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TheRCOscillator
IntheAmplifierstutorialwesawthatasinglestageamplifierwillproduce180ofphaseshiftbetweenitsoutputand
inputsignalswhenconnectedinaclass-Atypeconfiguration.Foranoscillatortosustainoscillationsindefinitely,
sufficientfeedbackofthecorrectphase,ie"PositiveFeedback"mustbeprovidedwiththeamplifierbeingusedasone
invertingstagetoachievethis.
InanRCOscillatorcircuittheinputisshifted180throughtheamplifierstageand180againthroughasecond
invertingstagegivingus"180+180=360"ofphaseshiftwhichisthesameas0therebygivingustherequired
positivefeedback.Inotherwords,thephaseshiftofthefeedbackloopshouldbe"0".
InaResistance-CapacitanceOscillatororsimplyanRCOscillator,wemakeuseofthefactthataphaseshiftoccurs
betweentheinputtoaRCnetworkandtheoutputfromthesamenetworkbyusingRCelementsinthefeedbackbranch,
forexample.
RCPhase-ShiftNetwork
Thecircuitontheleftshowsasingleresistor-capacitornetworkandwhoseoutputvoltage"leads"theinputvoltageby
someanglelessthan90.Anidealsingle-poleRCcircuitwouldproduceaphaseshiftofexactly90,andbecause
180ofphaseshiftisrequiredforoscillation,atleasttwosingle-polesmustbeusedinanRCoscillatordesign.
Howeverinrealityitisdifficulttoobtainexactly90ofphaseshiftsomorestagesareused.Theamountofactualphase
shiftinthecircuitdependsuponthevaluesoftheresistorandthecapacitor,andthechosenfrequencyofoscillations
withthephaseangle(Φ)beinggivenas:
PhaseAngle
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Inoursimpleexampleabove,thevaluesofRandChavebeenchosensothatattherequiredfrequencytheoutput
voltageleadstheinputvoltagebyanangleofabout60.ThenthephaseanglebetweeneachsuccessiveRCsection
increasesbyanother60givingaphasedifferencebetweentheinputandoutputof180(3x60)asshownbythe
followingvectordiagram.
VectorDiagram
ThenbyconnectingtogetherthreesuchRCnetworksinserieswecanproduceatotalphaseshiftinthecircuitof180at
thechosenfrequencyandthisformsthebasesofa"phaseshiftoscillator"otherwiseknownasaRCOscillatorcircuit.
WeknowthatinanamplifiercircuiteitherusingaBipolarTransistororanOperationalAmplifier,itwillproduceaphase-
shiftof180betweenitsinputandoutput.Ifathree-stageRCphase-shiftnetworkisconnectedbetweenthisinputand
outputoftheamplifier,thetotalphaseshiftnecessaryforregenerativefeedbackwillbecome3x60+180=360as
shown.
ThethreeRCstagesarecascadedtogethertogettherequiredslopeforastableoscillationfrequency.Thefeedback
loopphaseshiftis-180whenthephaseshiftofeachstageis-60.Thisoccurswhenω=2π?=1.732/RCas(tan
60=1.732).ThentoachievetherequiredphaseshiftinanRCoscillatorcircuitistousemultipleRCphase-shifting
networkssuchasthecircuitbelow.
BasicRCOscillatorCircuit
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ThebasicRCOscillatorwhichisalsoknownasaPhase-shiftOscillator,producesasinewaveoutputsignalusing
regenerativefeedbackobtainedfromtheresistor-capacitorcombination.Thisregenerativefeedbackfrom
theRCnetworkisduetotheabilityofthecapacitortostoreanelectriccharge,(similartotheLCtankcircuit).
Thisresistor-capacitorfeedbacknetworkcanbeconnectedasshownabovetoproducealeadingphaseshift(phase
advancenetwork)orinterchangedtoproducealaggingphaseshift(phaseretardnetwork)theoutcomeisstillthesame
asthesinewaveoscillationsonlyoccuratthefrequencyatwhichtheoverallphase-shiftis360.Byvaryingoneormore
oftheresistorsorcapacitorsinthephase-shiftnetwork,thefrequencycanbevariedandgenerallythisisdoneby
keepingtheresistorsthesameandusinga3-gangedvariablecapacitor.
Ifalltheresistors,Randthecapacitors,Cinthephaseshiftnetworkareequalinvalue,thenthefrequencyofoscillations
producedbytheRCoscillatorisgivenas:
Where:
?istheOutputFrequencyinHertz
RistheResistanceinOhms
CistheCapacitanceinFarads
NisthenumberofRCstages.(N=3)
Sincetheresistor-capacitorcombinationintheRCOscillatorcircuitalsoactsasanattenuatorproducinganattenuation
of-1/29th(Vo/Vi=β)perstage,thegainoftheamplifiermustbesufficienttoovercomethelossesandinourthree
stagenetworkabovetheamplifiergainmustbegreaterthan29.
Theloadingeffectoftheamplifieronthefeedbacknetworkhasaneffectonthefrequencyofoscillationsandcancause
theoscillatorfrequencytobeupto25%higherthancalculated.Thenthefeedbacknetworkshouldbedrivenfromahigh
impedanceoutputsourceandfedintoalowimpedanceloadsuchasacommonemittertransistoramplifierbutbetter
stillistouseanOperationalAmplifierasitsatisfiestheseconditionsperfectly.
TheOp-ampRCOscillator
WhenusedasRCoscillators,OperationalAmplifierRCOscillatorsaremorecommonthantheirbipolartransistors
counterparts.Theoscillatorcircuitconsistsofanegative-gainoperationalamplifierandathreesectionRCnetworkthat
producesthe180phaseshift.Thephaseshiftnetworkisconnectedfromtheop-ampsoutputbacktoits"non-inverting"
inputasshownbelow.
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Op-ampRCOscillatorCircuit
Asthefeedbackisconnectedtothenon-invertinginput,theoperationalamplifieristhereforeconnectedinits"inverting
amplifier"configurationwhichproducestherequired180phaseshiftwhiletheRCnetworkproducestheother
180phaseshiftattherequiredfrequency(180+180).Althoughitispossibletocascadetogetheronlytwosingle-
poleRCstagestoprovidetherequired180ofphaseshift(90+90),thestabilityoftheoscillatoratlowfrequenciesis
generallypoor.
OneofthemostimportantfeaturesofanRCOscillatorisitsfrequencystabilitywhichisitsabilitytoprovideaconstant
frequencysinewaveoutputundervaryingloadconditions.BycascadingthreeorevenfourRCstagestogether(4x45),
thestabilityoftheoscillatorcanbegreatlyimproved.RCOscillatorswithfourstagesaregenerallyusedbecause
commonlyavailableoperationalamplifierscomeinquadICpackagessodesigninga4-stageoscillatorwith45of
phaseshiftrelativetoeachotherisrelativelyeasy.
RCOscillatorsarestableandprovideawell-shapedsinewaveoutputwiththefrequencybeingproportionalto1/RCand
therefore,awiderfrequencyrangeispossiblewhenusingavariablecapacitor.However,RCOscillatorsarerestrictedto
frequencyapplicationsbecauseoftheirbandwidthlimitationstoproducethedesiredphaseshiftathighfrequencies.
ExampleNo1
DeterminethefrequencyofoscillationsofaRCOscillatorcircuithaving3-stageseachwitharesistorandcapacitorof
equalvalues.R=10kΩandC=500pF
ThefrequencyofoscillationsforaRCOscillatorisgivenas:
Thecircuitisa3-stageoscillatorwhichconsistsofthree10kΩresistorsandthree500pFcapacitorsthereforethe
frequencyofoscillationisgivenas:
InthenexttutorialaboutOscillators,wewilllookatanothertypeofRCOscillatorcalledaWienBridge
Oscillatorswhichusesresistorsandcapacitorsasitstankcircuittoproducealowfrequencysinusoidalwaveform.
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