拉扎維《模擬集成電路設計》第二版Ch14課件

Chapter14:NonlinearityandMismatch14.1Nonlinearity14.2Mismatch2Nonlinearity:GeneralConsiderationsNonlinearcharacteristicdeviatesfromastraightlineastheinputswingincreasesE.g.,Common-sourcestageordifferentialpair3Nonlinearity:GeneralConsiderationsNonlinearinput/outputcharacteristiccanbeapproximatedbyapolynomialintherangeofinterestForsmallx,y(t)

α1x,indicatingthatα1isthesmall-signalgaininthevicinityofx04Nonlinearity:GeneralConsiderationsNonlinearitycanbequantifiedbyspecifyingmaximumdeviationofcharacteristicfromanidealoneForvoltagerangeofinterest[0,Vin,max],passstraightlinethroughendpointsofactualcharacteristicandobtainmaximumdeviationVNormalizetomaximumoutputswingVout,max1%nonlinearityforaninputrangeof1Vmeans5Nonlinearity:GeneralConsiderationsNonlinearitycanalsobecharacterizedbyapplyingasinusoidatinputandmeasuringharmoniccontentofoutputIfthenMagnitudeofnthharmonicgrowsroughlyinproportiontonthpowerofinputamplitudeQuantifiedbysummingthepowerofallharmonicsexceptfundamentalandnormalizingtopoweroffundamental,metriccalledas“totalharmonicdistortion”(THD)Forathird-ordernonlinearity,6NonlinearityofDifferentialCircuitsDifferentialcircuitsexhibit“odd-symmetric”characteristicEven-ordertermsα2jinpolynomialmustbezero:DifferentialcircuitdrivenbyadifferentialsignalproducesnoevenharmonicsConsidertwoamplifiersprovidingequalsmall-signalvoltagegainof 7NonlinearityofDifferentialCircuitsIfaninputVmcosωtisappliedtoeachcircuit,forcommon-sourcestage,AmplitudeofsecondharmonicnormalizedtofundamentalisForthedifferentialpair,itcanbeshownthatIf,thenDifferentialpairexhibitsmuchlessdistortionforsamegainandoutputswing,atthecostofhigherpower

8EffectofNegativeFeedbackonNonlinearityExpectedthatnegativefeedbackwouldyieldhigherlinearityforaclosed-loopsystemConsidera“mildlynonlinear”systembelowAssumecoreamplifierhasaninput/outputcharacteristicApplyasinusoidalinputpostulatingthatoutputcontainsafundamentalandsecondharmonicapproximatedasThroughsimpleanalysis,wecanget

9EffectofNegativeFeedbackonNonlinearitySmallnonlinearitymeansα2andbaresmallquantities,sothatandhencebcanbefoundasNormalizeamplitudeofsecondharmonictothatoffundamentalWithoutfeedback,thisratiowouldbeNegativefeedbackreducesrelativesecondharmonicbyafactorofandgainby

10EffectofNegativeFeedbackonNonlinearityFeedforwardamplifierinafeedbacksystemsuffersfromgainerrorForafeedforwardgainA0andfeedbackfactorβ,relativegainerrorisapproximately1/(βA0)PossibletoderivearelationshipbetweengainerrorandmaximumnonlinearityofoverallfeedbackcircuitInabovefig.,nonlinearityisalwayslessthangainerrorChoosehighopen-loopamplifiergainsothattoguarantee

11CapacitorNonlinearityForalinearcapacitor,whileforavoltage-dependentcapacitorTotalchargeonacapacitorsustainingavoltageV1isChargedependson“history”ofvoltageratherthaninstantaneousvalueExpresseachcapacitorasConsidernoninvertingamplifierbelowAtthestartofamplificationmode,C1hasavoltageofVin0andC2avoltageofzero

12CapacitorNonlinearityAssumingwhereMisthenominalclosed-loopgain,chargeacrossC1isSimilarly,if,chargeacrossitattheendofamplificationmodeisEquatingQ1andQ2andsolvingforVout,Forandforsmallα1,Secondtermrepresentsnonlinearityresultingfromcapacitorvoltage-dependence

13NonlinearityinSamplingCircuitsOn-resistanceofMOSswitchesvarieswithinputandoutputlevelsNMOSswitchinFig.(a)exhibitsrisingresistanceasVinandVoutincreaseComplementarytopologyofFig.(b)displaysvaryingequivalentresistanceasVinandVoutgofrom0toVDDRonreachesapeakhereduetodependenceofmobilityontheverticalfieldinthechannel

14NonlinearityinSamplingCircuitsWeapplyalargesinusoidtotheinput,whereV0=VDD/2andseekharmonicsattheoutputFirstassumeresistanceislinearandwriteoutputasInpractice,bandwidthmustbelargeenoughtonegligiblyattenuatethesignal,i.e.,sothatAssumethisexpressionholdsforthenonlinearcircuitifRonisrepresentedproperlyPhaseshiftfrominputtooutputvariesasVinandVoutvary,creatingdistortion

15NonlinearityinSamplingCircuitsForaperiodicinput,RonalsovariesperiodicallyandcanbeapproximatedbyaFourierseriesForaroughlysymmetricbehaviorofRon,thetime-domainbehaviorbelowisobservedwhereRonvariesattwicetheinputfrequencyThus,

16NonlinearityinSamplingCircuitsForcosinetermswithargumentsmuchlessthan1rad,Ifonlyfirsttwoharmonicsareretained,thenInadifferentialsamplingswitch,even-orderharmonicsaresuppressed

17LinearizationTechniquesPrinciplebehindlinearizationistoreducedependenceofcircuit’sgainoninputlevelMakegainrelativelyindependentofbiascurrentsSimplestmethodisbymeansofalinearresistorOveralltransconductanceofdegeneratedCSstageisForlargegmRS,thisapproaches1/RS,aninput-independentvalue

18LinearizationTechniquesDifferentialpaircanbedegeneratedasshowninFigs.(a)and(b)InFig.(a),degenerationresistorsconsumeheadroomofISSRS/2CircuitofFig.(b)doesnothavethisissuebutsuffersfromhighernoiseandoffsetvoltage

19LinearizationTechniquesDegenerationresistorcanbereplacedbyaMOSFEToperatingindeeptrioderegion[Fig.(a)]Forlargeinputswings,M3maynotremainindeeptriodeVbmusttrackVin,CMsothatRonisdefinedaccuratelyFig.(b)showsmoreapracticalsolutionwhereM3andM4areindeeptriodeforVin=0AsVG1>VG2,M3staysintriodesinceVD3=VG3–VGS1

M4eventuallyenterssaturationsinceVD4riseswhereasVG4,VS4fall

(a)(b)20LinearizationTechniquesMOSFEToperatingintrioderegioncanprovidealinearID/VDScharacteristicifVDSisheldconstantThistechniqueemploysamplifiersA1andA2withcascodedevicesM3andM4toforceVXandVYtobeequaltoVbforvaryinginputlevelsgm1=gm2=issmallsinceVDSmustbelowtoensureM1,M2remainintrioderegionVin,CMmustbetightlycontrolledtotrackVbtodefineID1andID2

21LinearizationTechniquesAnotherapproachtolinearization:“post-correction”Viewtheamplifierasacascadeofvoltage-to-current(V/I)converterandacurrent-to-voltage(I/V)converterIftheV/IconvertercanbedescribedasandtheI/Vconverteras,thenVoutisalinearfunctionofVin,fore.g.Figs.(a),(b),(c)

22LinearizationTechniquesPossibletolinearizedifferentialpairfurtherbyaddinglocalfeedbackSenseoutputvoltagebymeansofM3andM4andreturnaproportionalcurrenttothesourcesofM1andM2AssumecircuitissymmetricandI1=…=I4IgnoringCLMandbody-effect,ID1=I3andID2=I4regardlessoftheinputsignal

23LinearizationTechniquesInputtransistorsmaintainaconstantVGSasVin=Vin1–Vin2variesCurrentthroughRS(Isig)mustbeprovidedonlybyM3andM4,wehaveOutputvoltageofthistopologycanbefoundtobeLargenumberofdevicesinsignalpathproducesignificantnoiseDependenceofrOuponVDSinshort-channeldevicesintroducessomenonlinearity

24MismatchNominally-identicaldevicessufferfromfinitemismatchduetouncertaintiesinmanufacturingprocessGatedimensionsofMOSFETssufferfromrandom,microscopicvariationsandintroducemismatchesbetweentwotransistorsidenticallylaidoutMOSdevicesexhibitVTHmismatchessinceVTHisafunctionofdopinglevelsinthechannelandgatewhichvaryrandomly

25MismatchStudyofmismatchconsistsoftwosteps:IdentifyandformulatethemechanismsleadingtomismatchbetweendevicesAnalyzetheeffectofdevicemismatchesupontheperformanceofcircuitsForaMOSFETinsaturation,Mismatchesbetweenμ,Cox,W,L,andVTHresultinmismatchesbetweenID’s(foragivenVGS)orVGS’s(foragivenID)oftwonominally-identicaltransistorsIntuitively,asWandLincrease,theirrelativemismatchesW/WandL/L,i.e.,largerdevicesexhibitsmallermismatches

26MismatchAllmismatchesdecreaseasthearea,WLincreasesAsWLincreases,randomvariationsexperiencegreater“averaging”,fallinginmagnitudeFortheabovecase,L2<L1becauseifthedeviceisviewedasmanysmallerparalleltransistors,eachwithwidthW0,equivalentlengthisOverallvariationisgivenbyL0

isthestatisticalvariationoflengthofatransistorwithwidthW0

27MismatchμCoxandVTHsufferfromlessmismatchifdeviceareaincreasesAlargetransistorcanbedecomposedintoaseriesandparallelcombinationofsmallunittransistorswithdimensionsW0andL0,eachexhibiting(μCox)jandVTHjTheseexperiencegreateraveragingasnumberofunittransistorsincreasesAVTHandAKareproportionalityfactors

28EffectofMismatchMismatchesleadtothreedistinctphenomena:DCoffsetsFiniteeven-orderdistortionLowercommon-moderejectionDCOffsets:IndifferentialpairofFig.(a),withVin=0andperfectsymmetry,Vout=0butwithmismatchesVout

0Circuitsuffersfroma“dcoffset”equaltotheobservedvalueofVoutwhenVinissettozero

29EffectofMismatchMoremeaningfultospecifyinput-referredoffsetvoltage,definedastheinputlevelthatforcestheoutputtogotozeroNotethatIfadifferentialpairistoamplifyasmallinputvoltage,outputcontainsamplifiedreplicasofboththesignalandtheoffsetInacascadeofdirect-coupledamplifiers,thedcoffsetmayexperiencesomuchgainthatitdrivesthelatterstageintononlinearoperation

30EffectofMismatchDCoffsetalsoaffectstheprecisionwithwhichsignalscanbemeasuredIfanamplifieristodeterminewhethertheinputsignalisgreaterorlessthanareference,VREF,thentheinput-referredoffsetimposesalowerboundontheminimumVin–VREFthatcandetectedreliablyInput-referredoffsetvoltageofadifferentialpaircanbefoundasMoreaccurately,

31EffectofMismatchEven-OrderDistortion:Mismatchesintroducefiniteeven-ordernonlinearityindifferentialcircuitsIfthetwosignalpathsinadifferentialcircuitarerepresentedbyandllllllthedifferentialoutputisgivenbyFor,thisreducesto

32EffectofMismatchIf,thesecondharmonichasanamplitudeof,i.e.,proportionaltothemismatchbetweensecond-ordercoefficientsoftheinput/outputcharacteristicAthighfrequencies,signalsexperienceconsiderablephaseshift,even-orderdistortionmayarisefromphasemismatchIncircuitsdissipatingahighpower,thermalgradientsacrossthechipmaycreateasymmetries

33OffsetCancellationTechniquesDifferentialamplifierwithaninput-referredoffsetisfollowedbytwoseriescapacitors[Fig.(a)]AsshowninFig.(b),inputsareshortedtogether,drivingamplifieroutputtoVout=AvVOSAssumeVXandVYareshortedduringthisperiodaswellAvVOSisstoredacrossC1andC2,zerodifferentialinputresultsinzerodifferentialoutputAfterS1andS2turnoff,thereiszerooffsetvoltageProperCMvoltageneededatinputandoutput

34OffsetCancellationTechniquesThistechnique“measures”theoffsetbysettingthedifferentialinputtozeroandstorestheresultoncapacitorsinserieswiththeoutputRequiresadedicatedoffset-cancellationperiodduringwhichactualinputisdisabledCalled“outputoffsetstorage”,thistechniquereducesoverallmismatchifS3-S4donothavechargeinjectionmismatchLargeAvmaysaturateoutput,henceAvofroughly10isused

35OffsetCancellationTechniquesInapplicationrequiringhighvoltagegain,topologyofFig.(a)maybeusedCalled“inputoffsetstorage”,thisincorporatestwoseriescapacitorsattheinputandplacesamplifierinunity-gainfeedbackloopduringoffsetcancellationFromFig.(b),VOS,inequalVOS/Av

ifS3andS4matchperfectly

36OffsetCancellationTechniquesOffsetcancellationcanisolatesignalpathfromoffsetstoragecapacitorsbyuseof“auxiliary”amplifierConsiderabovecircuit,whereAauxamplifiesthedifferentialvoltageV1storedacrossC1andC2andsubtractstheresultfromtheoutputofA1If,thenforVin=0,Vout=0andcircuitisfreefromoffsetsC1andC2donotappearinthesignalpath

37OffsetCancellationTechniquesV1isgeneratedbyaddingasecondstage,A2andtheoutputissensedbyAauxduringoffsetcancellatio