Three

IEEETRANSACTIONSONSOLID-STATECIRCUITS,VOL.35,NO.2,FEBRUARY2000221

Three-StageLargeCapacitiveLoadAmplifierwith

Damping-Factor-ControlFrequencyCompensation

KaNangLeung,PhilipK.T.Mok,Member,IEEE,Wing-HungKi,Member,IEEE,and

JohnnyK.O.Sin,SeniorMember,IEEE

Abstract—Anoveldamping-factor-controlfrequencycompen-

sation(DFCFC)techniqueisprentedinthispaperwithdetailed

theoreticalanalysis.Thiscompensationtechniqueimprovesfre-

quencyrespon,transientrespon,andpowersupplyrejection

foramplifiers,especiallywhendrivinglargecapacitiveloads.

Moreover,therequiredcompensationcapacitorsaresmalland

canbeeasilyintegratedincommercialCMOSprocess.

AmplifiersusingDFCFCandnestedMillercompensation

(NMC)drivingtwocapacitiveloads,100and1000pF,were

fabricatedusinga0.8-

V=

󰀖V

mCMOSprocesswith

tn

=

0.72Vand

tp

slewrate,3.54-

󰀖󰀖

sttlingtime,and426-Wpowerconsumption

V/s

󰀖

areobtainedwithintegratedcompensationcapacitors.Compared

totheNMCamplifier,thefrequencyandtransientresponsof

theDFCFCamplifierareimprovedbyoneorderofmagnitude

withinsignificantincreaonthepowerconsumption.

IndexTerms—Dampingfactor,frequencycompensation,large

capacitiveload,multistageamplifier.

I.I

NTRODUCTION

W

ITHtherapiddecreainthesupplyvoltageinVLSI,

morecircuitdesignersareawareoftheimportanceof

low-voltagemultistageamplifiers.However,allmultistage

amplifierssufferclo-loopstabilityproblemsduetotheir

multiple-polenature.Therefore,manyfrequencycompensation

topologieshavebeenpropod[1]–[6].

AsmentionedbyEschauzieretal.[1]andHuijsingetal.

[2],multistageamplifierssufferbandwidthreduction,anda

single-stageamplifierisoptimumonbandwidth.Compared

toasingle-stageamplifier,thegain-bandwidthproductsofa

two-stagesimpleMillercompensated(SMC)amplifieranda

three-stagenestedMillercompensated(NMC)amplifierare

reducedtohalfandonequarter,respectively[1],[2].Asaresult,

otheradvancedtopologies,suchasmultipathNMC(MNMC),

hybridNMC(HNMC),multipathHNMC(MHNMC),and

nestedGm-Ccompensation(NGCC),weredevelopedto

overcomethebandwidthreductionproblem[1]–[5].Forthe

topologies,whicharebadonNMC,pole–zerocancellation

andfeed-forwardtechniqueareudtoextendthebandwidth.

However,fromthefindingsshowninFig.1,thebandwidth

improvementsbytheabove-mentionedtopologiesoverNMC

ManuscriptreceivedJuly2,1999;revidSeptember30,1999.This

workwassupportedbytheRGCCompetitiveEarmarkedRearchGrant

HKUST6007/97E,HongKongSARGovernment.

TheauthorsarewiththeDepartmentofElectricalandElectronicEngineering,

TheHongKongUniversityofScienceandTechnology,ClearWaterBay,Hong

Kong,China.

PublisherItemIdentifierS0018-9200(00)00938-0.

arenotsufficient,andtheprovidedbandwidthsarenarrower

thanthebandwidthofasingle-stageamplifier.Inaddition,

tradeoffsbetweenbandwidthandotheramplifiercharacteristics

suchasttlingtimeandpowerconsumptionarerequired.In

particular,higherpowerconsumptionisneededtoincrea

thebandwidthwhentheamplifierisrequiredtodrivealarge

capacitiveloadsuchastheerroramplifierinalinearregulator.

Furthermore,bothsmall-signalandttlingbehaviorshouldbe

improvedatthesametimeinordertoobtainafastamplifier

[7].Nevertheless,theabove-mentionedtopologiesaremainly

concernedwiththeimprovementofthefrequencyrespon.

Anotherissuetobeconsideredistheoptimumnumberof

gainstages.Generally,frequencycompensationtechniquesfor

three-stageamplifiersareadequateforpracticalpurpossince

three-stageamplifiersmaintainagoodcompromibetweenthe

voltagegain

222IEEETRANSACTIONSONSOLID-STATECIRCUITS,VOL.35,NO.2,FEBRUARY2000

Fig.1.Bandwidthcomparisonofdifferentfrequencycompensationtopologies(takeNMCasthereference).

isthedominantpole.Tostabilize

theNMCamplifier,theNMCamplifiershouldhavethird-order

Butterworthfrequencyrespon[9]inunity-feedbackconfigu-

andshouldobeythefollowingdimension

ration,and

conditions[1]–[3]:

(a)

and

(b)

Fig.2.(a)Structureofathree-stageNMCamplifier.(b)Equivalent

small-signalcircuitofthethree-stageNMCamplifier.

pendson

.From(1)and(3),thenondominantpolesde-

andthusdependsontheloadingcapacitance

negativecapacitivefeedbackloopsbyand

,,andand

isrequired,andthenondominantpoleswilllocate

atratherlowfrequencies.Therefore,thebandwidthofanNMC

amplifierispoor.

and

Substitutingthedimensionconditionsof

into(1),thecondandthirdpolewillformacomplexpole

withdampingfactorof

andphamarginare[1]

(4)

(5)

Fromtheaboveresults,thegain-bandwidthproductdecreas

astheloadingcapacitanceincreas.Theonlymethodtoin-

LEUNGetal.:THREE-STAGELARGECAPACITIVELOADAMPLIFIERWITHDFCFC223

creathebandwidthofanNMCamplifieristoenlarge

byincreasingthequiescentcurrentandsizeofthetransistors

oftheoutputgainstage.Moreover,fromthedesignpointof

view,NMCisnotsuitableforlow-powerdesignastheprevi-

,maynotbevalid.

ouslystatedassumption,

Althoughsmallbiascurrentandsmalltransistorsizecanreduce

suchthatissmallerthan,thesamedoesnotapply

.Thisisduetothesmallbiascurrentattheinputstage

to

whichreducestheslewrateoftheamplifier[10]–[15]andthe

smallsizeoftheinputdifferentialpair,whichintroducesalarge

offtvoltage[15].Thus,NMCmaynotbesuitableforampli-

fiersdrivinglargecapacitiveloadsandinlow-powerdesigns.

III.DFCFC

Inthisction,detailedanalysisonthetransferfunction,sta-

bilitycriteria,slewrate,ttlingtime,andpowersupplyrejec-

tionratioofthepropodDFCFCstructurearediscusd.

A.StructureofDFCFC

Fromthediscussioninthepreviousction,thepoorband-

widthofanNMCamplifierismainlyduetotheprenceof

,whichispartofcapacitiveloadtotheamplifier[1],[6].

Byeliminating,thecapacitiveloadattheoutputisreduced.

Thenondominantpoleswillthenrelocateathigherfrequencies,

andthebandwidthoftheNMCamplifiercanbeextended.Nev-

ertheless,thetwonondominantpolesformacomplexpole.The

dampingfactorofthecomplexpoleisverysmall.Moreover,

thereisnocontrolofthedampingfactoras

isabnt.As

showninFig.3,thesmalldampingfactorcausafrequency

‘peak’toappearneartheunity-gainfrequencyoftheamplifier,aresmallerthanthecompensationcapacitances,loadingcapac-

andthisprohibitsstableclo-loopoperation.(isgenerallylargerthanotherparasitic

Inordertoobtainalargerbandwidthandstabilizetheam-capacitancesasitdependsonthesizeofthetransistorofthe

plifieratthesametime,DFCFCisud.Thestructureandthe

equivalentcircuitareshowninFig.4.Therearetwoadditional

buildingblocks:1)thefeed-forwardtransconductancestageisthedom-

(FTS)and2)thedamping-factor-control(DFC)block.Theinantpole.Itshouldbenotedthattheeffectof

functionoftheFTSistoimplementapush–pulloutputstage

toimprovetheslewingperformance.TheDFCblockisudto

controlthedampingfactorofthenondominantcomplexpoleto

maketheamplifierstable.Theresultantopen-loopfrequency

responoftheDFCFCamplifierisshowninFig.3.The

DFCFCbandwidthiswiderthanthatoftheNMCamplifier.

Forthedetailsofthetwoadditionalblocks,theDFCblockis

,output,andthegain-bandwidth

simplyanegativegainstagewithtransconductance

Fig.3.Bodeplotofthefrequencyrespons.

resistance

tosim-

plifytheexpressionandwiththefollowingassumptions.1)The

and

dcgainoftheDFCblockisgreaterthanone;2)

itance,and

outputstage),thetransferfunctionisgivenby(6),shownatthe

bottomofthepage,where

iscan-

celedinthetransferfunction,soitisnotalwaysnecessaryto

.Theabovetransferfunctionholdstrueaslong

t

issmall,shouldbettoequal

as

;otherwi,ttofurtheroptimize

thesizeofthecompensationcapacitors.

From(6),shownatthebottomofthepage,itisobviousthat

thedampingfactorandlocationofthecomplexpolecanbecon-

trolledbyanoptimumvalueof

224IEEETRANSACTIONSONSOLID-STATECIRCUITS,VOL.35,NO.2,FEBRUARY2000

(a)

(b)

Fig.4.(a)StructureofaDFCFCamplifier.(b)Equivalentsmall-signalcircuitoftheDFCFCamplifier.

productiscontrolledby.Moreover,thenondominantpoles

locateathigherfrequenciesasthecond-orderfunctionde-

insteadof,which

pendsontheparasiticcapacitance

isloadingcapacitancedependentinNMCtopology.

C.StabilityCriteria,Gain-BandwidthProduct,andPha

Margin

Fromthepreviousction,itisknownthatthestabilityofthe

and

amplifiercanbecontrolledbyappropriatevaluesof

.Inthisction,thedimensionconditionsarecalculated.

Wemodelthetransferfunctionwithidealfunctionfirstand

thenapplytheresults.Tobegin,assumingthattheeffectof

thezerosisnegligibleandconsideringthatthepolesofthe

DFCFCamplifierinunity-feedbackconfigurationhavethird-

orderButterworthfrequencyrespon[9],thetransferfunc-

tioninunity-gainfeedback

isgivenby

withdamping

factor

,

LEUNGetal.:THREE-STAGELARGECAPACITIVELOADAMPLIFIERWITHDFCFC225

isobtainedbysolvingthecond-orderfunctionin(8)andis

givenby

(11)

Thegain-bandwidthproduct

(12)

andthephamargin

(13)

ByapplyingtheabovemodelingonDFCFC,threeequations

areobtainedbycomparingthecoefficientsofthedenominator

of(8)withthoof(6).

(14)

(15)

isderived.

,thedimensionconditionofinDFCFCisgiven

by

,itcanbeobtainedbyfirstly

substituting(15)into(14)toacquire

(19)

andthensubstituting(18)into(19)toobtain

(20)

Sinceitispreferabletohavethesameoutputcurrentcapability

forboththep-andthen-transistoroftheoutputstage,thesizes

ofthep-andn-transistorareudintheratioof3to1tocompen-

sateforthedifferenceinthemobilitiesofthecarriers.Thus,itis

reasonabletot

,and(18)and(20)arerewritten

as

(21)

(22)

where

anddependonthe

ratiosoftransconductancesandcapacitances,thestabilityofthe

DFCFCamplifierislessnsitivetoglobalvariationsofcircuit

parameters.

From(23),

ratio,andthevalue

uired

isre-

ducedby

andin(21)isadecreasingfunctionwith

issmallandonlyasmallamountofpoweris

dissipatedintheDFCblock.

Asthezerosoftheamplifierdependon(whichissmallas

provenpreviously)and

,theyareathigherfrequenciesthanthe

polesoftheamplifierandtheeffectfromthezeroscanbeneglected.

Therefore,thepreviouslystatedassumptionisvalid,andthepres-

enceofzerosdoesnotinvalidatethestabilitycriteria.

From(12)to(14),thegain-bandwidthproductandpha

marginoftheDFCFCamplifieraregivenby

(24)

(25)

Itcanbeshownfrom(24)thatthebandwidthofaDFCFCam-

plifieris

(i.e.,alargerloadingca-

pacitance).ReferringtoFig.1,thebandwidthoftheDFCFC

amplifiermaybeevenlargerthanasingle-stageamplifierwhen

insomeapplications,asmallercanbeudtode-

creathephamarginandfurtherincreathebandwidthof

theamplifier.

226IEEETRANSACTIONSONSOLID-STATECIRCUITS,VOL.35,NO.2,FEBRUARY2000

D.SlewRate

AftertheanalysisonACbehavior,thetransientbehavioris

studiedinthisctionandthenextction.Assumingthatthe

outputstageisofpush–pullorclass-ABtype,theslewrateis

notlimitedbytheoutputstage.Thus,theslewrateofamulti-

stageamplifierdependsontwofactors.Oneisthevalueofthe

compensationcapacitor

[10]–[15].In

mathematicalexpression,theslewrate

times,theim-

provementontheslewrateusingDFCFCisimprovedby

ratio.

Therefore,theslewrateofaDFCFCamplifierisbetterthanthat

oftheNMCcounterpart,especiallywhendrivingalargecapac-

itiveload.

E.SettlingTime

Settlingbehaviorofanamplifierisveryesntialinanalog

designsinceitdirectlyaffectstheperformanceofthecircuits

usingtheamplifier.Toenhancethettlingbehavior,thefirst

thingtoinvestigateisitsdependence.Neglectingtheshort

durationofthesmall-signalresponbeforeslewing,the

ttlingtime

canbemainlydividedintotwoperiods.

Theyaretheslewingperiod

[10],[11].Thedependenceoftheslewratehasbeen

discusdinthepreviousction,andtheslewrateisproven

tobegreatlyimprovedbyDFCFC.Forthequasi-linearperiod,

itisastrongfunctionofthephamargin[17],anditalso

dependsonhowcompresdpole–zerodoubletisbelowthe

unity-gainfrequencyoftheamplifier[1],[3].

InthecaofusingDFCFC,asthereisnopole–zerodoublet,

thequasi-linearperiodonlydependsonthephamargin.By

usingthestabilitycriteriastatedbefore,thephamarginofthe

DFCFCamplifierisapproximately60

(27)

where

m

CMOSprocesswith

LEUNGetal.:THREE-STAGELARGECAPACITIVELOADAMPLIFIERWITHDFCFC227

(a)

(b)

Fig.6.Circuitdiagramofthe(a)NMCamplifierand(b)DFCFCamplifier.

Fig.7.Micrographoftheamplifiers.

byM101-M108,M201-M204,andM301,respectively.For

theDFCFCcounterparts,theadditionalM302istheFTS,

andM401-M404istheDFCblock.Itshouldbenotedthat

sincethecircuitsaretodemonstratethepropodfrequency

compensationstructure,thecircuitstructuredisplayedinFig.6

isoneofmanymethodstoimplementthepropodstructure.

Additionalcircuitrytocontrolthedcoperatingpointofthe

DFCblockandtoimplementaclass-ABoutputstagewith

feedbackcontrolcanbeaddedtothecircuitstructuretobuilda

higherperformanceamplifier.

Tooptimizethevaluesofthecompensationcapacitorsinthe

DFCFCamplifiers,thevaluesof

are3pFforboth100and

inbothcas

1000pFloadingconditions.Thevaluesof

areobtainedfromthepreviousanalysisandarefine-tunedto

optimizethetradeoffbetweenthebandwidthandphamargin.

AsshowninTableI,sincethevaluesofthecompensationca-

pacitorsaremuchsmallerforDFCFC,thesizesoftheDFCFC

1

AMS.ThemicrographisshowninFig.7.FortheNMC

1

amplifiers,thefirst,condandthirdstagesareimplemented

AustriaMikroSystemeInternationalAG,A-8141Unterpremstatten,Aus-

tria.

228IEEETRANSACTIONSONSOLID-STATECIRCUITS,VOL.35,NO.2,FEBRUARY2000

(a)

(b)

Fig.8.Frequencyresponsofthe(a)NMCand(b)DFCFCamplifierwith

100-pFloadingcapacitance(onlythefrequenciesneartheunity-gainfrequency

areshown).

Fig.9.Transientresponsoftheamplifiersdriving100pF.

amplifiersaresmallandeasytointegrate.Ontheotherhand,the

NMCamplifierdrivinga1000-pFloadrequiresunrealisticlarge

compensationcapacitors

pF),

andthusintegrationisimpossible.

V.E

XPERIMENTALESULTS

R

ThefrequencyresponsmeasuredwiththeHP4194A

impedance/gain-phaanalyzerareshowninFigs.8and10,

whilethetransientresponsmeasuredwiththeLeCroy9354A

oscilloscopeareshowninFigs.9and11.Theperformancesare

tabulatedinTableI.

(a)

(b)

Fig.10.Frequencyresponsofthe(a)NMCand(b)DFCFCamplifier

with1000-pFloadingcapacitance(onlythefrequenciesneartheunity-gain

frequencyareshown).

Fig.11.Transientresponsoftheamplifiersdriving1000pF.

Asshowninthefiguresandtable,bycomparingtheDFCFC

amplifiertotheNMCcounterpart,DFCFCimprovesthegain-

bandwidthproductby4times,theslewrateby6times,thet-

tlingtimeby3times,andthenegativepowersupplyrejection

ratiobyatleast40dBforthecadriving100pF.Foralarger

loadingcapacitanceof1000pF,theimprovementismoresignif-

icant.Thegain-bandwidthproductisimprovedby18times.The

slewrateandttlingtimeareimprovedby14and9times,re-

spectively.Inaddition,thenegativepowersupplyrejectionratio

isenhancedbyatleast60dB.However,thereisonlynegligible

increaonthepowerconsumption.

LEUNGetal.:THREE-STAGELARGECAPACITIVELOADAMPLIFIERWITHDFCFC229

TABLEI

MRNMCDFCFCA

EASUREDESULTSOFTHEANDMPLIFIERS

TABLEII

CDMA

OMPARISONOFIFFERENTULTISTAGEMPLIFIERS

SincethebandwidthimprovementbyDFCFCwitha1000-pF

loadis18times,whichismuchgreaterthan4,thebandwidth

providedbytheamplifierisevenwiderthanasingle-stageam-

plifierundernearlythesamepowerconsumption.

ToprovideaclearerpictureontheimprovementsbyDFCFC,

acomparisontableforsomepublishedamplifiersusingdifferent

compensationtopologiesisshowninTableII.Twofiguresof

,aredefinedforsmall-signaland

merit,

large-signalperformances.

(28)

andpF/mWandV/

230IEEETRANSACTIONSONSOLID-STATECIRCUITS,VOL.35,NO.2,FEBRUARY2000

A

CKNOWLEDGMENT

TheauthorswouldliketothankProf.W.T.NgfromtheUni-

versityofToronto,Toronto,ON,Canada,forhisvaluablesug-

gestions,andtheyalsowouldliketothankS.F.LukandJ.Chan

fromHKUSTfortheirtechnicalassistance.

R

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