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  • NTUEEElectronics L.H.Lu 21

    CHAPTER2OPERATIONALAMPLIFIERS

    ChapterOutline2.1TheIdealOpAmp2.2TheInvertingConfiguration2.3TheNoninverting Configuration2.4DifferenceAmplifiers2.5IntegratorsandDifferentiators2.6DCImperfections2.7EffectofFiniteOpenLoopGainandBandwidthonCircuitPerformance2.8LargeSignalOperationofOpAmp

  • NTUEEElectronics L.H.Lu 22

    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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    (1+R2/R1)vi

  • 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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  • Superpositiontechniqueforlineartimeinvariantcircuit

    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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  • TheopampdifferentiatorTimedomainanalysis:

    Frequencydomainanalysis:

    Differentiatoroperation:

    Differentiatortimeconstant:RCGain(=RC)becomesinfiniteatveryhighfrequenciesHighfrequencynoiseismagnified(generallyavoidedinpractice)

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  • ThedifferentiatorwithseriesresistanceTopreventmagnifyinghighfrequencynoise,seriesresistanceRF isincluded

    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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    )/1( 12 RRVV OSO

  • 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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    tRCVVtd

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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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    ifA0 >>1+R2/R1 G G0 /(1+j/3dB)whereG0 =R2/R1 and3dB =A0b /(1+R2/R1)(A0 /|G0|)b

  • 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)

    NTUEEElectronics L.H.Lu 223

  • 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

    NTUEEElectronics L.H.Lu 224

  • SlewrateSlewrateisthemaximumrateofchangepossibleattheoutput:(V/sec)Slewratemaycausenonlineardistortionforlargesignaloperation

    FullpowerbandwidthDefinedasthehighestfrequencyallowedforaunitygainbufferwithasinusoidaloutputatvO,max

    NTUEEElectronics L.H.Lu 225

    maxdtdvSR O

    )1()( tOteVtv

    Inputstepfunction Smallsignaldistortion(finiteBW) Largesignaldistortion(SR)

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  • Example2.7(Textbook)Exercise2.26(Textbook)Exercise2.30(Textbook)

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