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Settling State Optimization for Folded-Cascode OTA with a Novel Compensation Strategy

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Settling State Optimization for Folded-Cascode OTA with a Novel Compensation Strategy

    Settling State Optimization for

    Folded-Cascode OTA with a Novel

    Compensation Strategy ChineseJournalofElectronics

    Vo1.16,No.1,Jan.2007

    SettlingStateOptimizationforFolded--Cascode oTAwithaNovelCompensationStrategy

    NINGNing,YUQi,WANGXiangzhan,"fangMohua,LIUYuanandDAIGuanghao (StateKeyLaboratoryo1:ElectronicThinFilmsandIntegratedDevices,UniversityoIElectr

    onicScienceandTechnologyoI

    China,Chengdu610054,China)

    Abstract--——Inthelightofstep..responseanalysisof thesecondordersystemandtheMinimum-settling-time (MST)theory,newClockfeedthroughfrequencycompen- sation(CFFC)strategyfortheFolded.CascodeOTAis proposed.Cadencesimulationwith0.35pmAMSSiCMoS modelsshowsthesettlingtimeofthecompensatedOTAis reducedby22.7%whenthecircuitisintheFast-Settling state.Asthecapacitorloadvariesfrom0.5pFto2.5pF, theimprovedsettlingtimeincreasesapproximatelylin- earlyfrom3.62nsto4.46ns,andthecircuitachievesfast settlingateverYloadvalue.Thismethodcanbeapplied toactiveSwitchedcapacitor(SC)networksanditsrelated flelds.

    Keywords——Clock~edthrough,Fastsettling,Folded- cascodeOTA,Minimumsettlingtime.

I.Introduction

    Nowadays,activeSwitchedcapacitor(SC)systemshave beenwidelyusedinADC,activefiltersJandcommunication

    networks.InSCcircuits,settlingperformanceisthemostcon- cernedparameterasthesettlingtimeofOsdeterminesthe

    maximumclock~equencyand,inthemeantime,theDCgain ofOTAsdecidestheoutputaccuracy.FOlded.Cascodeampli- tier,duetoitshighgainandfastsettlingproperty,hasbeena majorbasicelementinSCnetworks.

    Meanwhile.thesettlingtimeofOTAsisshowntobe

    stronglydependentonphasemargin.Inordertorealizethe desiredfastsettlingcharacteristics.accuratefrequencyshap- ingmustbeemployed.Severalconventionalapproachesof shapingfrequencyresponsehavebeenimplemented,whichare addingactivecircuittoprovidefeed-forwardpatht3J,introduc. ingMillerCapacitanceforpole-zerocancellation-4J'adjusting thevalueofloadcapacitance[5Jorincreasingthepowerdis- sipationofopampitself.However,thesemethodswillbeat thecostofaddingcomplexityofopampcircuits,theincreased difficuItiesofcircuitdesign,theuncertainloadcapacitanceor biascurrentandalso,itishardtogettherightphasemargin whereoptimally-dampedstatecanbeachieved.

    BasedonMSTtheory[

    thesecond-ordersystem,a

    andthestep-responseanalysisof

    novelCFFCmethodforFOlded.

    Cascodeamplifierispresented.Withoutsacrificinganyother specifications,thiscompensationimprovesOTA'ssettlingfea- turebyadjustingdampingfactorprecisely.Thedetailed

    theoreticalanalysisandCFFCmethodarediscussedinSec-

    tionsIIandIII,respectively.SectionIVgivestheCadence simulationandresultsanalysis.Finally,asummaryofconclu- sionsareprovidedinSectionV.

    II.AnalysisforSystemSettlingState

    Forageneralsecondordersystem,theopen-looptransfer functionisHop.ns)=A0/(1+s/1)(1+s/2),whereA0being low?~equencygain,0)1and0)2standingapartforthedominant andthefirstnon-dominantpclesofthesystem.Theclosed- loopfeedbackstructureofthesecondordersystemisshown atthetopofFig.1.Andthetransferfunctionis

    Hclosed(一爰×百而(1)

    where=C2/(C1+C2+Cin)beingthefeedbackfactor,Cin denotingtheinputparasiticcapacitance.

    Sincethestep-responseofthesecondordersystemisre- strictedbyphasemargin,whichisdirectlyreflectedby0)1/0)2, thedampingfactorofthesystemcanbemodifiedasEq.(2). 1

    叩丽'

    =

    a(?)/

    Dueto0)20)1>0,)(islimitedto

    (0<)(<1).FromEq.(3),therelation

    obtained.

    1

    ?(1)2')(/

    (3)

    betweenzeroandone

    .(l/2)-1canbe

    Fromthesystemstep-responseplottedinnormalizedam- plitudeversustime,asshowninFig.1,Thefollowingcircum-

stancescallbeseen:?lessdamped;?optimallydamped

    (MSTstate);?moredamped.Disthepermittedgainer- rorofthissystem.Settlingtimeisincreasedforeithermore orlessdamped.WhenK,thevoltageattheovershootpoint t=tp,equalsto(1+D),thecurveforanoptimally-damped statecanbeobtained,whichminimizesthesettlingtime.K

    . canbeadjustedbyoptimizing

    ManuscriptReceivedOct.2005;AcceptedJuly2006.ThisworkissupportedbytheNational

    NaturalScienceFoundationofChina

    (No.60072004).

    n?

    

    

    e

    h

    _

    n

    0

    C

    A

    em

    U

    d

    n

    a

    =

    Xn

    _

ChineseJ_oum0fofElectronics2007

c2

    Fig.1.Threeunderdampedstep-responsesforasecondorder feedbacksystem

    AsshowninEq.(2),t7isrelatedtow1,w2andA0j3.Givena certaingainerror,A0j3staysapproximatelyconstant.Hence, W1/W2canbechanged,byintroducingfrequencycompensa- tion,tooptimizeKwithappropriatephasemarginsothat thesettlingtimedecreasesaccordingly.

    III.ClockFeedthroughFrequency

    Compensation

    Accordingtothetheoriesabove.anovelCFFCmethod fortheFolded-Cascodeamplifierisproposed.Asillustrated inFig.2.withclockfeedthroughintroducedbyMOScapac- itorMC1andMC2,thegatebiasvoltagesofM0,Mrand Msarerectified.andthebranchcurrentsarealteredaswel1. Thus,thepositionsofw1andw2canbecontrolledtooptimize thedampmgfactort7forfastsettling.and1arereverse phaseclockswhileBN1BN2BN3BP2andBP1areall

    biasvoltages.OTA'soverallcurrent.whichequalstothesum ofcurrentthroughM9andM10,remainsconstantthroughout theclockperiod.

    Fig.2.OpamptopologyemployingCFFCmethod

    Thedominantpolec.

    dandthefirstnon-dominantpole

    ,6axecontributedbynodec(ord)anda(or6),respectively, whichcanbededucedfromthesystemtransferfunction. u.,d?[(gd.1,2ga.9,lO)(gd.3,4/g3,4)

    +(gd.7,sga.5,6/9lm5,6)1/co,d

    u.I6?9t3,4/I6

    (4)

(5)

    where_6and.

    drepresentthetotalcapacitanceatnode a(orb)andc(ord),c,dandwaI6correspondtow1andw2 ofEq.(1),respectively.Substitutinggds110A1-10.Ill0,

    g16=(2a16?II6)/.intoEqs.(4)(5)(definingaasthe

    transconductancecoefficientofM16and11oaschannel

    modulationcoefficientofM110),andsolvingforWI/W2gives w1

    =

    1

    C~,b1(A1,2A

    3,4

    ?--

    A5,6A

    

    T,s

    ,

    )11i2,_=-…一^2,

    dv……

    +(+A56Ats\(6)

    However,Eq.(6)istoocomplextoseehowtomodifythe valueofw1/2.Soithastobeexploredfurther.Keepingbias BP1,I910andtheparametersofM910invariable,thevolt

    agesatnodeaandbarechangeless,sothat. bisconstant

    inalltimeduetotherelationCd,bo((1+,b/)l/,where isthebuilt.inpotentia1.Astheloadcapacitanceismuch biggerthantheparasiticaloneattheoutput,Cc, dequalsap-

    proximatelytotheloadcapacitance.Thereby,.b/Cc.dholds constant.Thustherelation(w1/",2)o(I1,2issatisfied. Now,letustakeaccountofthelessdampedandaJla- lyzehowthesettlingtimeofOTAisoptimizedbytheCFFC method.InFig.2,theclockfeedthroughofMC2coupled tothebiasBN3producesanup-pulse,sothatthecurre~s /7,

    8throughMrandMsareenhanced.Meanwhile,theclock feedthroughiscoupledtotheBN2byMC1,producingadown- pulsethatreducesthecurrent/0ofM0.Sincethecurrents throughM9andM10remainconstant,/0decreaseswhile/T,8 increases.FromEq.f6)andEq.f2),itcanbeshownthatif w1/",2decreases,willincrease.Asaresult,Kisoptimized accordingly,whichensurestheoptimizeddampedstate.Thus, wecanadjustthecapacitorvalueofMC1andMC2sothat fastsettlingstatecanbeobtained.

    Astothemoredampedstate,thesamecompensationap- proachcanbeemployedtoachievefastsettling. IV.FindingsandDiscussions

    cadenceEDAsimulationisdonewith0.35#mAMSSi CMoSmode1.LetCandC2allbe1.5pF.Totalcurrentof

    thisOTAis6.04mA.theinputbeingastepsignalwith1V magnitude.andaregeneratedfromtheclockofSC system.Thesvstemgainerrorissetto0.1%.

    Table1andFig.3arethesimulationresultsshowingdifre

    encesofw1/2andthesettlingtimesoftheOTAwith/without CFFC.withthefixedloadcapacitance1.5pF.

    Table1.Comparisonofpoleswithout/with

    compensation

    Withoutcomp.Withcomp.

w1(Hz)17r3.61K179.59K

    2(Hz)522.O1M584.26M

    Ts(as)5.123.96

    Ao(dB)63.7463.95

    t70.6990.718

    AsdescribedinTlable1,w/w2isreducedfrom0.333e-3to

    0.307e-3byemployingCFFCcompensation.whichresultsin thatthesettlingtimedecreasesfrom5.12nsto3.96ns,while Aoj3keepnearlyinvariable.

    InFig.3,twosettlingsignalsaxeallbetweentheallowed gainerrorfdashedlines1.ItshowsthatCFFCshortensthe settlingtimeby1.16ns.or22.7%.Theglitchesattheendof

SettlingStateOptimizationforFolded

    CascodeOTAwithaNovelCompensationStrategy65 twocurvesareduetotheclockfeedthroughandcafflberidof withsuitabletimesequence

    1.0060

    1.0040

    1.0020

    

    1.0010

    1.0000

    0.9990

    0.9980

    0.9960

    0.9940

    2

    t(1lS)

    Fig.3.Systemstep-responseswith/withoutcompensation

    Asmentionedabove.itcanbeseenthatCFFCmethodre- duces0J1}2sothatqistunedtospeedupthesettlingprocess ofthisOTA.

    Fig.4showsthesettlingcharacteristicsrelatetovariable loadcapacitances.Onlyiftheloadcapacitanceis1.95pF, theamplifierwithoutCFFCsituatesintheMSTstate,whose settlingtimeis4.17ns.Meanwhile.theonewithCFFCcan achievefastsettlingateachvalueoftheload,byadjusting thebranchcurrentstoshapingphasemarginandthedamping factor.

    8.0

    7.0

    6.0

    

    5.0

    4.0

    3.0

    siITIUlationconditions

    0.51.01.52.02.5

    C(pFI)

    Fig.4.SettlingtimeofOTAsversusthecapacitanceloadfor commonvaluesoftheerrortolerance.O.1%

    Asthecapacitanceloadvariesfrom0.5pFto2.5pF.the improvedsettlingtimeincreasesapproximatelylinearlyfrom 3.62nsto4.46ns,whilethenon.optimizedsettlingtimealters irregularlyfrom5.75asto7.82ns.Thischaracteristiccanbe appliedtohighspeedSCcircuitswithvariableloadcapaci

    tances.

    V.Conclusions

    CFFcmethodshortensthesettlingtimewithoutsacrific.

    ingotherspecificationsoftheamplifier,andthesettlingtime isnearlylinearfunctionofloadcapacitance.Simulationre- sultsusing0.35/zmAMSSiCMOSmodelshowthatthenovel compensationmethodreducesOTA'ssettlingtimeby22.7% andgreatlyimprovesadaptabilitytovariousloadvalues. Moreover.CFFCmethodisadvantageousforitsgreatly improvedreusability,whichreducesthecomplexityofcircuit designasitdoesn'thavetochangeanyOTA'sparameter. References

    1lQi,YangMohuaeta1.,"80MSPSdual-ratesampling 0.34"mCM0Sswitched.capacitorfilter",ActaElectronica Sinica,Vl01.32,No.2,PP.259263,2004.

    2LibinYao,MichielSteyaert,wnlySansen,"Fast-settlingcMos two-stageoperationaltransconductanceamplifiersandtheir systematicdesign.Pfl0c.ofIEEEIScAS.Pheonix,Az,Us, pp.839842,2002.

    3JieYan,RandallL.Geiger,"Fast-settlingamplifierdesignusing feedforwardcompensationtechnique".Proc.ofIEEEISCAS. Lansing,MI,USA,PP.494-497,2000.

    4JoseSilva-Martinez,FloraCarreto-Castro,"Improvingthe highfrequencyresponseofthefolded-cascodeamplifiers".PrDc. ofIEEEISGAS.Atlanta,GA.UsA.PP.500-5031996.

    51HowardC.Yang,DavidJ.Allstot,"Considerationsforfastset

    tlingoperationalamplifiers.IEEETrans.onCircuitsandSys

    terns,Vl01.37,No.3,PP.326334,1990.

    NINGNingwasbornin1981.He

    fAMS1andRFICdesign.

    YANGMohuawasborninRenshou,SichuanProvincein

    1945.Heisaprofessor,Ph.D.advisoronmicroelectronicsandsolid. stateelectronicsinUniversityofElectronicScienceandTechnology

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