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TheWienBridgeOscillator
InthepreviousRCOscillatortutorialwesawthatanumberofresistorsandcapacitorscanbeconnectedtogether
withaninvertingamplifiertoproduceanoscillatingcircuit.Oneofthesimplestsinewaveoscillatorswhichuses
aRCnetworkinplaceoftheconventionalLCtunedtankcircuittoproduceasinusoidaloutputwaveform,istheWien
BridgeOscillator.
TheWienBridgeOscillatorissocalledbecausethecircuitisbasedonafrequency-selectiveformoftheWhetstone
bridgecircuit.TheWienBridgeoscillatorisatwo-stageRCcoupledamplifiercircuitthathasgoodstabilityatitsresonant
frequency,lowdistortionandisveryeasytotunemakingitapopularcircuitasanaudiofrequencyoscillatorbutthe
phaseshiftoftheoutputsignalisconsiderablydifferentfromthepreviousphaseshiftRCOscillator.
TheWienBridgeOscillatorusesafeedbackcircuitconsistingofaseriesRCcircuitconnectedwithaparallelRCofthe
samecomponentvaluesproducingaphasedelayorphaseadvancecircuitdependinguponthefrequency.Atthe
resonantfrequency?rthephaseshiftis0.Considerthecircuitbelow.
RCPhaseShiftNetwork
TheaboveRCnetworkconsistsofaseriesRCcircuitconnectedtoaparallelRCformingbasicallyaHighPass
FilterconnectedtoaLowPassFilterproducingaveryselectivesecond-orderfrequencydependantBandPass
FilterwithahighQfactorattheselectedfrequency,?r.
Atlowfrequenciesthereactanceoftheseriescapacitor(C1)isveryhighsoactslikeanopencircuitandblocksanyinput
signalatVin.Thereforethereisnooutputsignal,Vout.Athighfrequencies,thereactanceoftheparallelcapacitor,(C2)
isverylowsothisparallelconnectedcapacitoractslikeashortcircuitontheoutputsoagainthereisnooutputsignal.
However,betweenthesetwoextremestheoutputvoltagereachesamaximumvaluewiththefrequencyatwhichthis
happensbeingcalledtheResonantFrequency,(?r).
Atthisresonantfrequency,thecircuitsreactanceequalsitsresistanceasXc=Rsothephaseshiftbetweentheinput
andoutputequalszerodegrees.Themagnitudeoftheoutputvoltageisthereforeatitsmaximumandisequaltoone
third(1/3)oftheinputvoltageasshown.
OutputGainandPhaseShift
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Itcanbeseenthatatverylowfrequenciesthephaseanglebetweentheinputandoutputsignalsis"Positive"(Phase
Advanced),whileatveryhighfrequenciesthephaseanglebecomes"Negative"(PhaseDelay).Inthemiddleofthesetwo
pointsthecircuitisatitsresonantfrequency,(?r)withthetwosignalsbeing"in-phase"or0.Wecanthereforedefine
thisresonantfrequencypointwiththefollowingexpression.
ResonantFrequency
Where:
?ristheResonantFrequencyinHertz
RistheResistanceinOhms
CistheCapacitanceinFarads
ThenthisfrequencyselectiveRCnetworkformsthebasisoftheWienBridgeOscillatorcircuit.Ifwenowplace
thisRCnetworkacrossanon-invertingamplifierwhichhasagainof1+R1/R2thefollowingoscillatorcircuitisproduced.
WienBridgeOscillator
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Theoutputoftheoperationalamplifierisfedbacktoboththeinputsoftheamplifier.Onepartofthefeedbacksignalis
connectedtotheinvertinginputterminal(negativefeedback)viatheresistordividernetworkofR1andR2whichallows
theamplifiersvoltagegaintobeadjustedwithinnarrowlimits.Theotherpartisfedbacktothenon-invertinginput
terminal(positivefeedback)viatheRCWienBridgenetwork.
TheRCnetworkisconnectedinthepositivefeedbackpathoftheamplifierandhaszerophaseshiftajustonefrequency.
Thenattheselectedresonantfrequency,(?r)thevoltagesappliedtotheinvertingandnon-invertinginputswillbeequal
and"in-phase"sothepositivefeedbackwillcanceloutthenegativefeedbacksignalcausingthecircuittooscillate.
AlsothevoltagegainoftheamplifiercircuitMUSTbeequaltothree"Gain=3"foroscillationstostart.Thisvalueissetby
thefeedbackresistornetwork,R1andR2foraninvertingamplifierandisgivenastheratio-R1/R2.Also,duetothe
open-loopgainlimitationsofoperationalamplifiers,frequenciesabove1MHzareunachievablewithouttheuseof
specialhighfrequencyop-amps.
WienBridgeOscillatorSummary
ThenforoscillationstooccurinaWienBridgeOscillatorcircuitthefollowingconditionsmustapply.
1.WithnoinputsignaltheWienBridgeOscillatorproducesoutputoscillations.
2.TheWienBridgeOscillatorcanproducealargerangeoffrequencies.
3.TheVoltagegainoftheamplifiermustbeatleast3.
4.ThenetworkcanbeusedwithaNon-invertingamplifier.
5.TheinputresistanceoftheamplifiermustbehighcomparedtoRsothattheRCnetworkis
notoverloadedandaltertherequiredconditions.
6.Theoutputresistanceoftheamplifiermustbelowsothattheeffectofexternalloadingis
minimised.
7.Somemethodofstabilizingtheamplitudeoftheoscillationsmustbeprovidedbecauseifthe
voltagegainoftheamplifieristoosmallthedesiredoscillationwilldecayandstopandifitis
toolargetheoutputamplituderisestothevalueofthesupplyrails,whichsaturatestheop-amp
andcausestheoutputwaveformtobecomedistorted.
8.Withamplitudestabilisationintheformoffeedbackdiodes,oscillationsfromtheoscillator
cangoonindefinitely.
ExampleNo1
DeterminethemaximumandminimumfrequencyofoscillationsofaWienBridgeOscillatorcircuithavingaresistor
of10kΩandavariablecapacitorof1nFto1000nF.
ThefrequencyofoscillationsforaWienBridgeOscillatorisgivenas:
LowestFrequency
HighestFrequency
InourfinallookatOscillators,wewillexaminetheCrystalOscillatorwhichusesaquartzcrystalasitstankcircuitto
produceahighfrequencyandverystablesinusoidalwaveform.
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