MOS operational amplifier design-a tutorial overview

1 IEEEJOURNALOFSOLID-STATECIRCUITS, , ,DECEMBER1982969,SpecialPapersMOSO perationalAmplifierDesign ,FELLOW,IEEE, ,FELLOW,IEEE(ZnvitedPaper) ,input,noise,offsets,commonmodeandpowers upplyrejec-tion,powerdissipation, , ,implementa-tionofanalogfunctionsinMOSte chnologyhasbecomein-creasinglyimportant, andgreatstrideshavebeenmadeinrecentyears inimplementingfunctionssuchashigh-speedD AC S,sampleddataanalogfilters,voltagerefere nces,instru-mentationamplifiers,and HL!!!!cOUTv-(b)(c) (a)Bipolarimple-mentation.(b)CMOS implementation.(c) , (c) ,wewillanalyzethevariousperformancepa-ra metersoftheCMOS implementationofthiscircuit, ,typicallybyafactorontheorderof10-40fort ypicallyusedgeometriesandbiascurrents[3] .

2 Undercertainsimplifyingassumptions,volta gegaincanbeshowntobe(1) ,forconstantdraincur-rentdecreasingeithe rthechannellengthorwidthresultsinadecrea seinthegain,thelatterbecauseofthefacttha tVg~ ,alongwithnoiseconsiderations, ,thisisGRAYANDMEYER:MOSOPAMPDESIGN ANOVERVIEW971 09alr :~ :::~ :ooo1 FREQ,OFOCCURRENCE\,..7,&.e/.-5,:.4,&.?*I ,ampsSCALEDEPENDSONZ, , { ,MOSoperationflmpltiier.+V1M8 IrM5~ ,thesec-ondstagevoltagegainisA=gi??6(3)I -+MlM2--J++ 2go6+807 (JBIAS ,theoverallvoltageIIgainrequiredisontheo rderofseveralthousand[5], ,transistorbiascurrentsandchannel1 M3M41LM6lengthsandwidthsareusuallychosen suchthatthetransistor.)}

3 \/(Vz=-VT)isseveralhundredmillivolts, ,ifthedevicegeometryiskeptconstant,thevo ltagegainisinverselyproportionaltothesqu arerootofthedraincurrentsince(v&-vT) [4]. , ,ifdevicesizeandbiascurrentarekeptconsta nt,thegainisanincreasingfunctionofsubstr atedopingsince&d/dvd~ , , , , (2)g02+go4wheregmisthedevicetransconduct anceandgoisthesmallsignaloutputconductan ce,andassumingthatMlandlf2areapproachest oachievingmorevoltagegainor,alternativel y,achievingthesamevoltagegainwithsmaller devices, ,DCBiasing,andDCPowerSupplyRejectionThei nputoffsetvoltageofanoperationalamplifie riscom-posedoftwocomponents, ,thecomparativelyhighvoltagegainperstage (ontheorderof500)

4 ,becauseoftherelativelylowgainperstage, , ,iftheinputsofthefirststagearegrounded,t henthequiescentoutputvolt-ageatthedraino flkf4isequaltothevoltageatthedrainofi143 (M3andf144havethesamedraincurrentandgate -sourcevoltage,andhencemusthavethesamedr ain-sourcevoltage).However, ,forexample,each50mVdifferenceinthese972 IEEEJOURNALOFSOLID-STATECIRCUITS, , ,DECEMBER1982v+ ++1M7, ,theW/LratiosofM3,M4, ,thisconstraintwouldtaketheform()(W/L)3_ (W/L)4=1(W/L)5(W/L)6-(l#/L),~(W/L), (4)Inorderthatthisratiobemaintainedoverp rocess-inducedvariationsinchannellength, thechannellengthsofikf3,f144,andkf6usual lymustbechosentobethesame, (discussedlater)

5 Thatforlownoise,M3andM4havelowtranscondu ctance,andthatforbestfrequencyresponseun dercapacitiveloading, ,itislikelytodisplayadependenceonpowersu pplyvoltage, , ,inthiscaseassumedtoberesistors,areassum edtomismatchbyapercentageA,theninorderfo rtheoutputvoltageofthedifferentialamplif iertobezero, ~=~ ,theinputoffsetinthiscasedependsoftheact ivedevicesandthefractional(5)ontheI/gmra tiomismatchinthev-ZI xdf(v)v if(v)dv1=9rnI=f(v)[ * , ,theI/ ,theratiois( )/2, ,there-sultistypicallyasomewhatlargeroff setvoltagethaninthebi-polarcase[2].Asdis cussedinalatersection,theI/gmratioalsodi rectlyeffectstheslewrateforclassAinputst ages, , , [6].]

6 FrequencyResponse,Compensation,SlewRate, ,im-portantdifferencesarisebecauseofthem uchlowertranscon-ductanceoftheMOStransis torrelativetobipolardevices[7]. (a)ifthenondominantpolesduetothecapacita ncesatthesourceofMl-2,thecapacitanceatth egateofM3, [2],[8]becauseitoccurssofre-GRAYANDMEYER :MOSOPAMPDESIGN ANOVERVIEW973(a)+VIL Ta o J24R2gm2v2(LARGE) (a)Small-signalequivalentcircuitfortwo-s tageamplifier.(b)SmaU-signalequivalentc~ cuitwithC1andC2settozero, ,whichundertheassumptionthatthepolesarew idelyspaced,canbeshowntobeapproximatelyl ocatedat-1 1=(1+gm2R2)ccR,(6) 47m2 Ccp2=C2CI+ C2CC+-ccc,(7)(8)Notethatthepoleduetothec apacitiveloadingofthefirststagebytheseco nd,p~,hasbeenpusheddowntoaverylowfrequen cybytheMillereffectinthesecondstage,whil ethepoleduetothecapacitanceattheoutputno deofthesecondstage,pz, , ,theproblemisillustratedbyconsideringthe locationofthesecondpolePzandtherighthalf -planezerozrelativetotheunity-gainfreque ncygm~ (9)

7 Cdlgm1C2z&7m2 . (10)cdlL?ml , , (b).Forlowfrequencies,thiscircuitl?ehave slikeanin-tegrator,butathighfrequencies, ,thesecondstagebehaveslikeadiode-connect edtransistor,presentingaloadtothefirstst ageequalto1 ,thecircuitdisplaysagainathighfrequencie swhichissimplygm~/gm2, (b).Thepolarityofthisgainisoppositetotha tatlowfrequencies, ,thetransconductanceofthesecondstageisno rmallymuchhigherthanthefirstbecauseitiso ~ ,thetransconductancesofthetwostagestendt obesimi-lar, , , [7].Thisworkswell, [9].Inthiscircuit,notethatathighfrequenc ies, ,inturn, , ,ifaresistorofvalueequalto1/gm2isinserte dinserieswiththecompensationcapacitor,th evoltageacrossthisresistorwillcancelthes mall-signalvoltageappear-ingontheleftsid eofthecompensationcapacitor, ,oneobtainspolelocationswhichareclosetot hosefortheoriginalcircuit,andazerolocati onof1z=()1 (11)co -RZgm2 Asexpected,thezerovanisheswhenR=ismadeeq ualtol/gm~.

8 Infact,theresistorcanbefurtherincreasedt omovethezerointothelefthalf-planetoimpro vetheamplifierphasemargin[10]. , , , T) , , (V&-VT),thismaynotbethecase, , ,therequirementisthattheamplifierbeablet osettlei~ ,thefactorsdeterminingtheminimumpowerdis sipationtendtobethefactthattheremustbeen oughstandingcurrentintheamplifierclassAs ec-ondstagesuchthatthecapacitancecanbech argedintheallowedtime, ,inturn, ,thenthesamecommentwouldapplytoitsbiascu rrentsinceitsgm,togetherwiththeloadcapac itance,contributeanondominantpole,Thepre cedingdiscussionispredictedontheuseofcla ssAcircuitry( ,circuitswhoseavailableoutputcurrentisno tgreaterthanthequiescentbiascurrent).

9 Quiescentpowerdis-sipationcanbegreatlyre ducedthroughtlheuseofdynamiccircuitsandc lassBcircuits,asdiscussedlater,NoisePerf ormanceBecauseofthefactthatMOSdevicesdis playrelativelyhigh1/fnoise, , (11),V:qT OT=V:ql+ :q2+()~(K?q3+J %14)(14)whereithasbeenassumedthatgm,=gmz andthatgm~=gm~,Thus,theinputtransistorsc ontributetotheinputnoisedi-rectly, )iasconditionshasbeenstudiedbymanyauthor s[12]-[14].Considerabledis-crepancyexist sinthepublisheddataon1/fnoise, ,thegate-referredequivalentmean-squaredv oltagenoiseisapproximatelyinde-pendentof biasconditionsinsaturation, ,butitshouldbeem-phasizedthattheactualde pendencemustbeverifiedforeachprocesstech nologyanddevicetype[12],[15].

10 Thus,K~;,f. ()8fCOXWL~ (15)GRAYANDMEYER:MOSOPAMPDESIGN ANOVERVIEW975v eq2thatincreasingthewidthofthechannelint heloadsdoesnot&m!m2-J%improvethe1/~noise performance. uThermalNoisePerfoirnance-2 Theinput-referredthermalnoiseofanMOStran sistorism3 ogivenby[8]m4_ 2 eq;%4()V:q= (17a)v-(a) !Utilizingthesameapproachasfortheflicker noise, (a) :q=4kT4[+J-).3<2&CoX(W/L)lID(17b)Again,t hefirsttermrepresentsthethermalnoisefrom thein-puttransistors, ,thentheinputnoiseis(b) :,AvZ/ ..I100 IKIOKIOOKIMIOMFreq, , ,weobtainfortheequivalentinputnoisev:/f= K (%:;)(3 WIL1 COX(16)whereKnandKparetheflickernoisecoe fficientsforthen-channelandp-channeldevi ces, , , (PSRR) , , , , (openloop) ,iftheoperationalamplifierisconnectedina followerconfigu-rationandanacsignalissup erimposedononeofthepowersupplies, , ,theimpedenceofthecompensationcapacitord e-creases, ,thegainfromthenegativesupplytotheoutput 976 IEEEJOURNALOFSOLID-STATECIRCUITS, , ,DECEMBER1982 LPSRR+-1o 1------A.]