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8/11/2019 ENS466 Week3.Rev
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9/19/20
ENS/ELT466
TelecommunicationSystemsLab
Fall2013
Week3 Sept.17
PleaseturninLabReport#2now!
Oscillators
TelecommunicationSystemsLab(ENS466)
Fall2013Week3 Sept.17
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8/11/2019 ENS466 Week3.Rev
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TheCosineWaveMuchofcommunicationsengineeringisbuiltaroundthecosinesignal,givenby:
Here,Aistheamplitude,fisthefrequency,isthephase,and2fistheangularfrequency.
Thecosinefunctionisperiodic,repeatingitselfexactlyaftereveryperiod
T = 1/f. TheunitoffrequencyistheHertz(Hz),equivalenttosec1.
( ) cos(2 ), also written
( ) cos( ) or ( ) cos[( / ) ]
s t A ft
s t A t s t A t T
-1.5
-1
-0.5
0
0.5
1
1.5
0 1 2 3 4 5
s(t)
t(sec)
-1.5
-1
-0.5
0
0.5
1
1.5
0 1 2 3 4 5
s(t)
t (sec)
A=1
f=1Hz
=0
A=1f=5Hz
=0
Oscillators
Theoscillatorisafeedbackcontrolsystemthatproducesanoscillatingoutput(becomesunstable)onlyifthemagnitudeoftheloopgainis
1(Barkhausen
criterion). Mathematically,
A(s)1
Oscillatorsareelectroniccircuitsthatgenerateperiodicsignals:
cosinewaves,square
waves,triangularwaves,pulsetrains,etc.
Theyareusedtogeneratecarriers,clock
signals,andtestsignals.
Feedbacknetwork
Amplifier
Barkhausen criterion
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PhaseinOscillatorsForanoninvertingamplifier(i.e.,positiveinputvoltageswingcausesapositive
outputvoltageswing),sinusoidaloscillationisenabledwhenthephaseshiftthrough
thefeedbacknetworkiszero.
Therefore,thefrequencyofoscillationmaybesetby
controllingthephaseresponseofthefeedbacknetwork.
Feedbacknetwork
Amplifier
Willoscillateatfrequencywhere
phaseangleof(s)=0
AsingleRCelementyieldsbetween0and90 phaseshift.
Soatleasttworeactive
elementsarenecessarytomakeasinusoidaloscillator.
LCOscillators
AnLCoscillatormaybemechanicallytunedwithanadjustablecapacitororinductor.
LCoscillatorshavebecomelesspopularbecauseinductorstendtobebulkyandare
verydifficulttobuildintoanIC.
Atradiofrequencies,theclassicsolutionistouseanLCresonantcircuitcontaining
bothacapacitorandaninductor.
TheColpittsoscillatorisshownbelow
Amplifieroutput
Feedbackpath
LCresonantcircuit
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CrystalOscillators
Quartzcrystaloscillatorsprovidetheclocksignalsinyourwatch,yourcellphone,and
practicallyeverypieceofdigitalelectronicstoday
morethantwobillionare
manufacturedannually,accordingtoWikipedia.
Forafixedfrequencyoscillatorwithgreatstabilityandfrequencyprecision,quartz
crystaloscillators
rule. Quartzispiezoelectric,meaningthatelectricfieldscause
mechanicalmotionandviceversa,sothattheacousticresonancesofthecrystal
createelectricalresonancesthatcanreplaceanLCcircuit
andthecrystalsare
typicallyjustafewmminsize.
Quartzcrystalequivalentcircuit QuartzcrystalColpitts
oscillator
WienBridgeOscillator(1)
Thetransferfunctionofthefeedback
loopisgivenby:
Foraudiofrequencieswhereinductorswouldbetoolarge,twoRCstagescanbe
arrangedforzerophaseshiftfeedback,asinthisWienbridgeoscillator.
2
1 2
( )O
V Zs
V Z Z
Here,sisthecomplexfrequency
parameterusedinlinearcircuit
theory. ExpressingZ1andZ2interms
ofR1,R2,C1,andC2,allowsustofind
thecomponentvaluesneededto
achievezerophaseshiftatour
desiredoperatingfrequency.
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WienBridgeOscillator(2)Asshowninthisweeksassignmentnotes,bychoosingR1=R2=R
andC1=C2=C,the
transferfunctionmaybeexpressedas:
2
( )1
3O
V RCs
VRC j RC
For tohaveaphaseofzero,itmustbereal
thefactormultiplyingjmustbezero.
2
0
1 10 =
2RC f
RC
Bysettingthemagnitudeoftobe1,we
find:
=2f
i
RR
Duetothenonidealpropertiesofrealcomponents,Rf/Ri
willprobablyneedtobe
slightlygreaterthanitsidealvaluetoachieveoscillation.
SteadyStateOperationIftheloopgainisslightlylessthan1,oscillationwilldieout.
Iftheloopgainisslightly
greaterthan1,theamplitudeofoscillationwillkeepincreasing.
( ) 1A s
( ) 1A s
Inpractice,asteadystatecondition
happenswhenthesignallevelislarge
enoughtostartoverloadingtheamplifier.
If|(s)| istoolarge,theresultwillbe
severeclippingofthecosinewave. So
|(s)|shouldbejustlargeenoughto
causestableoscillation,butnolarger.
steady-state
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RelaxationOscillators
ElectronicrelaxationoscillatorsareeasilymadeusingRCcircuitswithoutany
inductorsorcrystals.
Becauserelaxationoscillationisintrinsicallyanonlineareffect,
itisbestunderstoodinthetimedomain.
Relaxationoscillatorsoccurwhenaphysicalsystemispushedgraduallyawayfromits
equilibriumposition,thenabruptlysnapsback.
Examplesaboundineverydaylife,
includingthescreechoftireswhenacarbrakesandthesustainednotesofaviolin.
RelaxationOscillatorFrequency
Theanalysisinthehandoutmakesseveralsimplifyingassumptions,includinginfinite
gainandnotimedelayintheopamp,sotheactualfrequencyobservedmaydiffer
somewhatfromthetheory.
Theoperatingfrequencyoftherelaxationoscillatoriscomputedbyconsideringthe
chargingtimeoftheRCcircuitandthereferencevoltagesetbytheresistivevoltage
dividerattheopampoutput,asexplainedinthehandout.
2
1 2
R
R R
1 12 ln
1T RC
f
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Summary
Oscillatorsareusedtogenerateperiodicsignalsforcarriers,clocksignals,andtest
signals. TheBarkhausen
criterionstatesthatthemagnitudeoftheloopgainmustbe 1
forthefeedbacksystemtooscillate.
Inasinusoidaloscillatorbasedonlinearcomponents,thephaseshiftaroundthefeedbackloopmustbezero.
LCoscillators,whichuseaninductorandacapacitortocreatearesonantcircuitthatsetstheoperatingfrequency,areusedforhighfrequencyRFdesigns.
Crystaloscillators,whosefrequencyissetbysoundwaveresonancesinapiezoelectriccrystal,areincludedinvirtuallyalldigitalelectronics.
Electronicrelaxationoscillators,whosefrequencyissetbythechargingtimeofanRCcircuit,aresimpleandinexpensive,foruseinnondemandingapplications.
Relaxationoscillatorsareinherentlynonlinearsystems,sotheyarebestanalyzedinthetimedomain,ratherthanthefrequencydomain.
LabReports(1)LabreportsforENS/ELT466shouldbewritteninthestyleofindustryinternaldocuments(ratherthanscientificresearchpapers).
Suchlabreportsarewrittentopresentmanagement
withanswerstotechnicalquestionsinsupportofdecisionmaking,ortodocumentprocedures
andknowledgeforuseinfutureprojects.
ForENS/ELT466,Isuggestorganizingthereportsin5or6sections:
Objective abrief
(oneortwosentences)outlineofthetopicsaddressedandthemethods
used.
Introduction
oneortwoparagraphsexplainingwhythetopicsareimportantandhowthe
answerswillinformusaboutcommunicationsystemsandotherelectronicapplications.
Procedures/Methods
astepbystepdescriptionofhowthestudywasconducted. The
lengthofthissectionmayvaryfromweektoweek.
Results&Discussion
thissectiondescribesyourobservations,referringtofiguresand
tablesasnecessary,anddiscusseswhatthoseobservationsmean.
Conclusions learningsfromthestudyarepresentedhere.
Usuallyoneortwoparagraphs,theConclusionsarethetakehomemessagesforthereader.
References
listsworkbyothersusedincompletingtheexperimentorreport. Youneed
notlistthelabhandoutsorlecturenotes,butshouldincludeotherreferencesyou
consulted(e.g.,librarybooks,Wikipedia,).
Youmightnothavereferencesinevery
report.
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LabReports(2)Labreports,likealltechnicaldocuments,shouldbewrittenwithyourreadersneedsinmind.
Theyshouldtellreaders(i)whatwasstudied;(ii)howthestudywasdone,inenoughdetailthataskilledworkercouldrepeatit;(iii)whatresultswerefound;and(iv)whatcanbelearned
fromthoseresults.
Reportsshouldbeconcise
(i.e.,brief,complete,andwellorganized),theyshouldbeaccurate,
andtheyshouldbereadable
(i.e.clear,grammatical,freeoftypographicalerrors).
Gradingcriteria:
20pointsaregrantedforcompletingthelabandhandinginalabreport.
Theremaining80
pointsareassignedaccordingtothequalityofthelabreport,asdescribedbelow
Content(32pts) shouldbecomplete,correct,andappropriate
Writing(24pts) shouldbeclearandgrammatical
Organization(16pts) shouldhaveheaders/sectionsasneeded,witha
clearlogicalflow
Presentation(8pts)
shouldbeneatandhaveminimaltypographicalerrors
Anoteaboutfigures.
Figuresareusedtopresentdatadirectlytoyourreaders,buttheyarenotasubstituteforanarrative(text)sectiononResults.
Eachfigureortableshouldbe
numbered(Romannumeralsfortablesandregularnumbersforfigures),andeachshouldhave
acaptionbrieflydescribingit.
Thetextsectionwillrefertothefigurebynumber,explaining
whattolookforineachone.
ENS466/ELT466 Assignmentsdue9/24 LabReport:
Labreport#3willcoverAssignment2.1;itisdueatthebeginning
ofclasson9/24
HomeworkAssignment: 2problemsandsomereadingaboutthe555timerchip.
Seethehomework
assignmentsheetpostedonBlackboard. Dueatthebeginning
ofclasson9/24
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8/11/2019 ENS466 Week3.Rev
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9/19/20
Week3:Backups/Alternates
TelecommunicationSystemsLab(ENS466)
Fall2013
Week3 Sept.17
