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CHAPTER2OPERATIONALAMPLIFIERS
ChapterOutline2.1TheIdealOpAmp2.2TheInvertingConfiguration2.3TheNoninverting Configuration2.4DifferenceAmplifiers2.5IntegratorsandDifferentiators2.6DCImperfections2.7EffectofFiniteOpenLoopGainandBandwidthonCircuitPerformance2.8LargeSignalOperationofOpAmp
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2.1IdealOpAmp
IntroductionTheirapplicationswereinitiallyintheareaofanalogcomputationandinstrumentationOpampisverypopularbecauseofitsversatilityOpampcircuitsworkatlevelsthatarequiteclosetotheirpredictedtheoreticalperformanceTheopampistreatedabuildingblocktostudyitsterminalcharacteristicsanditsapplications
OpampsymbolandterminalsTwoinputterminals:invertinginputterminal()andnoninverting inputterminal(+)OneoutputterminalTwodcpowersuppliesV+ andVOtherterminalsforfrequencycompensationandoffsetnulling
Circuitsymbolforopamp Opampwithdcpowersupplies
IdealcharacteristicsofopampDifferentialinputsingleendedoutputamplifierInfiniteinputimpedance
i1 =i2 =0(regardlessoftheinputvoltage)Zerooutputimpedance
vO=A(v2v1)(regardlessoftheload)InfiniteopenloopdifferentialgainInfinitecommonmoderejectionInfinitebandwidth
Differentialandcommonmodesignals
Twoindependentinputsignals:v1 andv2Differentialmodeinputsignal(vId):vId =(v2v1)Commonmodeinputsignal(vIcm):vIcm =(v1+v2)/2Alternativeexpressionofv1 andv2:
v1 =vIcmvId/2
v2 =vIcm+vId/2
Exercise2.2(Textbook)Exercise2.3(Textbook)
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2.2TheInvertingConfiguration
TheinvertingcloseloopconfigurationExternalcomponentsR1 andR2 formacloseloopOutputisfedbacktotheinvertinginputterminalInputsignalisappliedfromtheinvertingterminal
InvertingconfigurationusingidealopampTherequiredconditionstoapplyvirtualshortforopampcircuit: Negativefeedbackconfiguration Infiniteopenloopgain
Closedloopgain:G vO/vI = R2/R1 Infinitedifferentialgain:v2v1 =vO/A =0 Infiniteinputimpedance:i2 =i1 =0 Zerooutputimpedance:vO =v1i1R2 = vIR2/R1 VoltagegainisnegativeInputandoutputsignalsareoutofphase Closedloopgaindependsentirelyonexternalpassive
components(independentofopampgain) Closeloopamplifiertradesgain(highopenloopgain)
foraccuracy(finitebutaccurateclosedloopgain)
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Equivalentcircuitmodelfortheinvertingconfiguration Inputimpedance:RivI/iI =vI /(vI/R1)=R1Forhighinputclosedloopimpedance,R1 shouldbelarge,butislimitedtoprovidesufficientGIngeneral,theinvertingconfigurationsuffersfromalowinputimpedance Outputimpedance:Ro =0 Voltagegain:Avo =R2/R1
Othercircuitexampleforinvertingconfiguration
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Application:theweightedsummerAweightedsummerusingtheinvertingconfiguration
Aweightedsummerforcoefficientsofbothsigns
Exercise2.4(Textbook)Exercise2.6(Textbook)Exercise2.7(Textbook)
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2.3Noninverting Configuration
ThenoninvertingcloseloopconfigurationExternalcomponentsR1 andR2 formacloseloopOutputisfedbacktotheinvertinginputterminalInputsignalisappliedfromthenoninvertingterminal
Noninverting configurationusingidealopampTherequiredconditionstoapplyvirtualshortforopampcircuit: Negativefeedbackconfiguration Infiniteopenloopgain
Closedloopgain:G vO/vI =1+R2/R1 Infinitedifferentialgain:v+v =vO/A =0 Infiniteinputimpedance:i2 =i1 =v /R1 Zerooutputimpedance:vO =v +i1R2 =vI(1+R2/R1) Closedloopgaindependsentirelyonexternalpassive
components(independentofopampgain) Closeloopamplifiertradesgain(highopenloopgain)
foraccuracy(finitebutaccurateclosedloopgain)Equivalentcircuitmodelforthenoninverting configuration Inputimpedance:Ri = Outputimpedance:Ro =0 Voltagegain:Avo =1+R2/R1
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ThevoltagefollowerUnitygainbufferbasedonnoninverting configurationEquivalentvoltageamplifiermodel: InputresistanceofthevoltagefollowerRi = OutputresistanceofthevoltagefollowerRo =0 VoltagegainofthevoltagefollowerAvo =1
TheclosedloopgainisunityregardlessofsourceandloadItistypicallyusedasabuffervoltageamplifiertoconnectasourcewithahighimpedancetoalow
impedanceload
Exercise2.9(Textbook)
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Exercise1:Assumetheopampsareideal,findthevoltagegain(vo/vi) ofthefollowingcircuits.(1)(2)
(3)(4)
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2.4DifferenceAmplifiers
DifferenceamplifierIdealdifferenceamplifier: RespondstodifferentialinputsignalvId RejectsthecommonmodeinputsignalvIcm
Practicaldifferenceamplifier: vO =AdvId+AcmvIcmAd isthedifferentialgainAcm isthecommonmodegain Commonmoderejectionratio(CMRR):
Singleopampdifferenceamplifier
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Theconditionfordifferenceamplifieroperation:R2/R1 =R4/R3 vO =(R2/R1)(v2v1)Forsimplicity,theresistancescanbechosenas:R3 =R1 andR4 =R2DifferentialinputresistanceRid: Differentialinputresistance:Rid =2R1 LargeR1 canbeusedtoincreaseRidR2 becomesimpracticallylargetomaintainrequiredgain
GaincanbeadjustedbychangingR1 andR2 simultaneously
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Instrumentationamplifier
DifferentialmodegaincanbeadjustedbytuningR1CommonmodegainiszeroInputimpedanceisinfiniteOutputimpedanceiszeroItspreferabletoobtainalltherequiredgaininthe1st stage,leavingthe2nd stagewithagainofone
Exercise2.15(Textbook)Exercise2.17(Textbook)
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2.5IntegratorsandDifferentiators
InvertingconfigurationwithgeneralimpedanceR1 andR2 ininvertingconfigurationcanbereplacedbyZ1(s)andZ2(s)Theclosedlooptransferfunction:Vo(s)/Vi(s)=Z2(s)/Z1(s)Thetransmissionmagnitudeandphaseforasinusoidinput
canbeevaluatedbyreplacings withjInvertingintegratorTimedomainanalysis:
Frequencydomainanalysis:
AlsoknownasMillerintegratorIntegratorfrequency(int)istheinverseoftheintegratortimeconstant(RC)int =1/RCThecapacitoractsasanopencircuitatdc( =0) openloopconfigurationatdc(infinitegain)Anytinydcintheinputcouldresultinoutputsaturation
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TheMillerintegratorwithparallelfeedbackresistanceTopreventintegratorsaturationduetoinfinitedcgain,parallelfeedbackresistanceisincluded
Closedloopgain=1/(jRF+R/RF)Closedloopgainatdc=RF/RClosedloopgainathighfrequency( >>1/RFC)1/jRCCornerfrequency(3dBfrequency)=1/RFCTheintegratorcharacteristicsisnolongeridealLargeresistanceRF shouldbeusedforthefeedback
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Frequencydomainanalysis:
Differentiatoroperation:
Differentiatortimeconstant:RCGain(=RC)becomesinfiniteatveryhighfrequenciesHighfrequencynoiseismagnified(generallyavoidedinpractice)
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Closedloopgain=jRC/(1+jRFC)Closedloopgainatinfinitefrequency=R/RFClosedloopgainatlowfrequency(
Exercise2: ForaMillerintegratorwithR =10k andC =10nF,ashuntresistanceRF isusedtosuppressthedcgain.FindtheminimumvalueofRF ifaperiodsignalwithaperiodof0.1sisappliedattheinput.
Example2.4(Textbook)Example2.5(Textbook)Exercise2.18(Textbook)Exercise2.20(Textbook)
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2.6DCImperfections*
OffsetvoltageInputoffsetvoltage(VOS)arisesasaresultoftheunavoidablemismatchesTheoffsetvoltageanditspolarityvaryfromoneopamptoanotherTheanalysiscanbesimplifiedbyusingthecircuitmodelwithanoffsetfree
opampandavoltagesourceVOS atinputterminalTypicaloffsetvoltageisafewmV
Effectofoffsetvoltageforaclosedloopamplifier
AdcvoltageVOS(1+R2/R1)existsattheoutputatzeroinputvoltageInputoffsetvoltageiseffectivelyamplifiedbytheclosedloopgainastheerrorvoltageatoutputSomeopampsareprovidedwithtwoadditionalterminalsforoffsetnulling
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InputbiasandoffsetcurrentDCbiascurrentsIB1 andIB2 arerequiredforcertaintypesofopampsInputbiascurrentisdefinedbyIB =(IB1+IB2)/2InputoffsetcurrentisdefinedasIOS =|IB1IB2|TypicalvaluesforopampsthatusebipolartransistorsareIB =100nA andIOS =10nA
EffectofinputbiascurrentforaclosedloopamplifiersOutputdcvoltageduetoinputbiascurrent:VO =IB1R2 IBR2ThevalueofR2 andtheclosedloopgainarelimited.
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Effectofinputoffsetvoltageonthethe invertingintegratorTheoutputvoltageisgivenby
TheoutputvoltageincreaseswithtimeuntiltheopampsaturatesEffectofinputbiascurrentontheinvertingintegratorTheoutputvoltageisgivenby
Theoutputvoltagealsoincreaseswithtimeuntiltheopampsaturates
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2.7EffectofFiniteOpenLoopGainandBandwidthonCircuitPerformance
PracticalopampcharacteristicsOpampwithfiniteopenloopgain:A(j)=A0Opampwithfiniteopenloopgainandbandwidth:A(j)=A0/(1+j/b)Frequencyresponseofopamp:
OpenloopopampThefrequencyresponseofanopenloopopampisapproximatedbySTCform:
A(j)=A0/(1+j/b)Atlowfrequencies( b),theopenloopopampisapproximatedby|A(jw)|A0/bUnitygainbandwidth (ft =t/2)isdefinedasthefrequencyatwhich|A(jt)|1t =A0b
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InvertingconfigurationusingopampwithfiniteopenloopgainClosedloopgain:
ClosedloopgainapproachestheidealvalueofR2/R1 asA0 approachestoinfinite TominimizethedependenceofG onopenloopgain,weshouldhaveA0 >>1+R2/R1
Inputimpedance:Outputimpedance:
Invertingconfigurationusingopampwithfinitegainandbandwidth
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Exercise3: Consideraninvertingamplifierwheretheopenloopgainand3dBbandwidthoftheopampare10000and1rad/s,respectively.Findthegainandbandwidthofthecloseloopgain(exactandapproximatedvalues)forthefollowingcases:R2/R1 =1,100,200,and2000.Exercise4:Anopamphasanopenloopgainof80dBanda3dBbandwidthof10rad/s.(1) TheopampisusedinaninvertingamplifierwithR2/R1 =100.Findthecloseloopgain
atdcandat =1000rad/s.(2) TwoidenticalinvertingamplifierswithR2/R1 =100arecascaded.Findthecloseloop
gainatdcandat =1000rad/s.(3) Forthecascadedamplifierin(2),findthefrequencyatwhichthegainis3dBlower
thanthedcgain.
Exercise2.12(Textbook)Exercise2.26(Textbook)Example2.6(Textbook)Exercise2.27(Textbook)Exercise2.28(Textbook)
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2.8LargeSignalOperationofOpAmps
OutputvoltagesaturationRatedoutputvoltage(vO,max)specifiesthemaximumoutputvoltageswingofopampLinearamplifieroperation(fortherequiredvO vO,max):vO =vO,maxThemaximuminputswingallowedforoutputvoltagelimitedcase:vI,max =vO,max/(1+R2/R1)OutputistypicallylimitedbyvoltageincaseswhereRL islarge
OutputcurrentlimitsMaximumoutputcurrent(iO,max)specifiestheoutputcurrentlimitationofopampLinearamplifieroperation(fortherequirediO iO,max):iL =iO,max iFThemaximuminputswingallowedforoutputcurrentlimitedcase:
vI,max =iO,max[RL||(R1+R2)]/(1+R2/R1)OutputistypicallylimitedbycurrentincaseswhereRL issmall
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SlewrateSlewrateisthemaximumrateofchangepossibleattheoutput:(V/sec)Slewratemaycausenonlineardistortionforlargesignaloperation
FullpowerbandwidthDefinedasthehighestfrequencyallowedforaunitygainbufferwithasinusoidaloutputatvO,max
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Example2.7(Textbook)Exercise2.26(Textbook)Exercise2.30(Textbook)
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