模擬集成電路中的頻率補償

本文格式為Word版，下載可任意編輯——模擬集成電路中的頻率補償

Feature

Two-Stage

OperationalAmplifiers:

Power-and-Area-EfficientFrequencyCompensationforDrivingaWideRangeofCapacitiveLoad

DIGITALVISION

DigitalObjectIdentifier10.1109/MCAS.2023.939783Dateofpublication:18February2023

26IEEECIRCUITSANDSYSTEMSMAGAZINE

1531-636X/11/$26.002023IEEEFIRSTQUARTER2023

B5a2114a0a12a1

CM2

ItcanbeobservedthatBCMisnotaffectedbythetypeofpoles,nomattertheyaretworealpolesoracom-plexpair(thedampingfactormustbenolessthan1/2accordingto(4)).Providingthattheeffectivecapaci-tanceisagivenconstraint,theBCMcanbeextendedbyincreasingthevalueofa0(i.e.reducingthevalueofCbwhileincreasingRbtofullyutilizethecharacteristicofsmallparasiticCpb).Forexample,ifa1$2a0isthere-quirementforastablelocalloop,BCMis$0.732a0(i.e.0.732(gmb1/Cb)).Intermsofthepowerbudget,thebiascurrentcanbeaccuratelymeasuredbythetransconductanceofalltransistors[17].ThetotaltransconductanceofeachCMis2gmb1.Thecurrent-mirrorCM’sbandwidthBCM21isgivenby,B2gmb1CM215M11CbFIRSTQUARTER2023

From(11),itwouldbepossibletodemonstratethat

thefrequencyperformanceoftheproposedCMissu-perior,whencomparedwiththecurrent-mirrorCM

becauseMmustbesettobegreaterthanonetoper-formcapacitanceamplification.AsforothercomplexCMs,duetotheexistenceofparasiticlow-frequencypoles,theirbandwidthisevensmallerthanthatofacurrent-mirrorCM.Toprovetheforgoingassertions,differentdesignsaimingtoobtain9-pFeffectivecapacitancewith10-mAquiescentcurrentdissipationarecarriedout.Figure9(a)and(b)showsthefrequencycharacterizationoftheproposedCMswithdifferentvaluesofRbandCb.AsshowninFig.9(b),BCMoftheproposedCM’sincreaseswithalargerRbthatcorrespondstoasmallerCb.How-ever,themagnitudepeakingalsogrowsfastasshowninFig.9(a);theupperboundaryofBCMislimitedbythestabilityimposedbythelocalresistivefeedback.Figure10(a)and(b)showsthemagnitudeandphase

responsesofdifferentCMs,respectively.Noticethatthe

phaseresponsesofthebasiccurrentmirrorandcurrent-mirrorCMareintentionallyinvertedfromdrop,beginning

IEEECIRCUITSANDSYSTEMSMAGAZINE

33

small-signalequivalentmodeloftheOpAmp.gm1andgm2representthetransconductanceofM1andM2,respec-transconductanceofM7andM8tively,withgm15gm2.Thetransconductance,isgmb.gmListhesumofM9andM10’s

whichincludestheaceffectoftheclass-ABstage.The

outputconductanceofeachstageisdenotedbygob,go1,andgoL,respectively.Cpb,Cp1,andCp2thatlumpedintotheloadcapacitorCL,representtheparasiticcapacitancesatthecorrespondingstages.AsmallCbamplifiedbythepro-posedCMhaslargeeffectivecapacitanceandcausesthetwopolesassociatedwiththeinputandoutputnodesof

thesecondstagetosplitapart,leadingtowidelyspaced

dominantandnon-dominantpoles.ThepurposeofCdistoadjustthepositionofthefirstnon-dominantpoleand

handleawiderangeofloadcapacitance.Anarea-efficientMOSCAPbefitsCdforareareduction.

A.LocalFeedbackLoop

AnalysisoftheProposedOpAmp

WhentheproposedCMisincorporatedintothetwo-stageOpAmp,itintroducesalocalfeedbacklooparoundthesecondstage.ToanalyzethestabilityoftheOpAmpundervaryingcapacitiveload,thelocalloopisbrokenatthenodeVbasshowninFig.11(b).InadditiontotheassumptionsmadeforanalyzingtheproposedCM,thelocaltransferfunctionTL1s2iscalculatedwiththefol-lowingassumptions:

1)Thegainofallthestagesaremuchgreaterthan1;2)TheparasiticcapacitanceCpb,Cp1,andCp2aremuchsmallerthanCb,whileCLismuchlargerthanCb.Hence,TL1s2isgivenby,TL1s2

2

sgmL1gmbRb212Cb

.

ggss

CbCbRbCpbo1oLa11pdba11p1ba11sg1s2b

mbgmb

(12)ThemagnitudeplotofTL1s2isshowninFig.12within-creasinglylargeCL.Thedominantpoleofthelocalloopisvpd5goL/CL

whilethefirstnon-dominantpoleisvp15go1/1Cp11Cd2.vistheUGFofthelocalloopandothertwohigh-frequencypolesareproducedbytheCM,whicharegmb/Cb,and1/1RbCpb2,respectively.Ofcourse,theymightexhibittheformoftwocomplexpoles.

AsdescribedinFig.12,whenCLissmall,vmmightbelocatedcloseto,gmb/Cband1/1RbCpb2.WithmuchsmallerCL,thePMofthelocalloopworsenstocauseasignificantpeakingintheoveralltransferfunctionoftheOpAmp[27].Therefore,theOpAmphasalowerlimitfordrivingcapacitiveloads.Toevaluatethelimit,thePM

FIRSTQUARTER2023

ofthelocalloopisassumedtobelargerthan45,and

expressedasvm

PMblocal902arctan

gmb/C.(13)

12

v2$45mgbCpb

mb/Cb

From(4),gmb/Cbissettobeequalto1/1RbCpb2tomake

fulluseoftheproposedCM.Solving(13)withthiscondi-tion,impliesthattheminimumCLthatensuresastablelocalloopis

C15112gmL1gmbRb212C2b

L5

2gmb1Cp11Cd2

IfCdisnotadded,theminimumCLisstillverylarge.

SotheOpAmpisunabletohandlesmallcapacitiveloadwithoutCd.

Sincevm,gmb/Cb,and1/1RbCpb2determinethehigh-frequencypolesoftheOpAmp’soveralltransferfunc-tion,alargervmsuggestsalargerPM.AsCLincreases,vmisreduced,asshowninFig.12.Althoughthelocalloop’sPMimproves,theOpAmp’sPMdegrades.Thistrendcontinuesuntilthemid-bandlocalloopgainbe-comeslessthantheunity,whichisgivenby

gmL1gmbRb212Cb

g,1.(15)

o1CL

Underthiscondition,thelocalloopfailstocontrolthehigh-frequencybehavioroftheOpAmp.Therefore,thetransferfunctionoftheOpAmpisobtainedbymere-lyconsideringtheopenloopgivenbelow:

g1gmbRb112Cb

m1gmLa11s

A2gmb

v1s2

gC

p1d

o1goLa11s

gba11sCL

o1

gb

oL

IEEECIRCUITSANDSYSTEMSMAGAZINE

35

before,thereisanLHPzerovz1inthetransferfunction.avoidingtheconductionofparasiticdiodeinMR,orToguaranteethestabilityoftheoverallloop,vz1mustdiode-connectedMRitself.belocatedabovetheGBW,thuscontributingtothe

OpAmp’sPM,whichistranslatedtothefollowingcondition,D.NoiseAnalysis

KnowingtheinternalnoisetransferfunctionsoftheOpAmpeasesthedevicesizing.Thesimplifiedsche-gm121gmbRb212

,2.(20)

maticoftheproposedOpAmpanditssmall-signalgmbgmbRbequivalentcircuitforthenoiseanalysisareshowninFig.13(a)and(b),respectively.Yoirepresentsthelumpedadmittanceatthecorrespondingnode.C.DesignConsiderations

ThenoisegeneratedbythetailcurrentsourceMb6is

fortheClass-ABOutputStage

Aclass-ABoutputstage[45]isemployedtoenhancethetransientperformanceoftheOpAmp.TheroleofCbatistwofold.First,itcanbeexploitedtoincrease

thegainoftheOpAmpbecauseitisbymeansofCbat

thatthetransconductanceofM10,gm10,takeseffect.In

ordertoincreasethelow-frequencygain,alargerCbat

isdesired.Second,alargerCbatiscriticaltoensurean

accuratevoltagetransferfromthegateofM9tothatof

M10.Hence,Cbatlargerthan10Cgs10isselected.

ThesaturationvoltageVdsatofM9hastobethe

sameasthatofM10sothatM9andM10haveequalcur-rentboostcapabilityduringtransients.Besides,a

relativelylowVdsatcanreducethedrasticchangeof

voltageattheoutputofthefirststage,decreasingor

FIRSTQUARTER2023IEEECIRCUITSANDSYSTEMSMAGAZINE

37

egligibleatthefrequenciesofinterest.Alsothenoisen

contributionofcascodetransistorsM5andM6islesssignificant.Hence,theanalysismainlyfocusesonthenoisecontributionofRb,M7,M8,andM9asthenoiseoftransistorsM1,M2,M3,andM4canbeeasilyreferredtotheinputstage,usinganequivalentinput-referredvoltagenoisesource.Theinput-referrednoisetransferfunctionsofthenoisesources:Rb,M7,M8andM9,arerespectivelygivenby,

11s11s

Cbgm7gm7

22

An,M81s225gm8gm1

#

a11s

2Cb

1211sRCbpb

gm7

#Av1s22(23)

gm7Rb11Cb

11s

gm7

2Cb

111sRbCpb2

go81sCp8gm7

#An,M91s2025#Av1s202

gm1gm7Rb11Cb

11s

gm7

(24)

a11s

An,Rb1s2025gm8gm1

#

1gm7Rb112Cb

#Av1s22(21)

An,M71s225gm8gm1

11sRbCb

##Av1s22(22)

gm7Rb11Cb

11s

gm7

whereAv(s)isthetransferfunctionoftheproposedam-plifier.Fromeqs.(21)–(24),itcanbeobservedthatthenoiseduetoRb,M7andM8generatesthemajorportionofthethermalnoisewithintheGBWoftheamplifier,whilethenoisecontributionofM9issuppressedbythegainofthefirststage.

38IEEECIRCUITSANDSYSTEMSMAGAZINE

FIRSTQUARTER2023

[2]T.Itakura,H.Minamizaki,T.Saito,andT.Kuroda“A402-outputTFT-LCDdriverICwithpowercontrolbasedonthenumberofcolorsse-lected,〞IEEEJ.Solid-StateCircuits,vol.38,no.3,pp.503–510,Mar.2023.[3]V.Dhanasekaran,J.Silva-Martnez,andE.Schez-Sinencio,“Designofthree-stageclass-AB16Vheadphonedrivercapableofhandlingwiderangeofloadcapacitance,〞IEEEJ.Solid-StateCircuits,vol.44,no.6,pp.1734–1744,June2023.

[4]K.N.LeungandP.K.T.Mok,“Analysisofmultistageamplier-fre-quencycompensation,〞IEEETrans.CircuitsSyst.I,vol.48,no.9,pp.1041–1056,Sept.2023.

[5]Y.P.TsividisandP.R.Gray,“AnintegratedNMOSoperationalampli-erwithinternalcompensation,〞IEEEJ.Solid-StateCircuits,vol.13,no.6,pp.748–753,Dec.1976.

[6]D.Senderowicz,D.A.Hodges,andP.R.Gray,“High-performanceresponseimprovement,〞IEEETrans.CircuitsSyst.II,vol.55,no.9,pp.853–857,Sept.2023.

[24]K.H.Chen,C.J.Chang,andT.H.Liu,“Bidirectionalcurrent-modecapacitormultipliersforon-chipcompensation,〞IEEETrans.PowerElectron.,vol.23,no.1,pp.180–188,Jan.2023.

[25]Z.Yan,“Two-stagelargecapacitiveloadamplierwithembeddedcapacitormultipliercompensation,〞inProc.IEEEISCAS’09,May2023,pp.2481–2484.

[26]L.J.Stotts,“IntroductiontoimplantablebiomedicalICdesign,〞IEEECircuitsDevicesMag.,vol.5,no.1,pp.12–18,Jan.1989.

[27]P.R.Gray,P.J.Hurst,S.H.Lewis,andR.G.Meyer,AnalysisandDe-signofAnalogIntegratedCircuits,4thed.NewYork:Wiley,2023.

[28]Y.Tang,M.Ismail,andS.Bibyk,“AdaptiveMillercapacitormul-tiplierforcompacton-chipPLLlter,〞IEEElectron.Lett.,vol.39,pp.NMOSoperationalamplier,〞IEEEJ.Solid-StateCircuits,vol.15,no.6,pp.760–766,Dec.1978.

[7]W.C.Black,Jr.,D.J.Allstot,andR.A.Reed,“AhighperformancelowpowerCMOSchannellter,〞IEEEJ.Solid-StateCircuits,vol.15,no.6,pp.929–938,Dec.1980.

[8]F.You,H.K.Embabi,andE.Schez-Sinencio,“MultistageampliertopologieswithnestedGm-Ccompensation,〞IEEEJ.Solid-StateCircuits,vol.17,no.6,pp.2000–2023,Dec.1997.

[9]R.D.JollyandR.H.McCharles,“Alow-noiseamplierforswitched-capacitorlters,〞IEEEJ.Solid-StateCircuits,vol.32,no.6,pp.1192–1194,Dec.1982.

[10]K.Ahuja,“AimprovedfrequencycompensationtechniqueforCMOSoperationalampliers,〞IEEEJ.Solid-StateCircuits,vol.18,no.6,pp.629–633,Dec.1983.

[11]B.RibnerandM.A.Copeland,“DesigntechniquesforcascodedCMOSopampswithimprovedPSRRandcommon-modeinputrange,〞IEEEJ.Solid-StateCircuits,vol.19,no.6,pp.919–925,Dec.1984.

[12]G.PalmisanoandG.Palumbo,“Acompensationstrategyfortwo-stageCMOSopampsbasedoncurrentbuffer,〞IEEETrans.CircuitsSyst.I,vol.44,no.3,pp.257–262,Mar.1997.

[13]J.Mathattanakull,“Designproceduresfortwo-stageCMOSopera-tionalampliersemployingcurrentbuffer,〞IEEETrans.CircuitsSyst.II,vol.52,no.11,pp.766–770,Nov.2023.

[14]P.J.Hurst,S.H.Lewis,J.P.Keane,F.Aram,andK.C.Dyer,“MillercompensationusingcurrentbuffersinfullydifferentialCMOStwo-stageoperationalampliers,〞IEEETrans.CircuitsSyst.I,vol.51,no.2,pp.275–285,Feb.2023.

[15]W.Aloisi,G.Palumbo,andS.Pennisi,“DesignmethodologyofMill-erfrequencycompensationwithcurrentbuffer/ampliers,〞IETProc.Circuits,DevicesSyst.,vol.2,no.2,pp.227–233,Apr.2023.

[16]V.SaxenaandR.J.Baker,“CompensationofCMOSop-ampsusingsplit-lengthtransistors,〞inProc.IEEEMWSCAS2023,Aug.2023,pp.109–112.

[17]A.D.Grasso,G.Palumbo,andS.Pennisi,“Comparisonofthefre-quencycompensationtechniquesforCMOStwo-stageMillerOTAs,〞IEEETrans.CircuitsSyst.II,vol.55,no.11,pp.1099–1103,Nov.2023.[18]U.Dasgupta,“Issuesin“Ahuja〞frequencycompensationtech-nique,〞inProc.2023IEEEInt.Symp.Radio-FrequencyIntegrationTech-nology,2023,pp.326–329.

[19]R.J.ReayandG.T.A.Kovacs,“Anunconditionallystabletwo-stageCMOSamplier,〞IEEEJ.Solid-StateCircuits,vol.30,no.5,pp.591–594,May1995.

[20]G.A.Rincon-Mora,“ActivecapacitormultiplierinMiller-compensat-edcircuits,〞IEEEJ.Solid-StateCircuits,vol.35,no.1,pp.26–32,Jan.2000.[21]R.Suryanarayan,A.Gupta,andT.N.Blalock,“Aslewrateenhance-menttechniqueforoperationalampliersbasedonatunableactiveGm-basedcapacitancemultiplicationcircuit,〞inProc.13thACMGreatLakesSymp.VLSI,Apr.2023,pp.273–276.

[22]Q.Bian,Z.Yan,Y.Zhao,andS.Yue,“AnalysisanddesignofvoltagecontrolledcurrentsourceforLDOfrequencycompensation,〞inProc.IEEEInt.Conf.ElectronDevicesandSolid-StateCircuits,Dec.2023,pp.363–366.

[23]H.C.Lin,H.H.Wu,andT.Y.Chang,“Anactive-frequencycom-pensationschemeforCMOSlow-dropoutregulatorswithtransient-

4

2IEEECIRCUITSANDSYSTEMSMAGAZINE43–45,Jan.2023.

[29]H.LeeandP.K.T.Mok,“AnSCvoltagedoublerwithpseudo-contin-uousoutputregulationusingathree-stageswitchableopamp,〞IEEEJ.Solid-StateCircuits,vol.42,no.6,pp.1216–1229,June2023.

[30]F.Su,W.-H.Ki,andC.-T.Tsui,“Regulatedswitched-capacitordou-blerwithinterleavingcontrolforcontinuousoutputregulation,〞IEEEJ.Solid-StateCircuits,vol.44,no.4,pp.1112–1120,Apr.2023.

[31]S.Solis-Bustos,J.Silva-Martinez,F.Maloberti,andE.Snchez-Si-nencio,“A60-dBdynamicrangeCMOSsix-order2.4-Hzlow-passlterformedicalapplications,〞IEEETrans.CircuitsSyst.II,vol.47,no.12,pp.1391–1398,Dec.2000.

[32]K.Shu,E.Snchez-Sinencio,J.Silva-Martnez,andH.K.Embabi,“A2.4-GHzmonolithicfractional-Nfrequencysynthesizerwithrobustphase-switchingprescalerandloopcapacitancemultiplier,〞IEEEJ.Solid-StateCircuits,vol.38,no.6,pp.866–874,June2023.

[33]K.ChavaandJ.Silva-Martnez,“AfrequencycompensationschemeforLDOvoltageregulators,〞IEEETrans.CircuitsSyst.I,vol.51,no.6,pp.1041–1050,June2023.

[34]S.-R.Han,C.-N.Chuang,andS.-I.Liu,“Atime-constantcalibratedphase-lockedloopwithafast-lockedtime,〞IEEETrans.CircuitsSyst.II,vol.54,no.1,pp.34–37,Jan.2023.

[35]Y.-T.Wongetal.,“Near-thresholdstartupintegratedboostcon-verterwithslewrateenhancederroramplier,〞inProc.IEEEISCAS’09,May2023,pp.2409–2412.

[36]S.Pennis,“CMOSmultiplierforgroundedcapacitors,〞IETElectron.Lett.,vol.38,pp.765–766,J