The document discusses the operational amplifier (op-amp) focusing on the effects of negative feedback on input and output impedances for both non-inverting and inverting amplifier configurations. It explains concepts like input bias current, offset voltage, open-loop and closed-loop responses, and emphasizes how negative feedback influences bandwidth and gain. Additionally, it details compensation techniques for bias currents and their impact on the overall performance of op-amps.

1. Engr.Tehseen Ahsan
Lecturer, Electrical Engineering Department
EE-307 Electronic Systems Design
HITEC University Taxila Cantt, Pakistan
The Operational Amplifier (Part 2)

2. 12-5 Effect of Negative FeedBack On OP-AMP Impedances
ImpedancesofaNon-invertingAmplifier
InputImpedance
Theinputimpedanceofanon-invertingamplifiercanbedevelopedwiththeaidoffigure12-23.
ForthisAnalysis,assumeasmalldifferentialvoltage,Vd,existsbetweenthetwoinputterminalsasindicated.Thismeansthatyoucannotassumetheop-amp’sinputimpedancetobeinfiniteortheinputcurrenttobe0.
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3. 12-5 Effect of Negative FeedBack On OP-AMP Impedances Continue…
ImpedancesofaNon-invertingAmplifier
InputImpedancecontinue…
Theinputvoltagecanbeexpressedas3

4. 12-5 Effect of Negative FeedBack On OP-AMP Impedances Continue…
ImpedancesofaNon-invertingAmplifier
InputImpedancecontinue… 4

5. 12-5 Effect of Negative FeedBack On OP-AMP Impedances Continue…
ImpedancesofaNon-invertingAmplifier
OutputImpedance
Anexpressionforoutputimpedanceofanon-invertingamplifiercanbedevelopedwiththeaidoffigure12-24.
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6. 12-5 Effect of Negative FeedBack On OP-AMP Impedances Continue…
ImpedancesofaNon-invertingAmplifier
OutputImpedancecontinue…
ByapplyingKVLtotheoutputcircuitoffig12-24
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7. 12-5 Effect of Negative FeedBack On OP-AMP Impedances Continue…
ImpedancesofaNon-invertingAmplifier
OutputImpedancecontinue…
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10. 12-5 Effect of Negative FeedBack On OP-AMP Impedances Continue…
Voltage-FollowerImpedances
Sinceavoltagefollowerisaspecialcaseofthenon-invertingamplifierconfiguration,thesameimpedanceformulasareusedbutwithB=1.
Noticethatthevoltage-followerinputimpedanceisgreaterforagivenAolandZinthanforthenon-invertingamplifierconfigurationwithvoltage-dividerfeedbackcircuit.Alsotheoutputimpedanceismuchsmaller. 10

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12. 12-5 Effect of Negative FeedBack On OP-AMP Impedances Continue…
ImpedancesofanInvertingAmplifier
InputImpedance
Theinputimpedanceofaninvertingamplifiercanbedevelopedwiththeaidoffigure12-26.
Theinputsignalisappliedthroughaseriesresistor,Ri,toinverting(-) terminal.
TheinputimpedanceofaninvertingamplifierisZin(I)≈Ri12

13. 12-5 Effect of Negative FeedBack On OP-AMP Impedances Continue…
ImpedancesofanInvertingAmplifier
OutputImpedance
Aswithanon-invertingamplifier,theoutputimpedanceofaninvertingamplifierisalsodecreasedbythenegativefeedback,theexpressionisthesameasforthenon-invertingcase.
Theoutputimpedanceofboththenon-invertingandtheinvertingamplifierconfigurationsisverylow;infactitisalmostzeroinpracticalcases. 13

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16. 12-6 Bias Current and Offset Voltage
Thepracticalop-amphassmallinputbiascurrentstypicallyinnArange.Alsosmallinternalimbalancesinthetransistorseffectivelyproduceasmalloffsetvoltagebetweentheinputs.
EffectofanInputBiasCurrent
Figure12-29(a)nextslideisaninvertingamplifierwithzeroinputvoltage.
IdeallythecurrentthroughRiiszerobecausetheinputvoltageiszeroandthevoltageattheinverting(-)terminaliszero.
Thesmallinputbiascurrent,I1isthroughRffromtheoutputterminal.
I1createsavoltagedropacrossRfasindicated.
ThepositivesideofRfistheoutputterminal,thustheoutputerrorvoltageis+I1Rfwhenitshouldbezero16

17. 12-6 Bias Current and Offset Voltage Continue…
EffectofanInputBiasCurrent17

18. 12-6 Bias Current and Offset Voltage Continue…
EffectofanInputBiasCurrent
Figure12-29(b)previousslideisavoltagefollowerwithzeroinputvoltageandasourceresistanceRs.
InputbiascurrentI1,producesadropacrossRsandcreatesanoutputvoltageerrorasshown.
Thevoltageattheinvertingterminaldecreasesto-I1Rsbecausethenegativefeedbacktendstomaintainadifferentialvoltageofzeroasindicated.
Sincetheinvertingterminalisconnecteddirectlytotheoutputterminal,theoutputerrorvoltageis-I1Rs. 18

19. 12-6 Bias Current and Offset Voltage Continue…
EffectofanInputBiasCurrent
Figure12-30isanon-invertingamplifierwithzeroinputvoltage.
Ideallythevoltageattheinvertingterminalisalsozero.
TheinputbiascurrentI1,producesavoltagedropacrossRfandthuscreatesanoutputerrorvoltageofI1Rf19

20. 12-6 Bias Current and Offset Voltage Continue…
BiasCurrentCompensationinaVoltage-Follower
Theoutputerrorvoltageduetobiascurrentinavoltage- followercanbesignificantlyreducedbyaddingaresistorRfequaltothesourceresistorRsinthefeedbackpathasshowninfigure12-31nextslide.
ThevoltagedropcreatedbyI1acrosstheaddedresistorsubtractsfromthe-I2Rsoutputerrorvoltage.
IfI1=I2,thentheoutputvolageiszero
UsuallyI1doesnotequalI2buteveninthiscases,theoutputerrorvoltageisreducedasfollowsbecauseIOSislessthanI220

21. 12-6 Bias Current and Offset Voltage Continue…
BiasCurrentCompensationinaVoltage-Follower
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22. 12-6 Bias Current and Offset Voltage Continue…
BiasCurrentCompensationinOtherOp-AmpConfigurations
Practicalop-amphasverysmallfiniteinputbiascurrentsonbothofitsinputs.
Thesetwobiascurrents(I1andI2)canproduceasmalldcoutputvoltage(VOUT(error))evenwhentheinputvoltageiszero.
TheeasiestwaytominimizethisproblemisbyincludingacompensatingresistorRcinserieswiththenon-invertinginputofanon-invertingamplifierasshowninfigure12-32(a)nextslide.
ThecompensatingresistorRcvalueequalstheparallelcombinationofRiandRf.
RcProvideshighinputimpedancewhichwillsignificantlyreducethemagnitudesofbiascurrents.
Theinvertingamplifierissimilarlycompensatedshownin12-32(b)22

23. 12-6 Bias Current and Offset Voltage Continue…
BiasCurrentCompensationinOtherOp-AmpConfigurations23

24. 12-6 Bias Current and Offset Voltage Continue…
EffectofInputOffsetVoltage
InputOffsetVoltageCompensation
HOMEREADINGASSIGNMENT24

25. 12-7 Open-Loop Response
Inthissection,wewilllearnabouttheopen-loopfrequencyresponseandtheopen-loopphaseresponseofanop-amp.
Open-loopresponsesrelatetoanop-ampwithnoexternalfeedback.
Thefrequencyresponseindicateshowthevoltagegainchangeswithfrequency.
Thephaseresponseindicateshowthephaseshiftbetweentheinputandoutputsignalchangeswithfrequency.
Theopen-loopgain,liketheβofatransistor,variesgreatlyfromonedevicetothenextofthesametypeandcannotbedependentupontohaveaconstantvalue.
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26. 12-7 Open-Loop Response Continue…
VoltageGainisFrequencyDependent
Previously,allofthevoltagegainexpressionswerebasedonthemidrangegainandwereconsideredindependentofthefrequency.
Themidrangeopen-loopgainofanop-ampextendsfromzerofrequencyuptoacriticalfrequencyatwhichthegainis3dBlessthanthemidrangevalue.
Op-Amparedcamplifiers(nocouplingcapacitorsbetweenstages), andthereforenolowercriticalfrequency.
Anopen-loopresponsecurve(BodePlot)foracertainamplifierisshowninfigure12-36nextslide.
Noticethatthecurverollsoff(decrease)at-20dBperdecade(-6dBperoctave).
Themidrangegainis200,000,whichis106dBandthecritical(cutoff)frequencyisapproximately10Hz.
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27. 12-7 Open-Loop Response Continue…
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28. 12-7 Open-Loop Response Continue…
3dBOpen-LoopBandwidth
GenerallytheB.Wequalstheuppercriticalfrequencyminusthelowercriticalfrequency.
BW=fcu-fcl
Sincefclforanop-ampiszero,theB.Wissimplyequaltotheuppercriticalfrequency.
BW=fcu
Fromnowon,wewillrefertofcuassimplyfc;andwewilluseopen- loop(ol)orclosed-loop(cl)subscriptdesignators,forexample,fc(ol). 28

29. 12-7 Open-Loop Response Continue…
Unity-GainBandwidth
Noticeinfigure12-36thatthegainsteadilydecreasestoapointwhereitisequaltounity(1or0dB).Thevalueofthefrequencyatwhichthisunitygainoccursistheunity-gainbandwidthdesignatedfT
fT=AolBW=Aolfcu=Aolfc(ol)
Gain-Versus-FrequencyAnalysis
TheRClag(low-pass)circuitswithinanop-ampareresponsiblefortheroll-offingainasthefrequencyincreases.Frombasicaccircuittheory,theattenuationofanRClagcircuitsuchasinfigure12-37nextslideisexpressedas29

30. 12-7 Open-Loop Response Continue…
Gain-Versus-FrequencyAnalysis
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31. 12-7 Open-Loop Response Continue…
Gain-Versus-FrequencyAnalysis31

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33. 12-7 Open-Loop Response Continue…
PhaseShift
AnRCcircuitcausesapropagationdelayfrominputtooutputthuscreatingaphaseshiftbetweentheinputsignalandoutputsignal.
AnRClagcircuitsuchasfoundinanop-ampstagecausestheoutputsignalvoltagetolagtheinputasshowninfigure12-39.Frombasicaccircuittheory,thephaseshiftθis33

34. 12-7 Open-Loop Response Continue…
PhaseShift34

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37. 12-7 Open-Loop Response Continue…
CompleteFrequencyResponse
Previouslyanop-ampwasassumedtohaveaconstantroll-offof-20dB/decadeaboveitscriticalfrequency.Formostop-ampsitisthecase.
However,thesituationismorecomplexwhenICop-ampmayconsistoftwoormorecascadedamplifierstages.
Thegainofeachstageisfrequencydependentandrollsoffat-20dB/decadeaboveitscriticalfrequency.
Thereforethetotalresponseofanop-ampisacompositeoftheindividualresponsesoftheinternalstages.
Asanexample,athree-stageop-ampisrepresentedinfigure12-41(a)nextslide,thefrequencyresponseofeachstageisshowninfigure12-41(b),sincegainsareaddedsothatthetotalop-ampfrequencyresponseisshowninfigure12-41(c)37

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39. 12-7 Open-Loop Response Continue…
CompletePhaseResponse
Inmultistageamplifier,eachstagecontributestothetotalphaselag.
SinceeachRCcircuitcanproduceuptoa-90˚phaseshift. Thereforeanop-ampwiththreeinternalstagescanhaveamaximumphaselagof-270˚.
Thephaselagofeachstageislessthan-45˚whenthefrequencyisbelowthecriticalfrequency,equalto-45˚atthecriticalfrequencyandgreaterthan-45˚whenthefrequencyisabovecriticalfrequency.
Thephaselagsofthestages(threestages)ofan-ampareaddedtoproduceatotalphaselagasfollows39

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41. 12-8 Closed-Loop Response
Op-Ampsarenormallyusedinaclosed-loopconfigurationwithnegativefeedbackinordertoachieveprecisecontrolofthegainandbandwidth.
Recallthatthemidrangegain(midrangeopen-loopgain)isreducedbynegativefeedback.Foranon-invertingamplifier41

42. 12-8 Closed-Loop Response Continue…
EffectofNegativeFeedbackonBandwidth
Theclosed-loopcriticalfrequencyofanop-ampis
fc(cl)=fc(ol)(1+BAol(mid))
Thisexpressionshowsthattheclosed-loopcriticalfrequencyfc(cl)ishigherthantheopen-loopcriticalfrequencyfc(ol)bythefactor1+BAol(mid).
BWc(cl)=BWc(ol)(1+BAol(mid)) 42

43. 12-8 Closed-Loop Response Continue…
EffectofNegativeFeedbackonBandwidth
Figure12-42nextslidegraphicallyillustratestheconceptofclosed- loopresponse.
Whentheopen-loopgainofanop-ampisreducedbynegativefeedback,thebandwidthisincreased.
Theclosed-loopgainisindependentoftheopen-loopgainuptothepointofintersectionoftwogaincurves.
Thispointoftheintersectionisthecriticalfrequencyfc(cl)fortheclosed-loopresponse.
Noticethattheclosed-loopgainhasthesameroll-offrateastheopen- loopgain,beyondtheclosed-loopcriticalfrequency. 43

44. 12-8 Closed-Loop Response Continue…
EffectofNegativeFeedbackonBandwidth44

45. 12-8 Closed-Loop Response Continue…
Gain-BandwidthProduct
Anincreaseinclosed-loopgaincausesadecreaseinthebandwidthandviceversa.
Thisistrueaslongastheroll-offrateisfixed.
Unity-GainBandwidth
fT=AclBWcl=Aclfcl=Aclfc(cl) 45

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