedoubted23 3.2.3 dBvand dBv 72 8.1.3 What tolookfor24 3.2.4 Converting dBvtodBu (ortodBm across 72 8.2 Frequency response600ohms) 72 8.2.1 Distinguishing frequencyresponse,24 3.2.5 Relating dBv, dBu and dBm tospecifi-frequencyrange, andpower bandwidthcations 74 8.2.2 Graphicversus printedspecs25 3.2.6 dBw 74 8.2.3 What isagoodfrequency response spec?25 3.3 Relating the decibel toacoustic levels 75 8.3 Noise25 3.3.1 dBSPL 75 8.3.1 What isnoise?26 3.3.2 dBPWL76 8.3.2 White noise27 3.4 What isrms? 76 8.3.3 Pink noise28 3.5 Volume, level and gain 77 8.3.4 Shaping thenoise29 3.6 Loudness 78 8.3.5 EIN:ameasure of micpreamplifier noise29 3.6.1 Equal loudness contours and phons 78 8.3.6 Specifying output noise30 3.6.2 What wecan deduce from equal loudness 80 8.3.7 Other types of noisecontours81 8.4 Harmonicdistortion31 3.6.3 Loudnesscompensation81 8.4.1 What isharmonicdistortion?82 8.4.2 Measuring harmonicdistortion84 8.4.3 Factorsaffecting harmonicdistortionSection4. Dynamic Range specifications33 4.1 Dynamicrange85 8.5 Intermodulationdistortion33 4.1.1 A definition85 8.5.1 Measuring IMdistortion33 4.1.2 The dynamic range of atypicalrock86 8.5.2 Sourcesof IMdistortionconcert86 8.5.3 Howmuch distortion istolerable?33 4.1.3 The electrical dynamic range of thesound86 8.5.4 Transient intermodulation distortionsystem87 8.6 Input and output impedances34 4.1.4 The acoustical dynamic range of the system88 8.6.1 Confusion about input and output35 4.2 Headroomimpedances35 4.2.1 A definition88 8.6.1.1 Outputimpedance36 4.2.2 Why headroom isimportant89 8.6.1.2 Inputimpedance37 4.3 Manipulating dynamic range inapractical sound90 8.6.2 The implicationsof impedance mismatchessystem91 8.6.3 Impedanceand frequency37 4.3.1 Why not build asound system with excess92 8.7 Standard operating levelsdynamicrange?92 8.7.1 General classification of levels37 4.3.2 What happens when the sound system is93 8.7.2 Expressing the widepower range of asoundinadequate?system39 4.3.3 Howtofit wide program dynamics into a94 8.7.3 How impedance relatesto levelsound system with limited dynamic rangespecifications42 4.3.4 Howmuch headroom isadequate?94 8.7.3.1 Power vsimpedance94 8.7.3.2 Overloading an outputSOUNdREiNfoRCEMENTHANdbookSection10. Microphones10.1 Methodsof transduction10.1.1 Dynamic10.1.2 Condenser10.1.3 Electretcondenser10.1.4 Ribbon10.1.5 Carbon10.1.6 Piezoelectric10.2 Functionaldesign10.2.1 Hand-held10.2.2 Stand-mounting10.2.3 Lavalier10.2.4 Contact pickup10.2.5 Pressureresponse10.2.6 Shotgun10.2.7 Parabolic10.2.8 Multi-elementarrays10.2.9 Noisecancelling microphones10.3 Acoustical andelectrical characteristics10.3.1 Pickup patterns10.3.1.1 Omnidirectional10.3.1.2 Cardioid10.3.1.3 Bidirectional or figure-810.3.1.4 Supercardioid10.3.2 Frequencyresponse10.3.3 Proximity effect10.3.4 Transientresponse10.3.5 Output level orsensitivity10.3.6 Overload10.3.7 Impedance10.3.8 Balanced and unbalancedconnections10.4Applicationinformation10.4.1 Windscreens andpopfilters10.4.2 Shock mounts10.4.3 Phantompower10.4.4 Effect of the number of openmicrophones10.4.5 Gain andmicrophone placement10.4.6 Stereorecording10.5 Wirelessintercom systems10.5.1 What isawireless intercom?10.5.2 Whouses wireless intercoms?10.5.3 What is the background of wirelessintercoms?10.5.4 Typesof wireless intercoms10.5.5 Frequenciesused10.5.6 Improved range andnoise reduction10.5.7 Evaluating and selecting asystem10.5.8 Conclusions10.5.9 Glossary of wireless intercom termsPageTC-2Page9595959696 8.897979799 8.9100 8.10101103103 8.11168169170170172 11.7172173173174174174175 11.8178 11.91781781791801987, 1989Section/Subsection &Title11.1211.1111.10Section11. Preamplifiers, Small Mixers,&Mixing Consoles11.1 General discussion11.2 Preamplifiers11.2.1 What are they, and what do they do?11.2.2 Impedanceconverters11.2.3 Phonopreamps11.3 Mixers11.4 Consoles11.4.1 What isaconsole?11.4.2 Howmixes differ:pre &post faderconsiderations11.4.3 Panning, summing and master faders11.5 Understanding consolespecifications11.5.1 Howmany inputs, mixes and outputs?11.5.2 Signal-to-noise ratio11.5.3 Maximum voltage gain11.5.4 Headroom11.5.5 Indicators11.6Transformer isolated versuselectronically balancedinputs&outputs .,116.1 Transformers versusdifferentialamps:priceconcerns11.6.2 Discrete versus ICdifferential amps11.6.3 The case forthe transformer11.6.4 Transformers and ACsafety11.6.5 MoreontransformersGain staging and gain structure11.7.1 Why does gain have tobemanipulated?areview of sound levels fedtothe console11.7.2 Gain control at themicrophone input11.7.3 Input attenuation orpadding11.7.4 Eliminating other causes of signal-level(&gain) related distortion11.7.4.1 Summing amp overdrive11. 7.4.2 Power ampoverdriveInterface withsub-mixersStage monitor mixing consoles11.9.1 What isastage monitor system?11.9.3 Why amonitor console ispreferable toamix from the main house console11.9.4 The importance of a high qualitymonitor mix11.9.5 Other benefits of aseparate monitorconsole11.9.6 Polarity (phase) reversal as a tool tofightfeedback11.9.7 Eliminating SCR dimmer noiseMicrophone splitting11.10.1The splitter transformer. .11.10.2 Additional isolation for high-noiseenvironments11.10.3Splitting amicwithout a transformerReducing feedback inthestage monitor system11.11.1Directional microphones11.11.2Polarity reversal (or"phase" reversal)11.11.3Ringing out amonitor system11.11.4 Aiming monitor loudspeakersEquipment placement11.12.1 Additionalmonitor console placementfactors11.12.2Main house mixing console placement10.6Wirelessmicrophonesystems10.6.1 What isawireless mic?10.6.2 Who uses wireless mics?10.6.3 What is the background of wirelessmics?10.6.4 Radio frequenciesused10.6.5 Technicalproblems10.6.6 Solutions10.6.8 Compatibility of wirelessmicsystems10.6.9 Antennacables10.6.10 Evaluating wirelessmicrophonesystems10.6.11Conclusions10.6.12Glossary of wirelessmicrophone terms180181182182183184185186186186187189189189190149152152153153154155155155157162162162164165166167168Page1391391391391401411421451461461471488.7.3.3 Howthe load affects outputvoltage8.7.4 What happens when hi-fi and proequipment mix8.7.4.1 Hi-fi output topro equipmentinput8.7.4.2 Pro equipment output tohi-fiinputSection/Subsection &TitleCrosstalk8.8.1 What causes crosstalk?8.8.2 Crosstalk in cables8.8.3Specification of crosstalk .Filter slope rates and turnover frequenciesSquare wave tests8.10.1Oscilloscopes8.10.2 What not toexpect with square wavesMiscellanySection9. Why Ears Don'tAlwaysCorrelateWith SpecsDifferent points of view9.1.1 Calibrated mics vsears9.1.2 Average ears vs"golden ears"Test equipment measurements vslistening tests9.2.1 Test signals versusprogram material9.2.2 Location and number of test microphones9.2.3 DynamicrangeStatic vsdynamic testsMasking effects and equipment interaction9.39.49.19.21131131131141141151161161161171171181181191191201201211211211211231231241251251261261271271291291291301301311311321321321331331351361361371381051051061071071091101111121987,1989SOUNdREiNFoRCEMENT HANdbookPage TC-3Page Section/Subsection & Title Page Section/Subsection & TitleSection12. Power Amplifiers193 12.1 General discussion193 12.2 Ohm's law &related equations193 12.2.1 Voltage, resistance and current194 12.2.2 Electricalpower195 12.2.3 Ohm's law chart196 12.2.4 Electrical power and amplifier gain197 12.3 Power ratings of amplifiers198 12.3.1 FTCpreconditioning198 12.3.2 Power bandwidth199 12.3.3 Slew rate and output power200 12.3.4 Bridged operation201 12.3.5 The effect of clipping202 12.4 The relationship between amplifier power and SPL204 12.5 Matching power amplifiers toloudspeakers204 12.5.1 Interpreting loudspeaker power ratings205 12.5.2 Impedancecalculations208 12.5.3 Constant-voltagedistributionsystemsSection13. Loudspeakers209 13.1 Introduction210 13.2 Common methodsof acoustic transduction210 13.2.1 Electromagnetictransduction211 13.2.2 Piezoelectrictransduction212 13.3 Lowfrequency drivers213 13.3.1 Directional characteristicsof conedrivers214 13.4 Lowfrequency enclosures215 13.4.1 Ventedenclosures216 13.4.2 Lowfrequency horns218 13.5 High frequency drivers219 13.6 Highfrequency horns222 13.7 Crossovers222 13.7.1 Generalmodel223 13.7.2 Passive, high level crossovers225 13.7.3 Active, lowlevel crossovers225 13.7.3.1 Headroom227 13.7.3.2 Efficiency227 13.7.3.3 Damping227 13.7.3.4 Distortion227 13.7.3.5 Biamp or triampversusconventionalsystem228 13.8 Full-range loudspeakers229 13.8.1 Effect of boundary conditions230 13.9 Loudspeaker specifications230 13.9.1 Frequencyresponse231 13.9.2 Power handling232 13.9.3 Sensitivity233 13.9.4 Impedance234 13.9.5 Directional characteristics236 13.10 Sources of distortion236 13.10.1Over-excursion236 13.10.2Intermodulationdistortion237 13.10.3Mechanicaldefects238 13.11 Typical failuremodes238 13.11.1Manufacturingdefects239 13.11.2Improperoperation241 13.11.3Failures dueto other components in thesignal chainSection14. SignalProcessingEqUipment244 14.1 Equalizers244 14.1.1 General discussion244 14.1.2 Common tonecontrols246 14.1.3 Multi-bandconventional equalizers248 14.1.4 Sweep-typeequalizers248 14.1.5 Parametric equalizers251 14.1.6 Graphicequalizers254 14.1.7 Paragraphicequalizers254 14.1.8 Tuning asound system with graphic(or paragraphic) equalization256 14.1.9 High pass and low pass filters259 14.2 Reverberation and delay261 14.2.1 Reverbchambers262 14.2.2 Duct-typereverbs262 14.2.3 Spring-typereverbs264 14.2.4 Plate-typereverbs264 14.2.5 Digitalreverberation266 14.2.6 Tapedelay267 14.2.7 Digital delay269 14.2.8 Analog delay270 14.3 Compressors&limiters270 14.3.1 General discussion271 14.3.2 Howcompressor/limiterswork272 14.3.3 Setupadjustments274 14.4 Noise gates&expanders274 14.4.1 General275 14.4.2 Noise gateapplications276 14.4.3 Expanderapplications277 14.5 Flangers and phasers277 14.5.1 Flanging278 14.5.2 Phasing278 14.5.3 What tolookfor279 14.6 ExcitersSection15. Cabling281 15.1 The importance of goodcables282 15.2 Types of cables, their construction and use282 15.2.1 Electrostatic andelectromagneticshielding283 15.2.2 Cableself-capacitance284 15.2.3 Single and dual conductor shielded cables287 15.2.4 Strain relief288 15.2.5 Unshielded cables and speaker cables289 15.2.6 Multicoreaudiocables("snakes")291 15.3 Connectors291 15.3.1 General291 15.3.2 Phone plugs297 15.3.3 Phono (pin) connectors299 15.3.4 XLRconnectorsSection16. SoundSystemTestEqUipment303 16.1 The volt-ohm meter305 16.2 Thesine wave oscillator307 16.3 Theoscilloscope309 16.4 The phase tester310 16.5 Thesound pressure level meter311 16.6 The real-timeanalyzer312 16.7 The loudnessmonitor312 16.8 SummarySection17. The Electronics313 17.1 Basic sound system types313 17.1.1 Sound reproductionsystems314 17.1.2 Sound reinforcement systems315 17.2 Developing alogical system architecture316 17.2.1 Functionalgrouping317 17.2.2 System examples325 17.3 Basicconnections325 173.1 Signal levels and impedance326 17.3.2 Unbalanced and balanced connections327 17.4Grounding328 17.4.1 Why isproper grounding important?329 17.4.2 Ground loops .330 174.3 Basic grounding techniques333 17.5 Using audiosignal transformers333 17.5.1 Properties and functionsof signaltransformers335 17.5.2 Somepracticalapplications337 17.6The main power source337 17.6.1 Verify the correct mains voltage338 17.6.2 Ensure there isagood earth ground339 17.6.3 Howtoobtain asafety ground whenusing atwo-wire outlet339 17.6.4 Improperly wired AC outlets: lifted grounds340 17.6.5 Improperly wired AC outlets: lifted neutral341 17.6.6 ACsafety tips341 17.6.7 Turn-onsequencing341 17.6.8 Power source integrity342 17.7 Configuring equipment racks343 17.8 Troubleshooting343 17.8.1 Absence of signal343 17.8.2 UndesiredsignalsSection18. the loudspeakers347 18.1 Analyzing theapplication347 18.1.1 The program material348 18.1.2 Theenvironment348 18.2 Directional control349 18.2.1 WideningdispersionPageTC-4SOUNdREiNfoRCEMENT HANdbook 1987, 1989Page Section/Subsection &Title Page Section/Subsection & Title350 18.2.2 Narrowingdispersion351 18.2.3 SPL estimations351 18.3 Placement considerations351 18.3.1 Directionality andcoverage353 18.3.2 Feedback control review353 18.3.3 Outdoor sound systems354 18.3.4 Controlling feedbackindoors354 18.3.5 Loudspeakerplacement indoors355 18.4 Connections355 18.4.1 Wiresize355 18.4.2 Connectors357 18.4.3 Polarity of connections358 18.4.4 Generalguidelines358 18.5 Setting electroniccrossovers358 18.5.1 Choice of crossover frequency and slope360 18.5.2 Setting upthe loudspeaker system361 18.5.3 Testing and optimizing thesystem363 18.5.4 High frequencydriver protectionnetworks364 18.6 Use of fill systems368 18.6.1 Balancing fill systems368 18.7 Testing and Equalization368 18.7.1 Singleloudspeakers369 18.7.2 Multiple loudspeaker systems370 18.7.3 Roomequalization404 20.2.5 Time codeand audio tape404 20.2.5.1 Printing SMPTE time code405 20.2.5.2 Copying SMPTE time code405 20.2.6 SMPTE-to-MIDI conversion406 20.3 Edit decision listsAppendixA. Logarithms409 A.1 Raising Numbers toaPower: The KeytoLogs409 A.2 Simple Logs(and Antilogs) to the Base10410 A.3 Less Obvious LogstoThe Base10411 A.4 Mathematical Propertiesof Logs412 A.5 One More LookAt Logsand DecibelsIndexColophonSection19. MIDI371 19.1 Interfacespecifications372 19.1.1 Hardwareconfiguration373 19.1.2 Data structure374 19.1.3 Channelmessages374 19.1.4 Systemmessages375 19.2 Control of musical instruments377 19.2.1 MIDImodes378 19.2.2 Controllers379 19.2.3 Patcheditor/librarianfunctions380 19.2.4 MIDIimplementation charts382 19.3 MIDIsequencing382 19.3.1 Basic theory383 19.3.2 Channels&tracks385 19.3.3 Hardware vscomputer-based sequencers385 19.3.4 Typical sequencer features386 19.3.4.1 Song editing386 19.3.4.2 Step editing386 19.3.4.3 Common editing features387 19.4 MIDI dataprocessors387 19.4.1 Thru boxes387 19.4.2 MIDImergers388 19.4.3 MIDIpatchers388 19.4.4 Mapping devices388 19.4.5 SysEx datastorage389 19.5 Automation through MIDI389 19.5.1 Instrument patchchanges390 19.5.2 Signalprocessors390 19.5.3 Consolefunctions391 19.5.4 Sync tomedia391 19.6 Troubleshooting391 19.6.1 Lack of response392 19.6.2 Stuck notes392 19.6.3 MIDIfeedback393 19.6.4 MIDI time delaysMachinecontrol20.2.4.1 Slave codeerror20.2.4.2 Slave codeoffset20.2.4.3 Flying offsets20.2.4.4 Slew20.2.4.5 Advanced transportcontrols20.2.4.6 Event triggers20.2.4Section20. Synchronization20.1 General discussion20.1.1 Basic theory20.1.2 Pulsemethods20.1.3 Timepiecemethods20.2 AMPTWIEBU time code20.2.1 Signalstructure20.2.2 Frame ratesand line references20.2.3 Longitudinal, vertical interval andvisible395395396397398398400401timecode402402402403403403403SOUNdREiNfoRCEMENT HANdbookLisr ofILLuSTRATioNSPage FigureNQ Title Page FigureNQ Title5-1 Acoustic power orsound pressure: the inverse 90square law 985-2 Sound and wind vectors5-3 Effect of wind velocity gradient onsound 100propagation 1015-4 Effect of temperature gradients onsoundpropagation1015-5 Absorption of sound inair vs. relativehumidity 1015-6 Typical acoustic and electrical feedback path5-7 Acoustic gainrelationships 1025-8 (A) Polar patterns for acardioid microphone5-8 (B) Polar patternsforasound reinforcement 102loudspeaker5-9 Using directional elements inasound system 102canincrease maximum available gainbeforefeedback8-178-108-168-198-188-158-138-148-118-128-68-78-88-98-38-48-5Section88-1 Aninadequate signal processor specification8-2 Frequency responseandpower bandwidthcurves are not identical.White noise energy vs. frequencyPink noiseenergy vs. frequencyFrequency spectrumof noise induced byanSCR dimmer ona60HzAC power lineGraphic representation of harmonic distortionRelationship of dBtopercent of signalTHD plot for atypical power amplifier outputBlock diagramshowing input terminationresistance and output source impedanceBlock diagram illustrates how load impedanceof an input terminates source impedance of apreceding outputMeasuring output source impedanceCrosstalk between twobusses in amixingconsoleFrequency response of an 80Hz, 3-pole filterA theoretically perfect square wave andagoodsquare wave fromafunction generatorAnoscilloscopedisplay of anear-perfectsquare wave"Magnification" of the square wave inFigure8-15, with expanded time baseSquare wave oscilloscope photo of acircuitwith 6 dBloctave roll-off below1 kHzSquare wave oscilloscope photo of acircuitwhich isimproperly terminated and isringingSine wave oscilloscope photo of abipolaramplifier withimbalanced power suppliesSection77-1 Block diagramsymbols: amplifiers7-2 Block diagram symbols: miscellaneouscomponents7-3 Block diagram symbols: transformers7-4 Block diagramsymbols: grounds7-5 Block diagramsymbols: indicators7-6 Block diagramsymbols: connectors7-7 Block diagram symbols: filtersand equalizers7-8 Block diagramsymbols: other functions7-9 Block diagram notation7-10 Microphonepreamplifier block diagram7-11 Graphic equalizer block diagram7-12 Digitaldelay block diagramSection66-1 Effect of boundary surfacesonsound trans-mission andreflection6-2 Effect of boundary surfacesonsound refrac-tion6-3 Formation of astanding wave byreflectionat aboundary6-4 Formation of astanding wave inaroom6-5 Roommodes at harmonic frequencies6-6 Reverberation ti.meequations6-7 Development of a reverberant field fromatheoretical point source of sound inthe centerof anacoustic environment6-8 Directional radiator in a reverberant field717376778081838487886364646465656667686959626356565758555353Section5Section44-1 Dynamic rangeand headroom4-2 2:1Compression of a90dBprogram4-3 1.21:1 Compression of a90dBprogram4-4 1.43:1Compression aboveathreshold4-5 Howacompander tape noise reduction systemovercomesdynamic rangelimitationsSection22-1 Model for measuring frequency response2-2 Plotted frequency response2-3 Derivation of afrequency responsespecifica-tion fromaplot2-4 A plot of "flat" frequency response2-5 A "flat" frequency responseplot of adevicewith very wide bandwidth2-6 Frequency response measured in1/3octavebands2-7 Construction of typical audio cables2-8 Frequency responseof a typical audiopoweramplifier2-9 Onandoff axis frequency responseof atypicalcardioid(unidirectional)dynamicmicrophone2-10 Frequency rangeof typical instruments andsinging voices2-11 Harmonic content of open stringsof the violinSection33-1 Nomograph relating level indBu (ordBmacross 600ohms) tovoltage3-2 The rms value of asine wave3-3 Equal loudnesscontours3-4 Filter curves for sound levl meter weightingcharacteristicsSection11-1 Representation of asound wave1-2 Representation of an audio signal1-3 Phase relationships between input &outputsignals1-4 Phaseaffects the way twosine waves addtogether1-5 Conceptualmodel of asound system1-6 A simple sound system.2729304643353839404245454652234748505117161412131311119910347123Page TC-6SOUNdREiNFoRCEMENTHANdbook 1987, 1989Page FigureNQ Title Page FigureNQ TitleSection 9151 11-1(B) The relationship between apreamp,amixer107 9-1 Simplified illustration of loudspeaker systemand aconsole: A large 24-input channel xbeing "fine tuned" to the environment4 output console with 2 effects send and108 9-2 Comparison of uncorrected and correctedreturncircuitsspectrum analysis forasound system,along154 11-2 A rack mount or line mixerwith graphic EQsettings needed toachieve154 11-3 A typical small, stand-alone mixerthecorrections158 11-4 Howpanpots work109 9-3 Sound fieldcomparison:(A) Sound field at159 11-5(A) Howsumming amplifiers are overdriven, andhuman ears and at a test michowtocorrect theproblem(B) Representative frequencyresponse at the160 11-5(B) Howsumming amplifiers are overdriven, andmicor earshowtocorrect the problem111 9-4 A square wave which shows "ringing" and a161 11-5(C) Howsumming amplifiers are overdriven, andtone burst test of that same circuithowtocorrect the problem163 11-6 Simplified block diagrams of different mixerSection 10configurations113 10-1 Construction of adynamic microphone165 11-7 Typical gain structure diagram foramixing113 10-2 Construction of acondenser microphoneconsole,showing headroom correlated with a114 10-3 Construction of aribbonmicrophonesimplified block diagram115 10-4 Construction of acarbon microphone166 11-8 Howatypical VUmeter with peak indicator116 10-5 Construction of apiezoelectric microphoneresponds toa test signal116 10-6 A fewtypical hand-held microphones167 11-9 Noise rejection inabalanced line117 10-7 Stand mount microphones176 11-10 Block diagram of asub-mixer connected toa118 10-8 A typical lavalier microphonemain mixing console118 10-9 A typical contact microphone179 11-11 Block diagram of atypical stage monitor118 10-10 A Crown pressure zone microphonesystem119 10-11 A typical shotgun microphone181 11-12 A monitor mixing system which also furnishes119 10-12 A parabolic micasubmixed feedtothe main house system120 10-13 Cross-sectional view of adual-element183 11-13 Anisolated micsplit feedthat allowsphantomdifferential microphonepowering of themic121 10-14 Polar pattern of acardioid microphone184 11-14 Use of additional transformers forisolation of122 10-15 Polar response of an omnidirectionalelectronically balanced inputs inthe presencemicrophoneof extreme noise123 10-16 Polar pattern of afigure-8microphone185 11-15 a"Y" connected (parallel wired)1:2 micsplit123 10-17 Polar pattern of asupercardioid microphonewith hard wiring instead of a transformer125 10-18 Proximity effect190 11-16 A suggested location for the mixing console in125 10-19 Comparison of transient response in typicalaconcert hallcondenser and dynamicmicrophones128 10-20 Balanced and unbalancedmicrophone Section 12connections 193 12-1 A simple DCcircuit129 10-21 Commonwindscreens 194 12-2 A simple ACcircuit129 10-22 A typicalshock-mounted microphoneona 195 12-3 Ohm's Law nomograph forACorDCstand 196 12-4 Sample circuit for power calculation130 10-23 Howphantom power and audio share the 196 12-5 A typical audio circuit:asignal source, asamecable power amplifier, and aload131 10-24 Spaced pair stereo micplacement, with 198 12-6 Power bandwidth of apower amplifierseparatesoloist mic 199 12-7 Slewing of astep131 10-25 Stereo microphonesinanX-Yconfiguration 199 12-8 Slew rate requirements are greater forhigher132 10-26 Sensitivity patterns of cardioid and figure-S poweramplifiersmics in an M-Sstereo configuration 200 12-9 Bridged mono operation: signal polarity133 10-27 Simplex wirelessintercom system (phase)relationships134 10-28 Half-duplex wirelessintercom system 200 12-10 Power amp bridged output connection134 10-29 Full-duplex wireless intercom system 201 12-11 Clipping of asine wave135 10-30 Wirelessintercom frequencybands 205 12-12 typical loudspeaker impedancecurve140 10-31 Commonly used international frequency 206 12-13 Series and parallel connection of loudspeakersbands 207 12-14 Series/parallelconnectionof loudspeakers140 10-32 Wireless microphone frequency bands used in 208 12-15 Constant voltagedistributed loudspeakerthe United States system142 10-33 Diversity receptionsystem143 10-34 Space diversity signal selectionSection 13143 10-35 Maximal ratio combining and equal gain210 13-1 Operation of a linear electromagnetic motorcombining210 13-2 Componentsof alinear electromagnetic motor143 10-36 Comparisonof signal selection and combining(inatypical driver)methods211 13-3 Bimorphs asused inpiezoelectric driverSection 11211 13-4 Cross-section of piezoelectric driver212 13-5 Cross-section of acone-type driver150 H-1(A) The relationship between a preamp,amixer213 13-6 Testing driver polarity with a batteryand a console: A small 12-input channel x213 13-7 Howthedirectional characteristicsof adriverstereo output mixer with an external RlAAvary with wavelengthpreamp foraphonograph 1987,1989Page FigureNQ TitleSOUNdREiNfoRCEMENT HANdbookPage FigureNQ TitlePage TC-7214 13-8 Reproductionof low frequenciesby an 260 14-16 The natural occurence of echoesunbaffled conedriver can result inacoustic 261 14-17 General design of an actual reverb chambercancellation 262 14-18 General design of aduct type reverb215 13-9 A vented,direct-radiator lowfrequency 263 14-19 General design of aspring type reverbenclosure 264 14-20 General design of a plate type reverb216 13-10 A ducted port low frequency enclosure 265 14-21 Block diagram of adigital reverb216 13-11 Cross-section of astraight exponential horn 267 14-22 A tape delay unit217 13-12 Cross-section of afolded, lowfrequency horn 268 14-23 Block diagram of a 4-input x 8-output digital(a"W-bin") delay line217 13-13 Cross-section of afolded, lowfrequency horn 269 14-24 Block diagram of an analog delay line(a"scoop") 270 14-25 Compression andlimiting characteristics218 13-14 Cross-section of atypical compression driver 272 14-26 Block diagram of acompressor/limiter219 13-15 Cross-section of apiezoelectric supertweeter 274 14-27 The action of anoise gate220 13-16 The designof an exponential radial horn 275 14-28 The action of an expander221 13-17 A variety of constant directivity horns 276 14-29 Using anoise gate totighten asnare drum222 13-18 A typicalz-way loudspeaker system and itsidealizedcrossover responsecharacteristicsSection15223 13-19 Idealizedcrossover responsecharacteristics282 15-1 Howshielding shuntselectrostatic noisefora3-way loudspeaker system283 15-2 Different types of cable shielding223 13-20 Typical location of apassive, high-level284 15-3 Cable resistance&capacitance createa lowcrossover network inside aloudspeakerpass filterenclosure285 15-4(a) Single and dual conductor cables for use with225 13-21 Typical location of an active (electronic)unbalancedsourcescrossover network, just ahead of thepower286 15-4(b) Single and dual conductor cables foruse withamplifierstransformer or differentially balancedsources226 13-22 Oscilloscope photos illustrate the headroom287 15-5 Using heat shrink tubing forstrain reliefadvantage of abiamplified system287 15-6 AvoidChinese handcuff type strain relief228 13-23 Twoof the many ways topackage a3-way290 15-7 Typical multi-core snake with stage boxandloudspeakersystempigtails229 13-24 HowSPL increasesdueto boundary effects292 15-8 Tip/ring/sleeve phone plugs and jacks in a231 13-25 Graphic specificationof loudspeakerbalancedcircuitfrequencyresponse293 15-9 A tip/ring/sleeve phone plug wired forstereo233 13-26 Graphicspecification of loudspeakerheadphonesimpedance294 15-10 A tip/ring/sleeve phone plug wired fora234 13-27 Beamwidth plot of aloudspeakersingle-cableeffectssend/return loop234 13-28 Onand off-axis frequency response curves of a295 15-11 Wiring atip/sleeve standard phone plugtypical full-rangeloudspeaker system296 15-12 Wiring a tip/ring sleeve standard phone plug235 13-29 Polar plots illustrating horizontal and vertical298 15-13 Wiring aphono plugdispersion of afull-rangeloudspeaker system300 15-14 Wiring a male XLR-3type connector236 13-30 Pushing (and pulling) adriver "tothe limits"301 15-15 Wiring afemaleXLR-3typeconnectorwith toomuch power can introduce distortionSection16Section14304 16-1 Continuity measurement with aVOM244 14-1 Typical bass and treble tone controls and how304 16-2 DCvoltage measurement with aVOMthey alter frequency response304 16-3 ACvoltage measurement with aVOM245 14-2 A typical family of bass and treble tone305 16-4 Driver testing with asine wave oscillator andcontrol curves, with control settings indicatedapower amplifier246 14-3 Typical3-band equalizer characteristic306 16-5 Loudspeaker testing with asine wave247 14-4 A 4-band equalizer with twoswitch-selectableoscillator and apower amplifierfrequenciesper band306 16-6 Measuring nominal operating levels with a248 14-5 A 3-band equalizer with the middle bandsine wave oscillator and a VOMhaving asweepable center frequency307 16-7 Measuring signal processor gain with asine249 14-6 A 3-band fully-parametricequalizerwave oscillator and a VOM250 14-7 Correcting special problems with a para-307 16-8 A typical oscilloscope andprobemetric EQ308 16-9 Oscilloscope display of asine wave251 14-8 A1/3 octave graphic equalizer308 16-10 Measurement of maximum output level253 14-9 Reducing feedbackandsmoothing the overall309 16-11 Checking the polarity of asignal processorsystem response with agraphic equalizer309 16-12 Checking the polarity of a loudspeaker253 14-10 The difference between non-combining and310 16-13 Frequency response curvescorresponding tocombining type filtersina graphic equalizersound pressure level meter weighting255 14-11 Reducing feedback andsmoothing the overallcharacteristicssystem response with aparagraphic equalizer311 16-14 Simplified block diagram of a real time256 14-12 Common high pass filtercharacteristicsanalyzer, as used forsound system tests257 14-13 Common lowpass filtercharacteristics312 16-15 The Dorrough loudnessmonitor258 14-14 A horizontal (sliding) lowpass filter functionsas asingle-ended noise reduction systemSection17259 14-15 Propagation of an impulse sound inthe317 17-1 A stereo playback systemenvironment shows natural occurenceof early319 17-2 A clubsound reinforcement systemreflections and subsequent reverberation.PageTC-8Page FigureNQ TitleSOUNdREiNfoRCEMENTHANdbookPage FigureNQ Title 1987,1989320 17-3(A) A typical concert sound reinforcement system:Input sources321 17-3(B) A typical concert sound reinforcement system:Signalprocessing322 17-3(C) A typical concert sound reinforcement system:Output group323 17-3(D) A typical concert sound reinforcement system:Common applicationsforsignal processors323 17-4 Concert stage monitor system326 17-5 Unbalanced and balancedconnections329 17-6 Formation of ground loops330 17-7 Single-point grounding330 17-8 Multiple-pointgrounds331 17-9 Foatingconnections331 17-10 Telescopingshields332 17-11 Combining grounding techniquesinapractical system333 17-12 Basic transformer types334 17-13 Unbalanced and balanced connection oftransformers334 17-14 Terminationof transformers335 17-15 A musical instrument DIbox336 17-16 Typical microphone transformer connection336 17-17 Isolated equipment rack input336 17-18 Microphonesplitter337 17-19 Standard duplex outlet338 17-20 Testing atwo-wire AC outlet339 17-21 Testing a2-wire outlet and a3 prong to2 prong adaptor340 17-22 Schematic of an outlet with alifted neutral341 17-23 Testing athree-wire AC outletSection19Section2020-1 Closed-loopsynchronization system20-2 Manchester biphasemodulation encoding20-3 SMPTE time codedata format (asingleframe)20-4 Vertical interval timecodeand longitudinaltime code20-5 Anexample of an edit decision list derivedfrom asegment of aTV newsshow promo20-6 Another segment of an edit decision list, fromadramatic videoprogram349349350352353356356356357360360361362363365365366366367368369372372373373373374375376378381382383384387395398399401Section18 40718-1 Splayed loudspeaker arrangement for widerdispersion 40818-2 Obtaining wider verticaldispersion frommultiplecabinets18-3 Intentionally narrow verticaldispersion18-4 High frequency coverage of an elevated full-range loudspeaker system18-5 Aiming dual speaker clusters oneither side ofthestage foroptimum coverage18-6 5-Way binding postsaccept dual banana plugsor bare wires, aswell asspade lugs and singlebananaplugs18-7 Phone plug and phone jack connectors18-8 3-Pin XLRtypeconnectors (in-line and panelmounted)18-9 A 4-Pin XLRconnector utilized forcarryingthe output fromtwochannels of power ampli-ficationtoabiamplified loudspeaker system18-10 Initial positioning of drivers inan all direct-radiator loudspeaker system18-11 Initial positioning of drivers in an all straighthorn-loaded loudspeaker system18-12 Initial positioning of drivers in amixed horn-loaded anddirect-radiator loudspeakersystem18-13 Test setup foroptimizing loudspeaker systemfrequencyresponse18-14 High pass filter network forprotection of thehigh frequencydriver18-15 Coverage problems of asingle loudspeakercluster (array) fora large audience18-16 Useof afillsystem toaugment the coverageof amain loudspeaker cluster18-17 Fill loudspeakers used toimprove mid andhigh frequencycoverage beneath abalcony18-18 The way sound waves propagate around18-1918-2018-2019-119-219-319-419-519-619-719-819-919-1019-1119-1219-1319-14obstructions explains why lowfrequenciestend tobuild up under balconiesElectronics required fordelaying the soundto rear fillloudspeakersChecking loudspeaker polarity with adry cellSine wave sweep test of a loudspeakerStandard MIDIcableMIDI: block diagram of actual interfaceTypical instrument MIDI portMIDI data byte structureMIDI message structureLike televisions, MIDI instruments may betuned tospecific receivechannelsSmall liveperformance setupLiveperformance setup using three keyboardsynthesizersMIDI1.0specification controller numbersTypical MIDI implementation chartMIDIsequencingA simple music sequencing systemCreating athirty-two channel MIDI systemUse of a thru boxSECTioN1.WI-tAT Is A SouxdSySTEM?1.1 TI-tE AudioSiGNALIn today's technologically sophisti-cated world, audio systems ofvarious types are a part of alniosteveryone's daily life. Nearly everyhome has astereo or asimple radio.Most businesses use some type ofintercom/paging system. Some autosound systems are more sophisticatedthan many home stereos.This handbook deals with aspecificclass of audio system which is properlyreferred to as a reinforcement system.For the purposes of this handbook, theterm sound system isused exclusivelyto refer to reinforcement systems. Re-inforcement systems of varying levelsof sophistication are used routinely byamateurs and professionals forpublicaddress and music performance.Sound reinforcement systems arenot generally as simple as homestereos. Although they operate on thesame principles, they require a higherlevel of understanding from theirusers.This handbook is an introduction tothose principles. Its purpose isto giveyou the understanding necessary todesign and operate moderate-scale re-inforcement systems. It can also serveas a reference when questions concern-ing such systems arise. Section 1introduces the basic concept of thesound system.TIMEFigure 1-1. Representation of asound wave (one cycleof a sine wave in air)YAMAHASOUNd REiNFoRCEMENTHANdbookPAGE 1+wa::::l~ 0wa:n,DISTANCEI ~ 1 CYCLE;:J CYCLE"'-/PERIOD~WAVELENGTHwa:::lI-::Jn,:2-c1.1.1Sound WavesWhat we hear as sound is 'a class ofphysical kinetic energy called acousti-cal energy. Acoustical energy consistsof fluctuating waves of pressure in aphysical medium - usually air.A single complete cycle of an acous-tical pressure wave consists of onehalf-cycle of compression (higherpressure) of the air molecules, followedby one half-cycle of rarefaction (lowerpressure) of the molecules. Sounds ofhigher amplitude (louder) compressand rarefy the air molecules to agreater extent than do lower amplitude(softer) sounds.The rate of air pressure fluctuationiscalled the frequency of the wave. Inorder tobe classified as sound, wavesof pressure in air must fluctuate at arate between 20 and 20,000 completecycles per second (cps). Frequencycorresponds to the musical attribute ofpitch. Although pitch isa more com-plex attribute than frequency (it alsoinvolves amplitude), generally speak-ing the higher the frequency, thehigher the perceived pitch of the sound.The unit Hertz (Hz) is now used toindicate frequency in cycles per second:20Hz =20cpsThe amount of time required foronecomplete cycle of asound wave iscalled the period ofthe wave. A wave'speriod is expressed in seconds percycle, and isfound by using the equa-tion:Period =1+FrequencySound waves travel through air atthe speed of 1130 ftJsec (344 m/sec)... atsea level onastandard temperatureday (which is 59 degrees Farenheit or15 degrees Celsius). The speed of soundis independent of frequency. Thephysical distance covered by onecomplete cycle of agiven frequencysound as it passes through air iscalledthe wavelength. Wavelength isexpressed by the equation:Wavelength =-fu!-eec:lgfJIQund.Frequency1.1.2 TheElectricalRepresentation of SoundSECTiON1An audio signal is an electrical rep-resentation of asound, in the form of afluctuating voltage or current. Withinthe limits of audio equipment, thesignal voltage or current fluctuates atexactly the same rate as the acousticalenergy that it represents, and theamplitudes of the acoustical soundwave and the electrical audio signalare scaled proportionately.The amplitude, orstrength, of anaudio signal iscalled the signal level.Many different operating levels exist inaudio systems. Level (acoustical orelectrical) isspecified in decibels.Section 4 describes the decibel indetail.isexpressed on the graph inship to a time reference called To' Thishappens to bethe start time of thewave, although it could beat any time within the wave's penod.The time reference may also be an-other signal. If it is, the referencesignal must resemble the signal whosephase is being measured: we can mean-ingfully compare only objects that arealike, or at least related. For example,Figure 1-3 shows an audio signalprocessor with one input (VIN) and oneoutput (VOUT ) 'The phase of the outputsignal is expressed in relation to theinput signal.C YCL .II1111111I11111 II I:I III 180027003600+-'CCD"-"-::J....Jo 0... 0 -I'-_.....,__ _Cl)CD "-0>0CO+-'o>IPHASE00+1.1.3 PhaseThe time relationship of asoundwave (or an audio signal) toa knowntime reference iscalled the phase ofthe signal. Phase isexpressed indegrees. One complete cycleof asinewave equals 360 degrees. .The time reference may be an arbi-trarily chosen, fixed instant in time.For example, Figure 1-2 shows a typeof audio signal called a sine wave. Asine wave isa pure tone, a fundamen-tal frequency with no harmonics(representing something like the soundof a flute). The phase of the sine waveFigure 1-2. Representation of an audio signal(one cycle of a sine wave)In Figure 1-3(b), the output isto be in phase with the input (both smewaves cross zero at the same time,going in the same direction). In (c), .theoutput is90 degrees out of phase WIththe input (one sine wave crosses zerowhen the other is at maximum, bothgoing in the same direction). In 1-3 (d),the output is180 degrees out of phasewith the input (both sine waves crosszero at the same time, but going inopposite directions). Note that thesephase relationships may change at .different frequencies, and often do WIthreal-world audio circuits.YAMAHASOUNd REiNfORCEMENTHANdbookPAGE 2WI-tAT Is A 1.1.4 Adding SineWavesSouNdSYSTEM?Vin- Signal Processor t--VoutFigure 1-3. Phase relationshipsbetween input and output signalsPhase is very important in soundsystems. The main reason that phasemust be controlled is that it affects howsounds add together.When audio signals are mixed in aconsole, or when sound waves mix inthe air, they add algebraically. Figure1-4 shows the effect of phase on theaddition of twosine waves of equallevel and frequency, but at differentphase relationships.In Figure 1-4 (a), the sine waves arein phase; they add to formasine waveoftwice the level of either one. In (b),the sine waves are 90 degrees out ofphase. They add to form asine wavethat is1.414 times higher in level thaneither one. In (c), the sine waves are180 degrees out of phase; they totallycancel one another.I (a) Input Signal1111(b) Output in PhaseIIII (d) Output 180 DegreeslOut of PhaseII-, I /1~ I / I1 II ITo --TIME.--Vout I----jl::.....--'------J ( 0~ 1 c) utput 90 DegreesI "-lOut of PhaseI I1 I1 IVout(a) 1+2(b)Signals 1 & 2Arein PhaseSignals1 & 2 are900Out of PhaseBoth signalssum tozero(cancellation)(c)Signals1 & 2 are1800Out of PhaseFigure 1-4. Phase affects the way two sine waves add togetherYAMAHASousdREiNfoRCEMENTHANdbookPAGE}1.2 TI-tEBASic PlJRPOSEof ASOlJNdSySTEMA sound system isa functionalarrangement of electronic componentsthat isdesigned toamplify (increasethe strength of) sound. This may bedone for any of several reasons. Thethree most common reasons are:A) To help people hear somethingbetter. For example, one personspeaking on astage may not beheard well at the back of a largehall. A sound system may be usedto make the sound more clearly au-dible. In this case, the intention isto make the voice at the back of thehall sound as loud as (not louderthan) it is when heard up close.B) To make sound louder for artisticreasons. A vocal group in a smallclub may beclearly audible but notnecessarily very exciting. A soundsystem can give the group muchgreater musical impact by makingit seem "larger than life."C) To enable people to hear sound inremote locations. Seminars or meet-ings sometimes draw larger crowdsthan the meeting room will hold. Asound system can bring thespeeches and discussion to asecondroom, so that the overflow crowdcan hear them.There are also sound systems whichare designed to reproduce recorded orbroadcast sound. In this case thegeneral requirements may be similarto the live sound reinforcement system,except that atape reproducer, compactdiscplayer, phonograph, or radio tunerwill be substituted for the microphoneor electronic musical instrument, andthere will be less concern about feed-back.1 . ~ ACONCEPTlJAlModEL of ASOlJNdSySTEMSound systems amplify sound byconverting it into electrical energy, in-creasing the power of the electricalenergy by electronic means, and thenconverting the more powerful electricalenergy back into sound.In audio electronics, devices thatconvert energy from one form intoanother are called transducers.Devicesthat change oneor more aspects of anaudio signal are called signal proces-sors. Using these terms, we can modelasound system in its simplest form, asillustrated below in Figure 1-5.The input transducer (i.e., micorpickup) converts sound into a fluctuat-ing electrical current or voltage whichisaprecise representation of thesound. The fluctuating current orvoltage is referred to as an audiosignal.The signal processing alters one ormore characteristics of the audiosignal. In the simplest case, it in-creases the power ofthe signal (asignal processor that doesthis iscalledan amplifier). In practical soundsystems, this block of the diagramrepresents a multitude of devices -preamplifiers, mixers, effects units,power amplifiers, and so on.The output transducer (i.e., theloudspeaker or headphones) convertsthe amplified or otherwise processedaudio signal back into sound.SECTiON1Input TransducerAcoustical toelectrical energyconversionAudioSignalSignal ProcessingElectricalmanipulation ofthe audiosignalAudioSignalOutput TransducerElectricaltoacoustical energyconversionYAMAHASOUNd REiNfORCEMENTHANdbookPAGE 4WI'IAT Is ASouadSySTEM?YAMAHASousd REiNFoRCEMENTHANdbookPAGE~1.4INpUTTRANSduCERSIn asound system, input transduc-ers convert sound into audio signals.The types of input transducers mostcommonly encountered in soundreinforcement systems are:A) Air Pressure or Velocity Micro-phones - convert sound wavestraveling in air into an audio signaltraveling in the mic cable.B)Contact Pickups - convert soundwaves in adense medium (wood,metal, skin) into an audio signal.Sometimes used on acousticstringed instruments such asguitar, mandolin, violin, etc. Usu-ally of the crystal type, occasionallycapacitive.C) Magnetic Pickups - convert fluc-tuating waves of induced magnet-ism into an audio signal. Found onelectric stringed instruments.D) Tape Heads - convert fluctuatingmagnetic fields (imprinted onmagnetic recording tape) into anaudio signal.E) Phonograph Pickups (car-tridges) - convert physical move-ment of astylus ("needle") into anaudio signal. In professional sys-tems, the moving-magnet typecartridge is the most common.F) Laser Pickups - convert im-printed patterns ona compact discinto a digital data stream that isthen translated by aDAC (Digital-to-Analog Converter) into an analogaudio signal.G) Optical Pickups - convert vari-ations in the density or transparentarea of a photographic film into anaudio signal. Used for most motionpicture sound tracks.Each type of input transducer hasits own characteristics, which must beunderstood if the transducer isto beused properly. Section 10 of this hand-book deals with microphones in detail.1.5 OUTpUTTRANSdUCERSIn asound system, output transduc-ers convert audio signals back intosound. The types of output transducersmost commonly encountered insoundreinforcement systems are:A)Woofer loudspeakers - designedspecifically to reproduce low fre-quencies (usually below 500Hz).Woofers sometimes are used toreproduce both low frequencies andsome mid frequencies (normally nothigher than 1.5 kHz). Typically,cone-type drivers are used aswoof-ers, measuring from 8 to18 inchesin diameter.B) Midrange loudspeakers-(formerly called "squawkers,"though this is an archaic term fromthe hi-fi world) - designed specifi-cally to reproduce mid frequencies(typically above 500 Hz). The high-est frequency reproduced by amidrange unit isusually not higherthan 6 kHz. If a cone-type driver isused as a midrange loudspeaker, itsdiameter typically ranges from5 to12 inches; if acompression driver isused, its diaphragm diameter mayrange from 2.5inches to 4 inches(with a fewspecial units up to about9 inches in diameter).C) Tweeter loudspeakers - de-signed to reproduce the highest fre-quencies (normally higher than1.5 kHz, and usually above 6 kHz).If acone-type driver is used, its dia-phragm diameter usually rangesfrom 2 to5 inches; compressiondriver diaphragms range fromunder 1.5 inches to about 4 inches.D) Full-range loudspeakers - inte-grated systems incorporatingwoofer and tweeter (and, if used,midrange) drivers in asingle enclo-sure. As the name implies, they aredesigned to reproduce the full audiorange (more or less). In practicalterms, their range rarely extendsbelow about 60Hz.NOTE: Afull-range driver is asingle loudspeaker which alone isdesigned to reproduce thefull audiofrequency range; this is not thesame as afull range multi-driversystem.E) Subwoofer loudspeakers - usedto extend the low frequency range offull-range systems to include fre-quencies down to 20or30 Hz. Theirrange rarely extends above about300 Hz. Cone-type drivers are usednearly exclusively, and typicallymeasure from15 to 24 inches indiameter, although a fewspecialunits are available with cone di-ameters approaching 5 feet.F) Supertweeter loudspeakers -used to extend the range of full-range systems in the highest fre-quencies (usually above 10 kHz).Typically, these are either compres-sion drivers or piezoelectric driversin professional sound systems,although hi-fi type systems usesome more esoteric technologies.G) Monitor loudspeakers - full-range loudspeakers that are pointedat the performer on stage, ratherthan out into the audience. Theyare used to return a portion of theprogram to the performer, to helphim or her stay in tune and in time,and are sometimes loosely referredto as "foldback." In recording stu-dios, astudio monitor orcontrolroom monitor loudspeaker isa fullrange, high accuracy loudspeakersystem designed to permit evalu-ation of the sound being recorded.H) Headphones - full-rangetransducers designed to fit snuglyon the ears. Some designs block outambient (external) sound, whileothers do not. Headphones aresometimes used in sound systemsas monitors for click-tracks, andmay be used by engineers to check alive mix or a recording during aper-formance. Headphones also appearas components of intercom systems.Each type of output transducer hasits own characteristics, which must beunderstood if the transducer isto beused properly. Section 13 of this man-ual deals with output transducers indetail.1.6 APRACTiCAL ModELof A SOUNdSySTEMFigure 1-6 (next page) shows asimple practical sound system, such asmight be used for a panel discussion ina lecture hall.The system in Figure 1-6 is designedto amplify the voice of three panelists(or board members, etc). The systemcan be conceptually analyzed as havingthree sections: (a) the input transduc-ers, (b) signal processing, and (c) theoutput transducers:A) Input Transducers - Threemicrophones convert the sound theypick upfrom the panelists intoaudio signals that travel down thecables to the signal processingequipment.B) Signal Processing - The threemicrophones are connected to indi-vidual inputs on the mixing console.The console serves the followingfunctions:1) Preamplification - Theconsole's microphone inputsection amplifies the level ofthe audio signal from eachmicrophone, bringing it up toline level.2) Equalization - The consoleprovides the means to adjustthe tonal balance of eachmicrophone individually. Thisallows the console oprator toachieve a more pleasing ormore intelligible soundquality.3) Mixing - The console addsthe equalized signals of themicrophones together toproduce a single line-leveloutput signal.The output of the console isconnected to a power amplifier.The power amplifier boosts theconsole's line level (0.1to100 mil-liwatts) output signal to a levelsuitable to drive the loudspeaker(0.5to 500 watts).C) Output Transducer - The loud-speaker converts the power ampli-fier output signal back into sound.The level of the sound is muchSECTiON1YAMAHASOUNd REiNfORCEMENTHANdbookPAGE 6WliAT Is ASouNdSYSTEM?higher than that of the three panel-ists speaking unaided.There is another less obvious, butequally important aspect of the soundsystem: the environment. When thesound output of the loudspeakerpropagates into the hall, it is alteredby the acoustical characteristics of thespace.The room may have little effect onthe clarity of the sound if, for example,the room is "dead" or nonreverberant.If the room is highly reverberant, andthe sound system isnot designed andinstalled to deal with the acoustics ofthe space, the effect on the sound maybeso severe as to render the soundInput TransducersI - - - - --- - - - - --II Microphones 1I 1I 1I 1I 1I 1I 1I 1I 1I 1system useless.The environment is an integral partof the sound system, and its effectsmust be considered when the system isinstalled. Sections 5 and 6 of thismanual deal in detail with the effectsof the environment onsound systems.Every sound system, no matter howlarge, is merely an extension of thisbasic model. The same principles thatapply to this simple sound system alsoapply to large-scale concert reinforce-ment systems.Output Transducer1111II111111:_ ~ o _ u 9 ~ ~ e _ a ~ ~ r __:~YAMAHASousdREiNfoRCEMENTHANdbookPAGE 111111111I tiillllll 1Power Amplifier ~: Mixing Console :L ISignal ProcessingFigure 1-6. A simple sound systemYAMAHASousdREiNfoRCEMENTHANdbookPAGE8SECTioN ,2.. .FREQUENCYRESPONSE2.1:& IOne of the most commonly-usedterms in audio isfrequencyresponse. In Section 2, we define thisterm, examine how it applies to varioustypes of audio equipment, and describethe relationship between frequency re-sponse and program materiaL, I ,/C)'\1/-CJ-/ "'The frequency response of adevicedescribes the relationship between thedevice's input and output with regardto signal frequency and amplitude.Another term for this is magnituderesponse. In its most common usage,the frequency response describes theusable range of signal frequencieswhich the device will pass from inputto output.Consider the system shown inFigure 2-1. An unknown signal proc-essing element (or black box) is fedfrom a variable-frequency sine wavegenerator, and adevice for indicatingsine wave level in decibels isconnectedto its output.SINE WAVEGENERATORDEVICEUNDER TESTLEVELINDICATORFigure 2-1. Model for measuring frequency responseFigure 2-2. Plotted frequency response(relative level versus frequency)of "Black Box" in Figure 2-11---Vf\~I....-'-\\\YAMAHASousdREiNfoRCEMENTHANdbookPAGE 9+20+15i +10..JW +5~..J 0W~ -5...~ -10-IS-2020 30 4050 100 200 500 1000 2000FREQUENCY (Hz)The ideal oscillator produces thesame output level at all frequencies (inreality the linearity is not alwaysperfect), so the input level to the blackbox is constant. As wesweep the oscillator fre-quency throughout theaudio range, however, wemay see that the outputlevel of the black box, asregistered by our meter,changes. If we make note ofthe level at each frequencyon agraph, we can producea chart like that shown inFigure 2-2. Here, the outputlevel (vertical axis) is5000 10000 20000 plotted against frequency(horizontal axis).The graph of Figure 2-2 is called afrequency response plot. It shows usthe range of frequencies that the blackbox will pass from input to output, andwhat fluctuations in output level (ifany) occur within that range.It is important to understand thatthe frequency response plot assumes aconstant input level to the deviceunder test. For precisely this reason, itgives us an indication of the fidelitywith which the device transfers asignal frominput to output. The lessdeviation there is in output level acrossthe stated frequency band, the morefaithfully the signal at the output willreflect the signal at the input.NOTES:1. If the input to a deviceunder testis not constant in level at all frequen-cies, a correction may be made to theoutput plot (or the input level canbeintentionally varied to make it con-stant). The resulting plot is said to be"normalized. "2. The term "frequency response" isused only to refer to signal process-ing devices and transducers - thatis, any devicesthrough which asignal passes. Whenreferring tosignal generating devices(oscilla-tors, musical instruments, and soon), the proper term to use is "fre-quency range. "2.1.1Basic SpecificationMethodsIn its simplest form, a typical fre-quency response specification mightread:FREQUENCY RESPONSE:30 Hzto18 kHz, 3 dBNote that the range (from 30 Hzto18 kHz) is accompanied by the quali-fier, + or - 3 dB." This iscalled the tol-erance ofthe specification. The toler-ance tells us the maximum deviation inoutput level that we can expect overthe stated range if the input levelremains the same at all frequencies.Without a stated tolerance, the fre-quency response specification isuse-less, since we are left to guess theunit's effect on the signal. There might,in fact, be horrendous peaks and/ordips in the response - and these couldalter the signal considerably. While atolerance of 3 dB is often assumed ifnot specified, such an assumption is atyour own risk... there is usually areason why such an important quali-fier is omitted fromaspecification!Figure 2-3 shows how such aspecifi-cation isderived from the frequencyresponse plot.SECTiON 211 I---4---------------------------r-------1 1. - - - -1- L -Average LI 1Figure 2-3. Derivation of a frequency response specification froma plot20 30FREQUENCY (Hz)18K 20KYAMAHASOUNd REiNfORCEMENTHANdbookPAGE 10FREQUENCYRESPONSE2.1.2 Octave RelationshipsAndMeasurementsFREQUENCY RESPONSE:20 Hz to30 kHz, +0, -3 dB.FREQUENCY RESPONSE:10 Hz to 40 kHz, +0, -3 dB.Figure 2-5. A "flat" frequencyresponse plot of a devicewithlverywide bandwidthFrequency response measurementsand specifications are sometimes madeon an octave or lis-octave basis. Suchmeasurements are far lower in resolu-tion than those described above. Theyare widely used with loudspeakers,however, because they provide goodcorrelation with the characteristics ofhuman hearing (and can be adjustedby corresponding one octave orl/s_octave equalizers or filter sets).The octave isaspecial musicalinterval between twotones, formedwhen the ratio between the frequenciesof the tones is2:1. The ear hears anequivalence between the tones whenthis is the case (for this reason, pitchesat successive octaves in the musicalscale are named with the same letter).With regard to frequency, the octaveinterval is much wider at high frequen-cies than at low frequencies. For ex-ample, one octave above 40 Hz is 80 Hz(a 40cycle wide interval), but an octaveabove 1,000 Hz is2,000 Hz (a1,000cycle wide interval). Yet we hear bothof these intervals as musically similar!This is because the ear's response tofrequency is logarithmic in character.(Logarithms are discussed in theAppendix of this handbook). Accord-ingly, audio response plots such asthose shown earlier in this sectionemploy a logarithmic scale to indicatefrequency. On this type of scale, thedivisions are packed closer and closertogether as the frequency increases...uptoa decade (10, 100, 1000, etc.),then the spacing interval repeats.Octave and lis-octave measurementsare designed to divide the linear audiofrequency scale, which we do notperceive to be linear, into perceptuallyequal increments. In frequency re-sponse measurements and specifica-tions, then, the average level in eachincremental division isgiven - nor-mally in bar graph form, as shown inFigure 2-6 (next page).Here, the center frequencies of thebands are spaced Ifs octave apart. Thespecific frequencies given on thehorizontal axis are standard centerfrequencies for lis-octave measure-ments: these same centers are alsoused for the filters in lis-octave graphicequalizers. The standard used isknown as "ISO" (International Stan-dards Organization), so you know ifyou have an equalizer with ISO,20K 40K20K:iOKFREQUENCY(Hz)FREQUENCY(Hz)20I I1020, ReferenceLevelI I I 1/X ~ - l d B- t- - - - - - - - - - - - t- - - -3dBI I I II I I II I I II I I II I I Itun uu_""\-=e--I II.L-_l-- ---,.---'I __If the frequency response of thedevice in question greatly exceeds thetotal range of human hearing (20 Hz to20 kHz), the frequency response maybespecified by simply stating the totalresponse deviation within the audiblerange. The specification for the devicewhose response isshown in Figure 2--5,forexample, might read:FREQUENCY RESPONSE:20Hz to 20kHz, +0, -1 dB.Alternately, if one chooses the -3 dBpoints as the frequency limits, thespecification would read:Figure 2-4. A plot of"flat" frequency responseIn such cases, the frequency re-sponse limits are usually taken to bethose points where the unit's output is3 dB below the average (reference)level. The frequency response specifica-tion for the device plotted in Figure2-4, then, would read:Some audio devices exhibit extraor-dinarily flat frequency response, asshown in Figure 2-4. Such a responsecurve would be characteristic of apower amplifier or line amplifier, forexample.YAMAHASousd REINfoRCEMENTHANdbookPAGE 11SECTiON 2A practical audio system isanet-work of many different types of devicesthrough which the signal must pass onits way to the listeners' ears. Eachstage in the system will have specificfrequency response characteristics, andwill therefore modify the signal tosome degree. Theoverall frequencyresponse of the systemisafunction of thecombined responses ofall the various ele-ments in the chain.The audio elementsthat exhibit the flattestfrequency responsecharacteristics areelectronic circuits andcables.2.2 FREQUENCYRESPONSE ofPRACTiCALAudioDEVicESAmplitude Response(1/3 octavebands)10dB -1~ = = = = = = = = = = = = = = = = = = = = = = = = = = = =l=============:::::=::::::=::OdB-10 dBstandard octave or l/a-octave spacing, itwill coincide with the bands measuredon an ISO standard Real TimeAnalyzer.Instead of a sine wave, the excita-tion signal used for measurements likethis isa special signal called pinknoise. Pink noise is a randomly-generated signal that excites all theaudio frequencies with equal energyper octave. It sounds very much like arushing waterfall.-20 dB-30 dB31.5 63 125 250 500 1K 2K 4K 8K 16KFigure 2-6. Frequency responsemeasured In 1/3-octave bandsSince there are more frequenciespacked into each upper octave thaneach lower octave, pink noise rolls offat higher frequencies. This meansthere is less energy at any single highfrequency than at any single low fre-quency so that when all the noise in anoctave is added up, it equals all thenoise in any other octave. When pinknoise is used as the excitation signal,the output of the device under test isfiltered in octave or lf3-octave bands,and the average energy in each band ismeasured separately.It is important to note that measure-ments like this can conceal as much asthey reveal. While they provide agoodpicture of the general characteristic ofa device's frequency response, verynarrow peaks or dips may be com-pletely missed by the technique. In areverberant space, the measurementmay say more about the room thanabout the loudspeaker under test.2.2.1Electronic CircuitsAndCablesCables are electrically the simplestpossible elements in the audio system,and this fact accounts fortheir gener-ally good response. Cables may intro-duce response problems at the fre-quency extremes, however, and theextent of such problems is determinedby the design of the cable, its length,and the type of circuitry to which it isconnected.The typical audio cable consists ofone or twosignal conductors sur-rounded by insulation and a shieldingconductor, as shown in Figure 2-7.The audio signal is carried in thecentral conductorfs). The shieldingconductor is connected to the electricalground point in the circuit, and servesto catch most induced static or radiointerference signals, shunting them offto ground. (Hum, which isoften causedby electromagnetic interference, is notgenerally attenuated by shields unlessYAMAHASOUNdREiNfORCEMENTHANdbookPAGE 12Figure 2-8. Frequency response ofa typicalaudio power amplifierFigure 2-8 shows atypical frequencyresponse plot of a high quality audiopower amplifier. Note that the re-sponse isabsolutely flat throughoutthe audio range, falling off only at thefrequency extremes.(a) (b)-\ ~ / -ReferenceLevelr--- --- -- "\ ~ ,I II IFREQUENCYRESPONSEthey are in the form of iron conduit;instead, twisting the dual conductorsin a balanced circuit isthe best meansto reduce hum. This is due to acharacteristic known as Common ModeRejection, which is explained inSection 11.6.)2-CONDUCTOR SHIELDED CABLE(UNBALANCED LINE)20FREQUENCY 1Hz)20KYAMAHASOUNdREiNfoRCEMENTHANdbookPAGE l'3-CONDUCTOR SHIELDED CABLE(USUALLY BALANCEDLINE)Figure 2-7. Construction oftypical audio cablesNOTE: The next paragraph may bea bit complex, but it does explainwhy cablescan affect frequencyresponse.Frequency response problems associ-ated with cables are generally due tocapacitance between the signalconductorfs) and shield in the cable,and capacitance between the conduc-tors themselves. This capacitance, inconjunction with the resistance of thecable, can act like an R-C low passfilter, cutting off high frequencies anddulling the sound. The effect ispropor-tional to the length of the cable, and isworse over very long cable runs, but ismostly dependent on the output imped-ance of the circuit that drives the cable.Special line driver amplifiers are usedto send signals over long cables. Somecables also exhibit considerable induc-tance between conductors, and depend-ing on the resistance (and impedance)of the circuit, the result can be an R-Lhigh pass filter that cuts offlowfrequency response. This is why it isimportant to use the right type of cablefora given job.Electronic circuits represent ahighly developed and controlled tech-nology. Unless they are specificallydesigned to alter the frequency spec-trum (like tone controls, for example),circuits can be and generally are madevery flat in frequency response.The low-frequency roIloff indicatedin Figure 2-8(a) issometimes called asubsonic filter pole. Its effect istoreject ultra-low frequencies that coulddamage loudspeakers and/or modulatethe audio to produce undesirabledistortion.The high-frequency rolloff(b) issometimes called a TIM (transientintermodulation distortion) filter. Thisintentional limiting of high-frequencyresponse serves to minimize TIM, andalso helps to reject supersonic frequen-cies that can damage tweeters.Similar characteristics can beexpected of any professional audiosignal processor. An exception is thedigital delay or digital signal processor,both of which use very steep input andoutput low pass filters (so-called anti-aliasing and reconstruction filters) toavoid problems associated with thedigital signal processing; in thesedevices, there will be asignificant roll-off above the cutoff frequency of thedevice - as high as 150 dB per octave.Unless the design intentionally limitsthe response, however, analog audiosignal processors should be flatthroughout the audio range.2.2.2 MicrophonesContemporary microphone technol-ogy i.s also highly developed, and it ispossible to make microphones withvery flat frequency response through- the audio range. Because practicalmicrophones are used in part for theirmusical or sonic characteristicshowever, they may exhibittypes of controlled deviations from flatresponse.One such deviation iscalled apresence peak. This isa broad peak inresponse of 3 to 6 dB, centered in theregion between about 2 kHz and 5 kHz.It has the effect of adding a bit ofcrispness to the spoken voice and can. 'Increase the intelligibility of words.Condenser type microphones oftenexhibit a peak in the neighborhood of8 kHz to10 kHz. This isgenerally dueto diaphragm resonance and can lendaslightly brittle or bright quality tothe sound.Ribbon type microphones sometimesexhibit both a presence peak and aslight low-frequency rise, usuallyaround 200 Hz. This lends to them awarm sound quality, making thempopular choices for both voice andcertain instruments.Generally speaking, the response ofpractical dynamic microphones used insound work falls off rapidly in theoctave above 10 kHz. Similarly, theirlow-frequency response may fall offgradually below about 100 Hz.Addi-tionally, the angle of sound incidenceupon the microphone may affect theso sounds comingIn from the SIdes may sound differentfromthose picked up on-axis' this isparticularly evident withmics. A sound reinforcement mic thatispopular forsolo vocals or individualinstruments may have a harsh re-sponse, with many resonances thatactually brighten the apparent sound help it to cut through a complexmIX; these same characteristics maymake s?-ch mic unsuitable forpickupof multiple Instruments or voices, andless-than-ideal for recording work. Noonemic is ideal for every application.The exact characteristic of anymicrophone is determined by a complexset of design factors, and one is well-advised both to check the data sheetand to try out the microphone. A newseries of microphones introduced byYamaha in 1986 utilizes uniquee-I-O'0e-LI- 90'E-V-10E-l-L180'-20-3020 50 100 200 500 1K 2K 5K 10K 20KFREQUENCY In HzFigure 2-9. Onand off axisfrequency response of a typicalcardioid (unidirectional)dynamic microphonematerials (beryllium laminated dia-phragms) and innovative manufactur-ing techniques (screen-etched precisionports, for example) to achieve extendedresponse and very smooth off-axischaracteristics. In any case, some ofthe most important characteristics of amicrophone may never be fully meas-ured and documented. The selection ofa microphone fora given applicationremains a highly subjective taskandthe ear isthe best guide. '2.2.3 LoudspeakersOf all the elements in practicalsound systems, loudspeakers aresubject to the greatest variations infrequency response. It is not uncom-mon to find narrow peaks and dips of10 dB or more in a loudspeaker'sresponse. In fact, an overall responsetolerance of 4 dB, measured on aI/3- octave basis, isconsidered verygood.This seemingly broad tolerance isconsidered good partly because loud-speaker transducers are asked tohandle relatively large amounts ofpower and produce fairly high soundpressures, so their design must allowcompromises for durability and effi-ciency. Practical loudspeakers alsomust use several transducers toreproduce the full audio range; themarrying of these transducers to formasingle functional unit isa complexmatter, and can drastically affect thesystem frequency response.Sound reinforcement loudspeakerscan be divided into two basic classes:full-range loudspeakers, and specialunits that cover limited ranges. TheSECTiON 2YAMAHASOUNdREiNfORCEMENTHANdbookPAGE 14FREQUENCYRESPONSEYAMAHASOUNdREINfoRCEMENTHANdbookPAGElatter are used to augment the former,extending their response.Generally, full-range reinforcementloudspeakers will have a frequencyresponse extending from about 100 Hzto between 10 kHz and 15 kHz. In mostapplications, this response issufficient.Some smaller loudspeakers, such asthose used for paging, may have morelimited response - but for voice, it isgenerally true that the loudspeakerresponse should extend from about300 Hz to at least 3.5 kHz.Of the special, limited-range units,the most common are subwoofers andtweeters. Subwoofers are loudspeakersdesigned to operate only below 300 Hz(typically below 100 Hz),and usuallyperform down to about 30 Hz. They areused to extend the bass response ofsystems. Tweeters usually work above5 to 8 kHz, and are used to extend thesystem's high-frequencyPractical loudspeakers are direc-tional - that is, they concentrate thesound that they radiate in aspecificdirection. As you move away from theirprimary axis, the sound not only dropsin level, but the frequency responsegets rougher.For further information on thefrequency response characteristics ofloudspeakers, see Section 13,"Loudspeakers."In order to relate the frequency re-sponse of a device or system to its soniccharacteristics, we need to get a senseof the frequency ranges covered bytypical program sources. VOiCEANdINSTRUMENTRANGES2.3.1 The Speaking VoiceCompared with the full range ofhuman hearing, the speaking voicecovers a relatively narrow frequencyband - roughly from100 Hz to 6 kHz.Within that range, the power distribu-tion of speech is heavily weighted inthe frequencies below about 1 kHz,with some 80 percent ofthe energyconcentrated in the range below500Hz.While speech has very little high-fre-quency content, however, almost all ofthe energy of consonants occurs above1 kHz. Therefore, loss of high frequen-cies can drastically affect speechintelligibility.As apractical minimum, the band-width of aspeech reproduction systemmust extend from 300 Hz to 3.5 kHz.This isthe frequency response of atypical telephonetypes of utility communications devicesexhibit similarly limited response.Generally, intelligibility may beimproved by introducing apeak in the response of 3 to 6 dB In theregion between 2 kHz and 5Sound reinforcement applicationsrequire somewhat higher fidelity thanatelephone, however. For this reason,public address systems should bereasonably flat from 100 Hz to at least8 kHz. A presence peak can improveintelligibility in such systems, too -but it can also increase the likelihoodof feedback,so it must be approachedwith care.2.3.2 The Singing Voiceand Musical InstrumentsFigure 2-10 (next page) isa veryuseful graph which describes the fre-quency ranges of musical instrumentsand trained singing voices.Musical signals are much more diffi-cult to characterize than speech. Thefrequency range and power spectrw;n ofa particular musical signal depend Inlarge part onstylistic matters - theinstrumental complement, the ar-rangement, the style of production, andso on. Some styles of music, for ex-ample, depend heavily on energybetween 20Hz and 100 Hz to achievetheir full intended impact, while thosefrequencies may be entirely absent inother styles.The sound reinforcement profes-sional therefore must learn to use hisor her ears to carefully analyze musi-cal material and correlate the sonicexperience with system performance.The ability to do this comes only withlong practice listening toa variety ofequipment with different soundsources. In sound work it's very impor-tant to always listen carefully andexamine what you hear, graduallybuilding a mental catalog of experi-ences from which to draw.2.3.3 HarmonicsLooking at Figure 2-10, we see thatit seems to show the frequency rangecovered by musical instruments aslimited to about 4 kHz. Yet we knowthat human hearing extends farbeyond this limit, and that asoundsystem whose frequency response isthis limited will sound dull, lacking inhighs. The apparent discrepancy is dueto the fact that Figure 2-10 does nottake harmonics into account.Every musical sound that we hear isin fact a composite of sine waves atdifferent frequencies and amplitudes.These sine waves combine to form thesound, and their frequency and ampli-tude relationships determine thequality, or timbre, of the sound. Theultimate waveform may be more of atriangle, squarewave or something noteasily described in a word.When a musical note with a complexwaveform has a distinct pitch (as op-posed to noise), that waveform canultimately be created by combining aset of precisely related sine waves.These sine waves are called harmonics,and their frequencies are related insimple integer multiples. The sinewave frequency at the pitch that wehear as the note is the fundamental,and it is usually (though not always)the strongest (highest amplitude) ofthe set of sine waves which comprisesthe complex waveform.SECTiON2SynthesizerFundamentalCan SeAsHigh As20 kHzNOTESPIANOKEYBOARD L:'U":W''''"-f;'' '.:J.C', lCL.LLLI--L.LLL.LLJ--L.LLL.LLJLLlLL.LLLLl-LL.LLLLl-LL-'-L.LLl--'-L-'-L.LLl.J---""'"f2SifW(g:l!:8::;15l;;L::!3 !- ' I / t+f-tt:,i" i\/ .. 6th HARMONIC(-84 dB) "''IIlol-,++-tH-t-t.' ..J '\ .. 7th HARMONIC(-92 dB) ...120110100-DJ90"0-..J80W70>W..J 60W50>i=40.._--I30Wa:2010020YAMAHASOUNdREiNfoRCEMENTHANdbookPAGE 81SECTiON 8amplifier is driven to a point where theoutput cannot produce adequatevoltage to trace the input waveform). Itcan be caused by other circuit faults ordesign errors. In loudspeakers, it canbe caused by resonances, voice coilrubbing or striking against the mag-netic structure, or diaphragm break-up. It is beyond the scope of thishandbook to explore the origins ofharmonic distortion in any greaterdetail.8.4.2 Measuring HarmonicDistortionHarmonic Distortion:2nd Harmonic, -60 dB,3rd Harmonic, -75 dB, relative tomaximum rated output at 1 kHz.We know such a spec has beenmeasured with an analyzer, ratherthan anotch filter. It is less susceptibleto inaccuracies due to noise, unlessthere isa very high noise level. Withan analyzer, we generally view thenoise voltage. Therefore, if we want toconvert adB distortion spec into apercent spec, we use the followingformula:%Distortion = 100. 10dB/20(V or SPL)PROBLEM: What isthe percent2ndHD of an output rated as follows:Second Harmonic Distortion:30 dB below maximum rated outputof 100 watts.Notice that the -60 dB distortionnumber in the first problem dB, wasreferenced to voltage (as indicated bythe dBu spec). In the second problem,This equation can be used for individ-ual harmonics, or for total harmonicdistortion. Ifwe are looking at dB inrelation to output power, then theequation is modified to reflect the 10log relationship, as follows:%Distortion(TI ) = 100 10dB/1OrowerYAMAHASOUNd REiNfORCEMENTHANdbookPAGE 82= 100 10-30110= 100.10-3= 100 .001=0.1%2ndHarmonic Distortion%HDpwrPROBLEM: What isthe percent2ndharmonic distortion of an outputwhose 2ndharmonic is60 dBbelowthe +4 dBu signal?% Distortion = 100 10--60/20= 100 10-3= 100 .001=0.1% 2ndHarmonic DistortionIf this spec is accompanied by a verylow output noise specification, you canassume that most of the 1% is,in fact,distortion... if the noise ishigh, thenperhaps a lot of the measured distor-tion is actually noise voltage. It isnotnecessary to be a detective if theequipment is measured using a waveanalyser.By using a wave analyzer, whichprecisely indicates signals present inbands as narrow as1;10 octave... or aspectrum analyzer that provides adetailed graphic view of the entireoutput waveform, with respect tofrequency and amplitude, individualharmonic frequencies can be identifiedand measured. Using such equipment,individual harmonics may be specified.For example, it is not uncommon to seethe following specification:One method of measuring harmonicdistortion isto inject a single fre-quency, sine wave test signal at theinput of the device under test, and tothen use a deep, very narrow bandrejection filter to eliminate that sametest signal at the device's output.Typically, such a filter would cut thetest signal by at least 80 dB. One thentakes asimple voltage measurement ofeverything that's left at the output andcalls that the total harmonic distortion.The problem with this measurement isthat it also measures any noise presentat the output. This is why manufactur-ers sometimes print aspec like this:Total Distortion & Noise:Less than 1% at +4 dBm.How TOREAd&INTERpRETSpEcificATioNSthe -30 dB distortion number was ref-erenced to power. Note that bothvalues represent a distortion of 0.1%.This is why percentages are most oftenused in describing distortion - theyavoid confusion.The same formulas apply to 3rdhar-monic, 4t hharmonic or total harmonicdistortion. Figure 8-7provides a handygraphic reference based on theseformulas, so you don't have to do themath if the values can be found on thechart.Ifyou want togo in the opposite di-rection, that is, to find the ratio in dBrepresented by apercent distortion,use the following formulas:For power ratios:dB= 10 log (% +100)For voltage ratios (or SPL ratios):dB= 20 log (% +100)Total dB= 10 log (10dB1/10 +10dB2I10...+ 10dBn110 )PROBLEM: What is the % THD fora circuit whose 2ndharmonic distor-tion is -40 dB,third harmonic is-65 dB, fourth harmonic is -50 dB,fifth harmonic is -70 dB, and allsubsequent harmonics are negligible(below -80 dB) relative to 252 mW(+24 dBm) output?Total dB= 10 log (10-40110 + 10-sSI10+10-50/10 +10-70/10)Total dB= 10 log (10-4 + lO-s.S+10-5 + 10-7)= 10 log (.0001 + .0000003162+ .00001 + .0000001)= 10 log (.0001104162)= 10 (-3.956967203)= -39.6 dB (approx)If you have separate specs for 2ndharmonic, 3rdharmonic, and so forth,you cannot simply add the figures toobtain the THD. Instead, you need toadd the dB value of each harmonicusing the following formula (then youcan find the % THD using one of thepreviously stated voltage/SPL refer-enced formulas):As you can see, the total distortion,in dB is not much greater than thesecond harmonic (0.4dB). The higherorder harmonics are so much lower inlevel that they are almost negligible inthis case. Now let's convert the numberof dBto a percentage.%THD= 100 10--39.6110= 100 10--396= 1000.0001096= .001%~POWER:.--- "'"..... 1.-'10 lOG ........~.10-1/ ~--l-A~ ...v~'",..,... 10-1-l/1\.... "'"~V\SPl, VOlTAGEio"OR DISTANCE:1/20 lOG./~100% 0.1% 1% 10%PERCENT OF SIGNALFigure 8-7. Relationshi p of dB to percent of signal700.01%U 50Zo~ 60~J:ID't:l....I 0~I-ZW 10:a:~c 20Z::JLL.s: 30o....I~ 40~YAMAHASOUNdREiNfoRCEMENTHANdbookPAGE 8}8.4.3 Factors AffectingHarmonic DistortionSpecificationsNone of the distortion specs pre-sented so far in this section have beenthorough. There are many things wewould like to know about a harmonicdistortion spec in order to determinewhether it represents an appropriatemeasurement of a real world operatingcondition, and to be able to duplicatethe measurement ourselves. It wouldbe wise to ask the following questions:a) At what operating level, or levels,was the measurement made?b) At what frequency, or over whatfrequency range, was the measure-mentmade?c) What input termination and outputload were used?c) Was noise part of the measurement,or was this apure distortion test?The distortion in almost all circuitswill rise dramatically and suddenly asthe maximum output voltage orpoweris reached. This is the result of clip-ping. The distortion will usually berated at some level below this rise. It isimportant to note that the percent dis-tortion may also rise at very low outputlevels. In this case, it isusually amatter of running into the residualnoise of the test equipment, or theequipment under test. That is, theharmonic components can only be somany dB below the signal when thesignal is very close to the noise floor.Aspecial case exists with digital audioequipment, where the actual distortioncomponents may remain at a fairlyconstant level regardless of the outputpower. In this case, the percent distor-tion willdecrease as the output poweris increased.Distortion willsometimes be higherat low frequenc