Electronics Ch2

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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)

    NTUEEElectronics L.H.Lu 23

  • 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)

    NTUEEElectronics L.H.Lu 24

  • Equivalentcircuitmodelfortheinvertingconfiguration Inputimpedance:RivI/iI =vI /(vI/R1)=R1Forhighinputclosedloopimpedance,R1 shouldbelarge,butislimitedtoprovidesufficientGIngeneral,theinvertingconfigurationsuffersfromalowinputimpedance Outputimpedance:Ro =0 Voltagegain:Avo =R2/R1

    Othercircuitexampleforinvertingconfiguration

    NTUEEElectronics L.H.Lu 25

  • Application:theweightedsummerAweightedsummerusingtheinvertingconfiguration

    Aweightedsummerforcoefficientsofbothsigns

    Exercise2.4(Textbook)Exercise2.6(Textbook)Exercise2.7(Textbook)

    NTUEEElectronics L.H.Lu 26

    )...(0 22

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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

    NTUEEElectronics L.H.Lu 27

    (1+R2/R1)vi

  • ThevoltagefollowerUnitygainbufferbasedonnoninverting configurationEquivalentvoltageamplifiermodel: InputresistanceofthevoltagefollowerRi = OutputresistanceofthevoltagefollowerRo =0 VoltagegainofthevoltagefollowerAvo =1

    TheclosedloopgainisunityregardlessofsourceandloadItistypicallyusedasabuffervoltageamplifiertoconnectasourcewithahighimpedancetoalow

    impedanceload

    Exercise2.9(Textbook)

    NTUEEElectronics L.H.Lu 28

  • Exercise1:Assumetheopampsareideal,findthevoltagegain(vo/vi) ofthefollowingcircuits.(1)(2)

    (3)(4)

    NTUEEElectronics L.H.Lu 29

  • 2.4DifferenceAmplifiers

    DifferenceamplifierIdealdifferenceamplifier: RespondstodifferentialinputsignalvId RejectsthecommonmodeinputsignalvIcm

    Practicaldifferenceamplifier: vO =AdvId+AcmvIcmAd isthedifferentialgainAcm isthecommonmodegain Commonmoderejectionratio(CMRR):

    Singleopampdifferenceamplifier

    NTUEEElectronics L.H.Lu 210

    ||

    ||log20

    cm

    d

    AACMRR

    vvRRRv I 2

    43

    4

    243

    121

    1

    22

    1

    12 /1

    /1IIO vRR

    RRvRRR

    RvvviRvv

    2//1

    /12/

    43

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    2IdIcmIdIcm vvRR

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    1

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    43

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    1

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    1

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    1

    2

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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

    NTUEEElectronics L.H.Lu 211

    1121 )/( IO vRRv

    243

    4

    1

    22 1 IO vRR

    RRRv

    243

    121

    1

    221 /1

    /1IIOOO vRR

    RRvRRvvv

    SetvI2 =0

    SetvI1 =0

    IdIcm vRR

    RRRRv

    RR

    RRRR

    1

    2

    43

    12

    1

    2

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    1log20

    RR

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    vI1

    vI2

    vO1

    vO2

  • Instrumentationamplifier

    DifferentialmodegaincanbeadjustedbytuningR1CommonmodegainiszeroInputimpedanceisinfiniteOutputimpedanceiszeroItspreferabletoobtainalltherequiredgaininthe1st stage,leavingthe2nd stagewithagainofone

    Exercise2.15(Textbook)Exercise2.17(Textbook)

    NTUEEElectronics L.H.Lu 212

    1

    2

    3

    4

    12

    1RR

    RR

    vvvA

    II

    Od

  • 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

    NTUEEElectronics L.H.Lu 213

    t ICtCC dtRtvCVdttiCVtv 00 1)(1

    )(1

    )(

    C

    t

    ICO VdttvRCtvtv

    0

    )(1

    )()(

    RCjZZ

    jVjV

    i

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    1)(

    )(

    1

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    RCVV

    i

    o

    1 f =90

  • TheMillerintegratorwithparallelfeedbackresistanceTopreventintegratorsaturationduetoinfinitedcgain,parallelfeedbackresistanceisincluded

    Closedloopgain=1/(jRF+R/RF)Closedloopgainatdc=RF/RClosedloopgainathighfrequency( >>1/RFC)1/jRCCornerfrequency(3dBfrequency)=1/RFCTheintegratorcharacteristicsisnolongeridealLargeresistanceRF shouldbeusedforthefeedback

    NTUEEElectronics L.H.Lu 214

    w(logscale)

    G(dB)

    RC1

    CRF1

    RCjRRjZjZ

    jVjV

    Fi

    o

    /1

    )(

    )(

    )(

    )(

    1

    2

  • TheopampdifferentiatorTimedomainanalysis:

    Frequencydomainanalysis:

    Differentiatoroperation:

    Differentiatortimeconstant:RCGain(=RC)becomesinfiniteatveryhighfrequenciesHighfrequencynoiseismagnified(generallyavoidedinpractice)

    NTUEEElectronics L.H.Lu 215

    dttdvCi I )(

    dttdvRCtv IO)(

    )(

    RCjZZ

    jVjV

    i

    o

    1

    2

    )(

    )(

    RCVV

    i

    o f =90

  • 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)

    NTUEEElectronics L.H.Lu 217

  • 2.6DCImperfections*

    OffsetvoltageInputoffsetvoltage(VOS)arisesasaresultoftheunavoidablemismatchesTheoffsetvoltageanditspolarityvaryfromoneopamptoanotherTheanalysiscanbesimplifiedbyusingthecircuitmodelwithanoffsetfree

    opampandavoltagesourceVOS atinputterminalTypicaloffsetvolt