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IntroductiontoCMOSOPAMPsandComparators

RoubikGregorian

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Thisbookisprintedonacidfreepaper. Copyright1999byJohnWiley&Sons.Allrightsreserved.PublishedsimultaneouslyinCanada.Nopartofthispublicationmaybereproduced,storedinaretrievalsystemortransmittedinanyformorbyanymeans,electronic,mechanical,photocopying,recording,scanningorotherwise,exceptaspermittedunderSections107or108ofthe1976UnitedStatesCopyrightAct,withouteitherthepriorwrittenpermissionofthePublisher,orauthorizationthroughpaymentoftheappropriatepercopyfeetotheCopyrightClearanceCenter,222RosewoodDrive,Danvers,MA01923,(978)7508400,fax(978)7504744.RequeststothePublisherforpermissionshouldbeaddressedtothePermissionsDepartment,JohnWiley&Sons,Inc.,605ThirdAvenue,NewYork,NY101580012(212)8506011,fax(212)8506008,EMail:PERMREQ@WILEY.COM.Fororderingandcustomerinformationcall,1800CALLWILEY.

LibraryofCongressCataloginginPublicationData

Gregorian,Roubik.IntroductiontoCMOSOPAMPsandcomparators/RoubikGregorian.p.cm."AWileyIntersciencepublication."IncludesIndex.ISBN0471317780(hardcover:alk.paper)1.OperationalamplifiersDesignandconstruction.2.ComparatorcircuitsDesignandconstruction.3.Metaloxidesemiconductors,Complementary.I.Title.TK7871.58.06G741999621.39'5dc219823233CIP

PrintedintheUnitedStatesofAmerica.1098765432

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Tomywife,AgnesAndourchildren,ArisandTalin

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Contents

Preface ix

1Introduction

1

1.1ClassificationofSignalProcessingTechniques 1

1.2ExamplesofApplicationsofOpAmpsandComparatorsinAnalogMOSCircuits

6

Problems 16

References 16

2MOSDevicesasCircuitElements

17

2.1Semiconductors 17

2.2MOSTransistors 21

2.3MOSTransistorTypes:BodyEffect 27

2.4SmallSignalOperationandEquivalentCircuitofMOSFETTransistors 30

2.5WeakInversion 39

2.6ImpactIonization 40

2.7NoiseinMOSFETS 41

2.8CMOSProcess 44

Problems 45

References 47

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3BasicAnalogCMOSSubcircuits

48

3.1BiasCircuitsinMOSTechnology 48

3.2MOSCurrentMirrorsandCurrentSources 55

3.3MOSGainStages 63

3.4MOSSourceFollowers 74

3.5MOSDifferentialAmplifiers 77

3.6FrequencyResponseofMOSAmplifierStages 84

Problems 92

References 94

4CMOSOperationalAmplifiers

95

4.1OperationalAmplifiers 95

4.2SingleStageOperationalAmplifiers 100

4.3TwoStageOperationalAmplifiers 106

4.4StabilityandCompensationofCMOSAmplifiers 112

4.5DynamicRangeofCMOSOpAmps 126

4.6FrequencyResponse,TransientResponse,andSlewRateofCompensatedCMOSOpAmps

132

4.7NoisePerformanceofCMOSOpAmps 137

4.8FullyDifferentialOpAmps 140

4.9CMOSOutputStages 149

4.10OpAmpswithRailtoRailInputCommonModeRange 164

Problems 170

References 173

5Comparators

175

5.1CircuitModelingofaComparator 175

5.2SingleEndedAutoZeroingComparators 177

5.3DifferentialComparators 182

5.4RegenerativeComparators(SchmittTriggers) 192

5.5FullyDifferentialComparators 198

5.6Latches 205

Problems 212

References 213

6DigitaltoAnalogConverters

214

6.1DigitaltoAnalogConversion:BasicPrinciples 214

6.2VoltageModeD/AConverterStages 218

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6.3ChargeModeD/AConverterStages 231

6.4HybridD/AConverterStages 234

6.5CurrentModeD/AConverterStages 238

6.6SegmentedCurrentModeD/AConverterStages 244

Problems 252

References 254

7AnalogtoDigitalConverters

255

7.1AnalogtoDigitalConversion:BasicPrinciples 255

7.2FlashA/DConverters 263

7.3InterpolatingFlashA/DConverters 270

7.4TwoStepA/DConverters 273

7.5SuccessiveApproximationA/DConverters 282

7.6CountingandTrackingA/DConverters 294

7.7IntegratingA/DConverters 295

Problems 300

References 301

8PracticalConsiderationsandDesignExamples

303

8.1PracticalConsiderationsinCMOSOpAmpDesign 303

8.2OpAmpDesignTechniquesandExamples 316

8.3ComparatorDesignTechniquesandExamples 349

Problems 355

References 355

Index 357

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Preface

Operationalamplifiers(opamps)andcomparatorsaretwoofthemostintricate,andinmanywaysthemostimportant,buildingblocksofananalogcircuit.Thesecomponentsareusedinsuchdevicesasswitchedcapacitorfilters,analogtodigital(A/D)anddigitaltoanalog(D/A)converters,amplifiers,modulators,rectifiers,peakdetectors,andsoon.Theperformanceofopampsandcomparatorsusuallylimitsthehighfrequencyapplicationanddynamicrangeoftheoverallcircuit.Withoutathoroughunderstandingoftheoperationandbasiclimitationofthesecomponents,thecircuitdesignercannotdetermineorevenpredicttheactualresponseoftheoverallsystem.HencethisbookgivesafairlydetailedexplanationoftheoverallconfigurationsandperformancelimitationsofopampsandcomparatorsexclusivelyinCMOStechnology.Whilethescalingpropertiesoftheverylargescaleintegration(VLSI)processeshaveresultedindenserandhigherperformancedigitalcircuits,theyhavealsochangedthedesigntechniquesusedforCMOSanalogcircuits.Therefore,themainpurposeofthesediscussionsistoillustratethemostimportantprinciplesunderlyingthespecificcircuitsanddesignprocedures.Nevertheless,thetreatmentisdetailedenoughtoenablethereadertodesignhighperformanceCMOSopampsandcomparatorssuitableformostanalogcircuitapplications.

Themainemphasisofthisbookisonphysicaloperationanddesignprocess.IthasbeenwrittenasaunifiedtextdealingwiththeanalysisanddesignofCMOSopampsandcomparators.Itisintendedforclassroomadoptiontobeusedasaseniororgraduateleveltextintheelectricalengineeringcurriculumofuniversitiesandalsoastrainingandreferencematerialforindustrialcircuitdesigners.Toincreasetheusefulnessofthebookasatextforclassroomteaching,numerousproblemsareincludedattheendofeachchaptertheseproblemsmaybeuseforhomeworkassignments.Toenhanceitsvalueasadesignreference,tablesandnumericaldesignexamplesareincludedtoclarifythestepbystepprocessesinvolved.Thefirsttwo

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chaptersprovideaconcise,basiclevel,and(Ihope)cleardescriptionofanalogMOSintegratedcircuitsandthenecessarybackgroundinsemiconductordevicephysics.TheremainderofthebookisdevotedtothedesignofCMOSopampsandcomparatorsandtothepracticalproblemsencounteredandtheirsolutions.ThebookalsoincludestwointroductorychaptersontheapplicationsofopampsandcomparatorsinA/DandD/Aconverters.Foramoredetaileddiscussionontheimportantsubjectofdataconverters,readersarereferredtothePrinciplesofDataConversionSystemDesignbyBehzadRezavi,andDeltaSigmaDataConverters:Theory,DesignandSimulationbyStevenR.Norsworthy,RichardSchreier,andGaborC.Temes.

ThisbookisbasedinpartonapreviousbookIcoauthoredwithGaborC.Temes,titledAnalogMOSIntegratedCircuitsforSignalProcessing.TheoriginalmaterialhasbeenaugmentedbythelatestdevelopmentsintheareaofanalogMOSintegratedcircuits,inparticularopampsandcomparators.Mostofthematerialandconceptsoriginatedfromthepublicationscitedattheendofeachchapteraswellasfrommanypracticingengineerswhoworkedwithmeovertheyears.

Sincetheoriginalbookevolvedfromasetoflecturenoteswrittenforshortcourses,theorganizationofthematerialwasthereforeinfluencedbytheneedtomakethepresentationsuitableforaudiencesofwidelyvaryingbackgrounds.HenceItriedtomakethebookreasonablyselfcontained,andthepresentationisatthesimplestlevelaffordedbythetopicsdiscussed.Onlyalimitedamountofpreparationwasassumedonthepartofthereader:mathematicsonthejuniorlevel,andoneortwointroductorylevelcoursesinelectronicsandsemiconductorphysicsaretheminimumrequirements.

Thebookcontainseightchapters.Chapter1providesabasicintroductiontodigitalandanalogsignalprocessing,followedbyseveralrepresentativeexamplesofcircuitsandsystemsutilizingCMOSopampsandcomparators.Thismaterialcanbecoveredinonelecture(twohourlecturesareassumedhereandthroughoutthepreface).

InChapter2thephysicsofMOSdevicesisdescribedbrieflyandlinearizedmodelsofMOSFETs,aswellasMOScapacitorsandswitchesarediscussed.ThetechnologyusedtofabricateCMOSdevicesisalsodiscussedbriefly.Onceagain,dependingonthebackgroundoftheaudience,twoorthreelecturesshouldsufficetocoverthecontentofthischapter.

Chapter3coverssomeofthebasicsubcircuitscommonlyutilizedinanalogMOSintegratedcircuits.Thesesubcircuitsaretypicallycombinedtosynthesizeamorecomplexcircuitfunction.Completecoverageofalltopicsofthischapterrequiresaboutthreelectures.

InChapter4circuitdesigntechniquesforrealizingCMOSoperationalamplifiersarediscussed.Themostcommoncircuitconfigurations,aswellastheirdesignandlimitations,areincluded.Fullcoverageofalltopicsinthischapterrequiresaboutfourlectures.

InChapter5theprinciplesofCMOScomparatordesignarediscussed.Firstthesingleendedautozeroingcomparatorisexamined,followedbysimpleandmul

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tistagedifferentialcomparators,regenerativecomparators,andfullydifferentialcomparators.Twolecturesshouldbesufficientforcompletecoverageofthischapter.

Chapters6and7,whichcoverCMOSdigitaltoanalogandanalogtodigitalconverters,serveaspracticalapplicationexamplesofopampsandcomparators.Thefundamentalsandperformancemetricsofthedataconvertersarepresentedfirst,followedbyadiscussionofpopulararchitecturesofNyquistrateconverters.Digitaltoanalogconvertersaredividedintovoltage,charge,andcurrentscalingtypes.Analogtodigitalconvertersincludehighspeedflash,mediumspeedsuccessiveapproximation,andlowspeedserialconverters.Completecoverageofalltopicsmayrequirethreetofourlectures.

InChapter8thedesignprinciplespresentedinChapter4and5areemployedtoworkoutseveraldesignexamplestoacquaintthereaderwiththeproblemsandtradeoffsinvolvedinopampandcomparatordesigns.Practicalconsiderationssuchasdcbiasing,systematicoffsetvoltage,andpowersupplynoisearediscussedinsomedetail.AlltopicsinthischaptercanbecoveredinthreelecturesifthedetaileddiscussioninSections8.2and8.3iscondensed,thematerialcanbepresentedintwolectures.

Thus,dependingonthedepthofthepresentation,fullcoverageofallmaterialinthebookmayrequireasmanyas20twohourlecturesorasfewas16.

Iamgratefultomanypeoplewhohavehelpedmedirectlyorindirectlyintheelaborateandsometimesoverwhelmingtaskofpublishingthisbook.Inparticular,IwouldliketothankmycolleaguesDrs.S.C.Fan,B.Fotouhi,B.Ghaderi,andG.C.Temes,whoreadandcriticizedversionsofthemanuscript.Theircommentshavebeenmosthelpfulandaregreatlyappreciated.MostofthedifficulttypingtaskwasdonebyMs.W.IrwinandD.Baker.Iamgratefulfortheirexcellentandpainstakinghelp.Last,butnotleast,Iwouldliketoexpressmygratitudetomyfamilyforgraciouslysufferingneglectduringthewritingofthisbook.Withouttheirunderstandingandsupportthisworkwouldnothavebeenpossible.

ROUBIKGREGORIANSARATOGA,CALIFORNIAJANUARY1999

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Chapter1Introduction

Operationalamplifiers(opamps)andcomparatorsaretwoofthemostimportantbuildingblocksforanalogsignalprocessing.Opampsandafewpassivecomponentscanbeusedtorealizesuchimportantfunctionsassummingandinvertingamplifiers,integrators,andbuffers.Thecombinationofthesefunctionsandcomparatorscanresultinmanycomplexfunctions,suchashighorderfilters,signalamplifiers,analogtodigital(A/D)anddigitaltoanalog(D/A)converters,inputandoutputsignalbuffers,andmanymore.Makingtheopampandcomparatorfasterhasalwaysbeenoneofthegoalsofanalogdesigners.Inthischapterthebasicconceptofdigitalandanalogsignalprocessingisintroduced.Thenathirdcategoryofsignalprocessing,thesampleddataanalogtechnique,whichisinbetweenthetwomainclassifications,isdescribed.Finally,afewrepresentativeexamplesaregivenofcircuitsandsystemsutilizingCMOSopampsandcomparators,toillustratethegreatpotentialofthesecomponentsaspartofanMOSLSIchip.

1.1ClassificationofSignalProcessingTechniques[14]

Electricalsignalprocessorsareusuallydividedintotwocategories:analoganddigitalsystems.Ananalogsystemcarriessignalsintheformofvoltages,currents,charges,andsoon,whicharecontinuousfunctionsofthecontinuoustimevariable.Sometypicalexamplesofanalogsignalprocessorsareaudioamplifiers,passiveoractiveRCfilters,andsoon.Bycontrast,inadigitalsystemeachsignalisrepresentedbyasequenceofnumbers.Sincethesenumberscancontainonlyafinitenumberofdigits(typically,codedintheformofbinarydigits,orbits)theycanonlytakeondiscretevalues.Also,thesenumbersarethesampledvaluesofthesignal,takenatdiscretetimeinstances.Thusboththedependentandindependentvariablesofa

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digitalsignalarediscrete.Sincetheprocessingofthedigitalbitsisusuallyperformedsynchronously,atimingorclockcircuitisanimportantpartofthedigitalsystem.Thetimingprovidesoneormoreclocksignals,eachcontainingaccuratelytimedpulsesthatoperateorsynchronizetheoperationofthecomponentsofthesystem.Typicalexamplesofdigitalsystemsareageneralpurposedigitalcomputeroraspecialpurposedigitalsignalprocessordedicatedto(say)calculatingtheFouriertransformofasignalviathefastFouriertransform(FFT),oradigitalfilterusedinspeechanalysis,andsoon.

Bycontrast,analogsignalprocessingcircuitsutilizeopamps,comparators,resistors,capacitors,andswitchestoperformsuchfunctionsasfilters,amplifiers,rectifiers,andmanymore.Tounderstandthebasicconceptsofthemostcommonlyusedconfigurationsofananalogcircuit,considerthesimpleanalogtransferfunction

ItiseasytoverifythattheRLCcircuitshowninFig.1.1acanrealizethisfunction(Problem1.1).Althoughthiscircuitiseasytodesign,build,andtest,thepresenceoftheinductorinthecircuitmakesitsfabricationinintegratedformimpractical.Infact,forlowfrequencyapplications,thiscircuitmaywellrequireaverylargevalued,andhencebulky,inductorandcapacitor.Toovercomethisproblem,thedesignermaydecidetorealizethedesiredtransferfunctionusinganactiveRCcircuit.ItcanreadilybeshownthatthecircuitinFig.1.1b,whichutilizesthreeoperationalamplifiers,iscapableofprovidingthetransferfunctionspecifiedin

Figure1.1Secondorderfilterrealization:(a)passivecircuit(b)activeRCcircuit.

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Figure1.2Switchedcapacitorrealizationofaresistivebranch.

Eq.(1.1).Thiscircuitneedsnoinductorsandmayberealizedwithsmalldiscretecomponentsforawidevarietyofspecifications(Problem1.2).Itturnsout,however,thatwhileintegrationofthiscircuitonabipolarchipis,inprinciple,feasible(sincetheamplifiers,resistors,andcapacitorsneededcanallbeintegrated),therearesomemajorpracticalobstaclestointegration.TheseincludetheverylargechipareaneededbytheRCcomponents,aswellasthestringentaccuracyandstabilityrequirementsfortheseelements.Theserequirementscannotreadilybesatisfiedbyintegratedcomponents,sinceneitherthefabricatedvaluesnorthetemperatureinducedvariationsoftheresistiveandcapacitiveelementstrackeachother.Theresultingpolezerovariationsaretoolargeformostapplications.

Priortomid1970s,analogcircuitssuchastheoneshowninFig.1.1wereimplementedusingintegratedbipolaropampsanddiscretepassivecomponents.Inthe1970stwodevelopmentsmadeitpossibletofullyintegrateanalogcircuitsinmetaloxidesemiconductor(MOS)technology.Thefirstdevelopmentwastheemergenceofatechniquecalledswitchedcapacitor(SC)circuits[6],whichisaneffectivestrategyforsolvingboththeareaandthematchingproblemsbyreplacingeachresistorinthecircuitbythecombinationofacapacitorandafewswitches.ConsiderthebranchesshowninFig.1.2.Here,thefourswitchesS1,S2,S3,andS4openandcloseperiodically,ataratewhichismuchfasterthanthatofthevariationsoftheterminalvoltagevAandvB.SwitchesS1andS4operatesynchronouslywitheachotherbutinoppositephasewithS2andS3.ThuswhenS2andS3areclosed,S1andS4areopen,andviceversa.NowwhenS2andS3close,Cisdischarged.WhenS2andS3open,S1andS4close,andCisrechargedtothevoltagevC=vAvB.Thiscausesachargeq=C(vAvB)toflowthroughthebranchofFig.1.2.Next,CisagaindischargedbyS2andS3,andsoon.IfthiscycleisrepeatedeveryTseconds(whereTistheswitchingperiodorclockperiod),theaveragecurrentthroughthebranchisthen

ThusiavisproportionaltothebranchvoltagevAvB.Similarly,forabranchcontainingaresistorR,thebranchcurrentisi=(1/R)(vAvB).ThustheaveragecurrentflowinginthesetwobranchesarethesameiftherelationR=T/Cholds.

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Figure1.3Secondorderswitchedcapacitorfiltersection.

Physically,theswitchestransformthecapacitorC,anondissipativememoriedelement,intoadissipativememoryless(i.e.,resistive)one.

ItisplausiblethereforethatthebranchofFig.1.2canbeusedtoreplaceallresistorsinthecircuitofFig.1.1b.Theresultingstage[3]isshowninFig.1.3.Inthiscircuit,switchesthatbelongtodifferent''resistors"butperformidenticaltaskshavebeencombined.Furthermore,thesecondoperationalamplifier(opamp)inFig.1.1b,whichactedmerelyasaphaseinverter,hasbeeneliminated.ThiswaspossiblesincebysimplychangingthephasingoftwooftheswitchesassociatedwithcapacitorC3,therequiredphaseinversioncouldbeaccomplishedwithoutanopamp.

AsFig.1.3illustrates,thetransformedcircuitcontainsonlycapacitors,switches,andopamps.Amajoradvantageofthisnewarrangementisthatnowalltimeconstants,previouslydeterminedbythepoorlycontrolledRCproducts,willbegivenbyexpressionsoftheform(T/C1)C2=T(C2/C1).HeretheclockperiodTisusuallydeterminedbyaquartzcrystalcontrolledclockcircuitandhenceisveryaccurateandstable.TheotherfactorofthetimeconstantisC2/C1,thatis,theratiooftwoonchipMOScapacitances.Usingsomesimplerulesinthelayoutoftheseelements,itispossibletoobtainanaccuracyandstabilityontheorderof0.1%forthisratio.Theresultingoverallaccuracyisatleast100timesbetterthanwhatcanbeachievedwithanonchipresistorandcapacitorfortheRCtimeconstant.

Adramaticimprovementisalsoachievableforthearearequiredbythepassiveelements.Toachieveatimeconstantintheaudiofrequencyrange(say10krad/s),evenwithalarge(10pF)capacitor,aresistanceof10M isrequired.Sucharesistorwilloccupyanareaofabout106m2,whichisprohibitivelylargeitisnearly10%oftheareaofanaveragechip.Bycontrast,foratypicalclockperiodof10s,thecapacitanceoftheswitchedcapacitorrealizinga10M resistorisC=T/R=105/107=1012F=1pF.Thearearequiredrealizingthiscapacitanceisabout2500m2,only0.25%ofthatneededbytheresistorthatitreplaces.

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TheseconddevelopmentthatmadetherealizationofthefullyintegratedanalogMOScircuitspossiblewasthedesignoftheMOSopamp.Perhapsthemostgenerallyusefulanalogcircuitfunctionisthatoftheoperationalamplifier.Priortoabout1977,thereexistedaclearseparationofthebipolarandMOStechnologies,accordingtothefunctionrequired[1,5].MOStechnology,withitssuperiordevicedensity,wasusedmostlyfordigitallogicandmemoryapplications,whileallrequiredanalogfunctions(suchasamplification,filtering,anddataconversion)wereperformedusingbipolarintegratedcircuits,suchasbipolaropamps.Sincethattime,however,rapidprogressmadeinMOSfabricationtechniquesmadeitpossibletomanufacturemuchmorecomplexandflexiblechips.Inaddition,newdevelopmentsoccurredincommunicationtechnology(suchasdigitaltelephony,datatransmissionviatelephonelines,adaptivecommunicationchannels,etc.)whichrequiredanaloganddigitalsignalprocessingcircuitryinthesamefunctionalblocks.Theanalogfunctionsmostoftenneededarefiltering(forantialiasing,smoothing,bandseparation,etc.),amplification,sampleandholdoperations,voltagecomparison,andthegenerationaswellasprecisescalingofvoltagesandcurrentsfordataconversion.Theseparationoftheseanalogfunctionsfromthedigitalonesmerelybecauseofthedifferentfabricationtechnologiesusedisundesirable,sinceitincreasesboththepackagingcostsandthespacerequirementsandalso,duetotheadditionalinterconnectionsrequired,degradestheperformance.HencetherewasstrongmotivationtodevelopnovelMOScircuits,whichcanperformtheseanalogfunctionsandwhichcanalsosharetheareaonthesamechipwiththedigitalcircuitry.

Comparedwithbipolartechnology,MOStechnologyhasbothadvantagesanddisadvantages.MOSdevicehasextremelyhighimpedanceatitsinput(gate)terminal,whichenablesittosensethevoltageacrossacapacitorwithoutdischargingit.Also,thereisnoinherentoffsetvoltageacrosstheMOSdevicewhenitisusedasachargeswitch.Furthermore,highqualitycapacitorscanbefabricatedreliablyonanMOSchip.ThesefeaturesmaketherealizationofsuchcircuitsasprecisionsampleandholdstagesfeasibleonanMOSchip[1].Thisisusuallynotpossibleinbipolartechnology.

Onthenegativeside,thetransconductanceofMOStransistorsisinherentlylowerthanthatofbipolartransistors.AtypicaltransconductancevalueforamoderatesizedMOSdeviceisaround2.5mA/Vforabipolartransistor,itmaybeabout50timeslarger.ThisleadstoahigheroffsetvoltageforanMOSamplifierthanforabipolaramplifier.(Atthesametime,however,theinputcapacitanceoftheMOStransistoristypicallymuchsmallerthanthatofabipolartransistor.)Also,thenoisegeneratedinanMOSdeviceismuchhigher,especiallyatlowfrequencies,thaninabipolartransistor.TheconclusionisthatthebehaviorofanamplifierrealizedonanMOSchiptendstobeinferiortoanequivalentbipolarrealizationintermsofoffsetvoltage,noise,anddynamicrange.However,itcanhavemuchhigherinputimpedancethanthatofitsbipolarcounterpart.

Asaresultoftheseproperties,thelargestuseoftheMOSopampisexpectedtobeaspartofanMOSLSI(largescaleintegration)chip.Herethedesignoftheopampcantakeadvantageoftheimportantperformancespecificationsthatareneeded.Theloadingoftheopampisoftenverylightandusuallyonlyasmall

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valuedcapacitorhastobedrivenbytheseopamps.Switchedcapacitorcircuitsfallespeciallyintothiscategory,whereelementvalueaccuracyisimportantbutthesignalfrequencyisnottoohighandthedynamicrangerequiredisnotexcessive.Voiceandaudiofrequencyfilteringanddataconversionareinthiscategoryandrepresentthebulkofthepastapplications.

InadditiontofrequencyselectiveswitchedcapacitorfilteringintroducedinFig.1.3,whichhasbeenthemostcommonapplicationofMOSopamps,therearemanyotherfunctionsforwhichopampsandcomparatorscanbeused.Theseincludeanalogtodigital(A/D)anddigitaltoanalog(D/A)dataconversion,programmablegainamplificationforAGCandotherapplications,peakdetection,rectification,zerocrossingdetection,andsoon.Theyhavealsobeenusedextensivelyinlargemixedsignalanalog/digitalsystemssuchasvoicecodecs,highspeeddatacommunicationmoderns,audiocodecs,andspeechprocessors.Thisrangewillexpandcontinuouslyasthequality(bandwidth,dynamicrange,powerconsumption,etc.)ofthecomponents,especiallyopampsandcomparators,improves.

1.2ExamplesofApplicationsofOPAMPsandComparatorsinAnalogMOSCircuits

Inthissection,afewselectedexamplesofpracticalanalogMOScircuitsaregivenwhereCMOSopampsandcomparatorsareusedextensively.Ofcourse,thereadershouldnotexpecttounderstandthedetailsofthesesystemsatthisstage.However,thediagramsmaygiveanideaofthepotentialsofthesecomponentsinanalogsignalprocessing.

Asmentionedearlier,oneofthemostimportantapplicationsofCMOSopampsisinswitchedcapacitorfilters.Figure1.4ashowsthecircuitdiagramofaseventhorderswitchedcapacitorfilter.ItsmeasuredfrequencyresponseisshowninFig.1.4b.Themeasuredpassbandvariationforthedeviceislessthan0.06dB.Thisrepresentsasuperiorperformance,whichcouldnothavebeenachievedwithoutextensivetrimmingusinganyotherfiltertechnology.

AnobviousapplicationofaCMOSopampistherealizationofchargemodedigitaltoanalogconverters(DAC).Itcanbeobtainedbycombiningaprogrammablecapacitorarrayandanoffsetfreeswitchedcapacitorgainstage.AnexampleofanNbitchargemodeDACisshowninFig.1.5,whereVrefisatemperaturestabilizedconstantreferencevoltage.TheoutputoftheDACistheproductofthereferencevoltageandthebinarycodeddigitalsignal(b1,b2,b3,...,bN).InChapter6thedesignofsuchcircuitsisdiscussedinsomedetail.

Modulators,rectifiers,andpeakdetectors[6]belongtoanimportantclassofnonlinearcircuits,whichcanbeimplementedwithacombinationofopampsandcomparators.Inanamplitudemodulatortheamplitudeofasignalx(t)(usuallycalledthecarrier)isvaried(modulated)bym(t),themodulatingsignal.Hencetheoutputsignaly(t)istheproductofx(t)andm(t),ory(t)=x(t)m(t).Aperiodiccarriersignal,whichisreadilygeneratedfromastableclocksource,isasquarewavealternatingbetweentwoequalvaluesV.Aneasywaytoperformmodulationwith

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Figure1.4(a)Circuitdiagram(b)measuredfrequencyresponseofaseventhorderswitchedcapacitorlowpassfilter.

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Figure1.5Multiplyingdigitaltoanalogconverter.

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Figure1.6Switchedcapacitormodulatorwithtwoclocksignals.

asquarewavecarrieristoswitchthepolarityoftheinputsignalm(t)periodically.AstrayinsensitiveswitchedcapacitormodulatorcircuitwhichperformsaccordingtothisprincipleisshowninFig.1.6.Theclockphases 1and 2areoperatedatthefastclockrate c,whilethephase achangesattheslowcarrierfrequencyrate

ca.Normally, cismuchlarger(byafactorof30ormore)than ca.

Anothernonlinearcircuitisafullwaverectifierthatconvertsaninputsignalv in(t)toitsabsolutevalue|v in(t)|.Asimplewayofimplementingaswitchedcapacitorfullwaverectifieristoaddacomparatortoanamplitudemodulator.ThecircuitofaswitchedcapacitorfullwaverectifierbasedonthemodulatorofFig.1.6isshowninFig.1.7a.HereAissetto"1"ifv in>0andto"0"ifv inVmax,theopampoutputgoeshighandM1conducts,chargingCuntilvout v inisreached.Ifv in

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Figure1.7Switchedcapacitorfullwaverectifier:

(a)completecircuit(b)offsetcompensatedcomparator.

A/DconverterisshowninFig.1.10.AnalogtodigitalconvertersarediscussedindetailinChapter7.

WiththerecentrapidprogressmadeinMOSfabricationtechniquesandtheemergenceofthesubmicronCMOStechnology,manyintricatesystemscontaininganaloganddigitalfunctionshavebeencombinedinafullyintegratedform.OnedrawbackofthesubmicronCMOStechnologyisthereductioninthepowersupplyvoltage,whichresultsinareducedsignalswingandhencealowerdynamicrange.Toimprovetheperformanceofthesystemandreducetheeffectsofnoiseinjectionfromthepower,ground,andclocklines,mostmodernhighperformancemixed

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Figure1.8Continuoustimepeakdetector.

Figure1.9FivebitsuccessiveapproximationA/Dconverter.

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Figure1.10ConceptualdiagramofanNbitA/Dconverter.

signalintegratedcircuitsmakeuseoffullydifferentialsignalpaths.Withopampsandcomparators,thefullydifferentialsignalpathsrequirefullydifferentialoutputsaswellasinputs,andtheyareknownasfullydifferentialopampsandcomparators.Sincethistechniqueusessymmetricallayout,manyofthenoisevoltages(powersupplynoise,clockfeedthroughnoise,offsetvoltages)appearascommonmodesignals.Theyaretoaconsiderableextentcanceledinthedifferentialoutputvoltagevoutatallfrequencies.AhighfrequencyhighQswitchedcapacitorbandpassfilterthatusesafullydifferentialsignalpathisshowninFig.1.11.Thisfilteristypicallyusedinaradiofrequency(RF)receiversystem,whichrequireshighselectivityathighfrequencies[7].Thetwocomplementaryswitchblocks(X1andX2)areshowninFig.1.12.ThefilterusesfullydifferentialsinglepoletransconductancefoldedcascodeopampswithsourcefollowercommonmodefeedbackasillustratedinFig.1.13[8].Thisopampachieves100MHzunitygainbandwidthand60dBofgainwith1mAoftotalcurrentconsumption.FullydifferentialopampsarediscussedindetailinChapter4.

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Figure1.11Schematicdiagramofasixthorderswitchedcapacitorallpolebandpassfilter.

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Figure1.12Twoswitchblocksforadoublesampling.

Anotherapplicationofthefullydifferentialopampsisinoversampling,ordeltasigmaA/Dconverters.Theoversamplingconvertersoperateatsamplingratesof16to512timestheNyquistrateandincreasethesignaltonoiseratiobysubsequentfiltering.Theoversamplingtechniqueslendthemselvesmostfavorablytoapplicationsthatrequirearelativelylowfrequency(12bits).Themostobviousapplicationofdeltasigmaconvertersisindigitaltelephony

Figure1.13Widebandopampforthefilter.

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Figure1.14(a)FullydifferentialCMOSimplementationofasecondorder

deltasigmamodulator(b)twophaseclockscheme.

anddigitalaudio.Figure1.14showsafullydifferential,switchedcapacitorCMOSimplementationofasecondorderdeltasigmamodulator[9].Itconsistsoftwoparasiticinsensitiveintegrators,acomparatorthatservesasa1bitA/Dconverter,andatwolevel(1bit)D/Aconverter.Useofafullydifferentialconfigurationattenuatespowersupplynoise,clockfeedthrough,andevenorderharmonicdistortion.Themodulatoroperatesontwophasenonoverlappingclocksconsistingofasamplingphaseandanintegrationphase.Itachieves16bitdynamicrangewithanoversamplingratioof256andasignalbandwidthof20kHz.

Page16

Astheexamplesaboveillustrate,presentdayCMOSopampsandcomparatorsandtheiruseinanalogMOScircuitshavereachedacertainlevelofmaturity.Already,almostanyanalogsignalprocessingtaskinthevoiceoraudiofrequencyrangehasapossiblesolutionusingsuchcircuits.Asfabricationtechnologyandcircuitsdesigntechniquescontinuetoadvance,thespeedanddynamicrangeofthesecircuitswillincrease,allowingtheiruseinsuchlargevolumeapplicationsasvideoandradiosystems,imageprocessing,highspeedtransmissioncircuits,andsoon.

Problems

1.1.ShowthatthecircuitofFig.1.1acanrealizethetransferfunctionofEq.(1.1).WhatshouldbetheelementvaluesR,L,andC?

1.2.CalculatethetransferfunctionoftheactiveRCcircuitofFig.1.1b.AssumethatthecircuitistorealizethetransferfunctionofEq.(1.1).Writetheavailableequationsfortheelementvalues.Howmanyelementvaluescanbechosenarbitrarily?

References

1.R.W.Brodersen,P.R.Gray,andD.A.Hodges,Proc.IEEE,67,6175(1979).

2.Y.Tsividis,Proc.IEEE,71,926940(1983).

3.R.Gregorian,K.W.Martin,andG.C.Temes,Proc.IEEE,71,941966(1983).

4.D.J.AllstotandW.C.Black,Jr.,Proc.IEEE,71,967986(1983).

5.P.R.GrayandR.G.Meyer,AnalysisandDesignofAnalogIntegratedCircuits,2nded.Wiley,NewYork,1984.

6.R.GregorianandG.C.Temes,AnalogMOSIntegratedCircuitsforSignalProcessing,Wiley,NewYork,1986.

7.BangSupSongandP.R.Gray,IEEE,J.SolidStateCircuits,SC21(6),924933(1986).

8.T.C.Choi,R.T.Kaneshira,R.W.Broderson,P.R.Gray,W.B.Jett,andM.Wilcox,IEEEJ.SolidStateCircuits,SC18(6),652664(1983).

9.B.P.Brandt,D.E.Wingard,andB.A.Wooley,IEEEJ.SolidStateCircuits,SC26(4),618627(1991).

Page17

Chapter2MOSDevicesasCircuitElements

InthischapterthephysicsofMOS(metaloxidesemiconductor)devicesisdiscussedbriefly.Themostimportantandsimplestcurrentvoltagerelationsaregiven,andsimplemodelsintroducedforMOStransistorsinlinearoperation.Thediscussionhereisinthesimplestpossibleterms,aimedatprovidingsomephysicalunderstandingofthehighlycomplexdeviceoperationforthecircuitdesigner.Precisionanddepthhaveregretfullybeensacrificedintheprocess.Theambitiousreaderisreferredtotheexcellentspecializedworkslistedasreferencesattheendofthechapter.

2.1Semiconductors

Inmetals(e.g.,aluminum,copper,silver)thataregoodelectricalconductors,theatomsarearrangedinaregularcrystalarray.Theelectronsfromtheouter(valence)shelloftheatomsarefreetomovewithinthematerial.Sincethenumberofatoms,andthusthenumberoffreeelectrons,isverylarge(ontheorderof1023cm3),evenasmallelectricfieldresultsinalargeelectroncurrenthencethehighconductivityobservedforthesemetals.

Thepictureisquitedifferentforaninsulatorsuchassilicondioxide(SiO2).Herethevalenceelectronsformthebondsbetweenadjacentatomsandhencearethemselvestiedtotheseatoms.Thusnofreeelectronsareavailableforconductionandtheconductivityisverylow.

Semiconductors(suchassiliconorgermanium)areinbetweenconductorsandinsulatorsintheirelectricalproperties.Atverylowtemperatures,thevalenceelectronsareboundtotheiratoms,whichagainformaregularlattice.However,asthetemperatureisraised,duetothethermalvibrationsoftheatoms,somebondswillbebroken,andanelectronescapesfromeachofthesebonds.Suchelectronsare

Page18

capableofconductingelectricity.Furthermore,eachfugitiveelectronleavesachargedeficit(calledahole)behindinthebond.Avalenceelectroninabondclosetoaholecaneasilymoveover,fillingtheholeandleavinganewholeinitsownbond.Theeffectisthesameasiftheholehadmovedfromonebondtothenext.Sincethehole''moves"inadirectionoppositethatofthemovingvalenceelectron,inanelectronicfielditbehaveslikeapositivelychargedparticle.

Electricalconductionisthuspossibleforasemiconductoratroomtemperature.Thedensityofthermallygeneratedelectronsandholesis,however,muchsmallerthanthatofthefreeelectronsinmetal.Typicalnumbersare1010chargecarrierspercubiccentimeterforsiliconand1013ingermanium.Inwhatfollows,thecurrentlydominantmaterial,silicon,isdiscussedexclusively.

Addingforeignelements(dopants)tothepuresiliconcanraisethenumberoffreechargecarriersinasemiconductor.Silicon(andgermanium)hasfourvalenceelectrons.Ifanatomofanelementwithfivevalenceelectrons(suchasarsenic,phosphorus,orantimony)isaddedtothesemiconductor,itmaytaketheplaceofasiliconatominthecrystallattice.Thusfourofitsvalenceelectronswillparticipateinthefourbondstyingtheatomtoadjacentsemiconductoratomsinthelattice.Thefifthvalenceelectronoftheforeignatom,however,willnothaveaplaceinanybondandwillthusbefreetomoveawayfromitsparentatom.Hencesuchadopantelement(calledadonor,sinceitcontributesfreeelectronstothesemiconductor)enhancestheconductivityofthematerial.

Addingatomsofanelementwiththreevalenceelectronswillalsocontributetotheconductivity.Nowtherewillbeabondlackingavalenceelectronforeachdopantatom.Thuseachsuchatomcreatesonehole.Thesedopants(e.g.,boron,aluminum,andgallium)arecalledacceptors,sincetheholeswillpropagatebyacceptingboundvalenceelectronsfromadjacentsemiconductoratoms.

Indopedsemiconductorstherewillbecarriersduetothermaleffectsaswellastothedonor(oracceptor)atoms.Materialscontainingdonorswillthushavebothfreeelectronsandholes,buttherewillbemoreelectronsthanholes.Suchsemiconductorswillbecalledntype,wherenstandsfornegative.Materialscontainingacceptorswillhaveamajorityofholestheyarecalledptypesemiconductors,wherepstandsforpositive.

Asemiconductorstructurecanalsobefabricatedthatcontainstwoadjacentregionsofdifferenttypes(Fig.2.1).Thesurfacejoiningthetworegionsiscalledapnjunction.Whenthejunctionisfabricated,therandomthermalmotionofthe

Figure2.1Apnjunctiondiode.

Page19

Figure2.2Ionlayersinapnjunction.

majoritycarriers(electronsinthentyperegion,holesintheptyperegion)willcauseelectronstospilloverfromthentyperegiontotheptyperegion.Viceversa,holeswillmovefromtheptyperegiontothentypesemiconductor.Thusthisrandommotion(calleddiffusion)resultsintheptypesemiconductorbeingchargednegativelywhilethentyperegionischargedpositively.Theeffectwillbestrongestnearthejunction:There,intheptyperegion,thenegativelychargedacceptoratomswillnolongerbeneutralizedbyholes,and(inthentyperegion)freeelectronswillnolongersurroundthepositivelychargeddonorions.Henceinthisareaadipolelayeroffixedionswillbeformed(Fig.2.2).Theelectricfield compensateforthelargernumberofavailablemajoritycarriers.

Theequilibriumwillbeupsetifavoltagesourceisconnectedtothewiressolderedtothesemiconductor(Fig.2.3).Assumefirstthatthepolarityofthesourceissuchthatitmakesthepregionmorepositivewithrespecttothenregionthatis,v>0inFig.2.3.Thenvwillreduce causedby,say,abatteryofv=0.8Vcanresultinalargemajoritycarriercurrent(say,

Figure2.3Circuitfortestingapndiode.

Page20

Figure2.4Currentversusvoltagecharacteristics

ofapnjunctiondiode.

i=1A)inthecircuit.Hencevwiththepolarityindicatedwillbecalledforwardvoltageandiforwardcurrent.

Letusnowreversethepolarityofthevoltagesourcesothatv

Page21

saturationcurrentISflowsforadcvoltagev,andsinceadjacentpositive(+Q)andnegative(Q)chargesarestoredinthedepletionregion(Fig.2.3).Sincethechargestoredisanonlinearfunctionofv,thecapacitanceisnonlinear.WeshalldefinethecapacitanceCbytheincrementalrelationC=dQ/dv.Itcanthenbeshown[1,Sec.3.32,Sec.6.5]thatforthedeviceillustratedinFig.2.3,

holds.Here S 1.04pF/cmisthepermittivityofthesilicon S= 0KS,where 0isthepermittivityoffreespace( 0 8.861014F/cm)andKS 11.7isthedielectricconstant(alsocalledtherelativepermittivity)ofsilicon.AistheareaofthejunctioninsquarecentimetersandNa(Nd)isthenumberofacceptor(donor)atomspercubiccentimeter.NotethatCdecreaseswith|v|.Itcanbeshown[1,Sec.3.3]thatthequantityunderthesquarerootsignis( S/xd)2,wherexd(incentimeters)isthewidthofthedepletionregionhenceC= SA/xdholds.

2.2MOSTransistors[1,2,Sec.9.2]

ConsidernextthestructureshowninFig.2.5.Itisasandwichofseverallayers:Fromtoptobottom,itcontainslayersofmetal,silicondioxide(SiO2,anexcellentinsulator),ptypesilicon,andasecondmetallayerconnectedtoground.Itiscalledametaloxidesemiconductor(MOS)structure.Letvbenegativethenanelectricfieldwillbecreatedacrossthedioxidelayer,whichwillattractpositivecharges(holes)totheregionRunderthetopmetalelectrode(Fig.2.5).ThusnegativechargeswillbestoredinthetopmetalelectrodeandpositivechargesinR.ThedevicewillthusbehaveasacapacitorCofmagnitude

where oxisthepermittivityoftheSiO2,and ox= 0Kox 0.35pF/cm,whereKoxisthedielectricconstantofSiO2(Kox 3.9).Aistheareaofthetopelectrode,

Figure2.5Metaloxidesemiconductor

(MOS)structure.

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Figure2.6Capacitanceversusvoltagecharacteristics

ofanMOSstructure.

andlisthethicknessoftheSiO2layer.*TheptypeSilayerbetweenRandthebottommetallayerbehavesasaresistorhencetheoverallstructuresimulatesalossycapacitor.

Next,letvbeasmallpositivevoltageinFig.2.5.Theelectricfieldwillnowrepelholes.Asaresult,thefixednegativelychargedionsinRwillbeabandonedbythemobileholes,andanetnegativespacechargewillappearinR,whichisnowadepletionlayer.Thuschargeisagainstoredinthetopelectrodeandacapacitoriscreated.Forverysmallvaluesof Eq.(2.3)willremainvalidforthemagnitudeofthecapacitance.Asthevalueofvisincreased,however,thechargeinRbecomesgreatersincethedepletionregionwidens.Sincetheaverageionisnowfartherawayfromthesurface,theeffectivevalueoflinEq.(2.3)increasesandCdecreases.

Ifvisincreasedevenfurther,aneweffectappears.Sincethethermalgenerationofholesandelectronsoccurscontinuouslyinthesemiconductor,ifthefieldcreatedbyapositivevisstrongenough,itcanattractthermalelectronstoRthesewillthenmovetothesurface.Whenthisoccurs,thecapacitorstorespositivechargesinthetopelectrode,whilenegativeones(electrons)arestoredinthesurfacelayer.Thus,inEq.(2.3),lagainbecomestheSiO2thickness,andhenceChasthesamevalueasithadfornegativevoltagev.TheoverallbehaviorofCasafunctionofvisillustratedschematicallyinFig.2.6,whichalsogivesthenamesofthethreeoperatingregions.Thenamesofthefirsttwoareevidentthethirdoneiscalledtheinversionregion,since(duetothehighvoltagev)mobileelectronsareattractedintoR,whichthusbehavesasann(ratherthanap)typematerial.Itshouldbenotedthatsincethermalelectronsaregeneratedataslowrate,thevoltagevmustbepresentforsometimebeforetheinversionlayerisformedhenceitwillnotappearifvisahighfrequency(say,f>1kHz)signalratherthanaconstantvoltage.

ConsidernextthestructureshowninFig.2.7.Anewfeatureisthepresenceoftwon+(i.e.,heavilydopedntype)regionsintheptypematerial.TheoneontheleftwillbecalledthesourceavoltagevSisconnectedtoit.Then+regiononthe

*Often,theoxidethicknesslismeasuredinangstroms(1=108cm).Usualvaluesoflarebetween50and200.

Page23

Figure2.7MOStransistor.

rightwillbecalledthedrainitsvoltageisdenotedbyvD.ThetopmetalelectrodewillbecalledthegateitsvoltageisvG.Thebodyofthesemiconductorisusuallycalledthesubstrateorbulk.TheoveralldeviceistheMOStransistor.Itsoperationisdiscussedbrieflynext.

Letthesourcebegrounded,sothatvS=0.Also,letvDhaveasmallpositivevalue,say0.5V.WewillconsiderthebehaviorofthedraincurrentiDasvGisraisedfromzerotohigherpositivevalues.Sincethegateisinsulatedfromtherestofthedevicebytheoxidelayer,itwillnotconductanycurrent.Then+drainregionandthesurroundingptypesubstrateformapnjunction.Sincethesubstrateisgrounded,whilevD>0,thisjunctionisreversebiased.HenceforvG=0,iD 0.

AsvGisincreased,theregionRunderthegatewillfirstbedepleted,theninverted,asdiscussedearlierinconnectionwithFigs.2.5and2.6.WhenRisdepleted,iDremainszero,sincetheareaaroundthedrainisstillreversebiased.However,thesituationchangeswhenvGissolargethatinversionoccurs,sothatRisfilledwithelectrons.Now,alayercontainingmobileelectrons,calledaninversionlayerorchannel,connectsthedraintothesource.Sincethedrainispositivewithrespecttothesource,electronswillflowfromthesourcetothedrainandapositivecurrentiD>0willbeobserved.ThesmallestvoltagevGnecessarytoproduceachanneliscalledthethresholdvoltageandisdenotedbyVT.Usually,VTisgivenasthevGvalueneededforiD=1Aitmayrangefromafractionofavolttoseveralvolts.

ItshouldbenotedthatforthestructureofFig.2.7,mostoftheelectronsinthechanneldonotoriginatefromthermaleffectsinthebulkinstead,theyaredrawnbytheelectricfieldduetovGoutofthesource.Someelectronsarealsodrawnfromthedrainhowever,sincevD>0,thedrainsubstratejunctionismorereversebiased,andhenceitisharderforelectronstoescapefromthedrain.

SinceapotentialdifferencevDexistsbetweenthetwoendsofthechannel,theelectronsinthechannelwillbeattractedtothedrain.Therefore,inadditiontotherandomthermalmotionoftheelectrons,asteadymotion(calleddrift)willoccur,whichcausesthecurrentflow.ForsmallvD,thechannelwillthereforebehaveasaresistor,andhenceiD vD/R,wherethechannelresistanceRisgivenby

Page24

Figure2.8PinchoffinanMOStransistor.

HereListhelengthandWthewidthofthechannel,andnisthemobilityoftheelectronsinthechannel,*definedbytherelation(electrondriftvelocity)=(mobility)(electricfield).Finally,Qnisthechargedensity(inC/cm2)oftheelectronsinthechannel.SincevGcanbeconsideredasthesumoftwoterms,VT(necessarytomaintainthedepletionregionunderthechannel)andvGVT(necessarytomaintainthechannel),wehave

whereCox= ox/listhecapacitance(perunitarea)oftheoxidelayerseparatingthegatefromthechannel.Hence,forsmallvD( ),therelation

holds.Thusthetransistoractsasaresistor,withresistanceR=[nCoxW/L(vGVT)]1controlledbyvG.

IfvDisincreasedsothatitisnolongernegligiblecomparedtovG,Eq.(2.6)willbecomeinaccurate.SincethepotentialofthechannelatthegroundedsourceiszerowhileatthedrainitisvD,wecanassumethatitsaveragepotentialisvD/2.Hencetheaveragevoltagebetweenthegateandchannelis(vGvD/2).ReplacingvGby(vGvD/2)inEq.(2.6)gives

Equation(2.7)remainsagoodapproximationforvD

Page25

fied.Asthefigureindicates,duetothevariationofthepotentialalongthechannel,thechargedensityQndecreasesnearthedrain.IfvD=vGVT,atthedrainthegatetochannelvoltageisnolongersufficienttomaintainthechannel.Thusthedepletionregionsurroundingthesource,thechannel,andthedrainextendsallthewaytothesurface.Thisphenomenonissometimescalledpinchoff,andtheregionwhereitoccursisthepinchoffpoint(Fig.2.8).IfvDisincreasedfurther,thepinchoffpointwillmovetowardthesource,sincetheareawherevGvD VTwillincrease.Hencethechannelwillnowextendonlyfromthesourcetothepinchoffpoint,thelatterbeingsomewhereunderthegate.Theregionbetweenthepinchoffpointandthedrainisdepleted.Electronsfromthechannelareinjectedintothisdepletionregionatthepinchoffpointandareswepttothedrainbythefieldcreatedbythepotentialdifferencebetweenthedrainandthepinchoffpoint.Thevoltage isthusdividedbetweenthetwoseriesconnectedregions:thechannelbetweenthesourceandthepinchoffpoint,andthedepletionregionbetweenthepinchoffpointandthedrain.Clearly,thelatterhasahigherresistance,andhencemostofvDSinfactappearsacrossit.AnyincreaseofvDwill,toagoodapproximation,resultinanequalvoltageincreaseacrossthedepletionregionandwillhardlychangeiD.Thus,forvDvGVT,fromEq.(2.7),

ThisphenomenoniscalledsaturationvDsat=vGVTisthedrainsaturationvoltageandiDsatasgivenbyEq.(2.8),isthedrainsaturationcurrent.

Thedraincurrentdoes,inreality,increasesomewhatwithincreasingvD.ThiscanbeattributedtothemoveofthepinchoffpointtowardthesourceforincreasingvDandhencetotheshortenedchannelasEq.(2.8)indicates,iDincreasesasLisreduced.Asanapproximation,thiseffect(oftencalledchannellengthmodulation)canbeincludedintheformulaforiD(vD)intheformofanaddedfactor(1+lvD).HerelisadeviceconstantthatdependsonL,onthedopingconcentrationofthesubstrate,andonthesubstratebias(discussedinthenextsection).ForL 10mm,typicallyl 0.03V21generally,l~1/L.

Itisusualtointroducetheabbreviations ThenthesaturationcurrentgivenbyEq.(2.8)becomes

whichincorporateschannellengthmodulation.Figure2.9showsthevariationofiDwithvGforconstantvD.Figure2.10illustratesitsdependenceonvDforvariousvGvalues,wherevG1,vG2,vG3.

AllderivationsofthissectionwereperformedforthestructureshowninFig.2.7,whosesource,drain,andchannelwereallntype.ThisdeviceiscalledannchannelMOS,orNMOStransistor.Asimilararrangementcanbeconstructedbycreatingp+drainandsourcediffusionsinanntypesubstrate.NowanegativevGisneededtocreateaptypechannelunderthegate,andanegativevDisusedto

Page26

Figure2.9Draincurrentversusgatevoltage

characteristicsofanMOStransistor.

attracttheholesinthechanneltothedrain.Also,iDwillbenegativeifthereferencedirectionofFig.2.7isused.TheresultingdeviceiscalledapchannelMOSorPMOStransistor.Formulas(2.3)to(2.9)remainvalidifsomesmallchangesaremade.Themobilitynofelectronsmustbereplacedbyp,theholemobilityinthechannel.Aswouldbeexpectedfromthemoreelaboratemechanismofholeconduction,p

Page27

Figure2.11Transistorsymbols.

ThecircuitsymbolsusedforNMOSandPMOStransistorsareshowninFig.2.11aandb,respectively.Ifthetypeisunimportant,thesimplifiedsymbolofFig.2.11cmaybeusedforbothNMOSandPMOSdevices.

Sincetheoperationofthedevicesdescribedinthissectionisdependentontheelectricfieldinducedbythegatevoltage,theyarecalledfieldeffectdevices(FETs),orMOSFETs.*

SincePMOStransistorsaremoreeasilyfabricatedthanNMOStransistors,theywereinitiallypredominant.However,later,whenthetechniquesforthereliableproductionofNMOSdevicesweredeveloped,thelatterbecamestandard.Themainreasonforthisisthehighermobilityofelectrons,whichmakestheNMOStransistorsfasterthanPMOStransistors.

2.3MOSTransistorTypes:BodyEffect

TheMOStransistorsdescribedinSection2.2,bothNMOSandPMOStypes,shareseveralfeatures.Inthestructure,thegateisinsulatedelectricallyfromtherestof

*Sincethechargecarriershereareeitherelectronsorholes(notboth),FETsarealsosometimescalledunipolardevices,tocontrastthemwithbipolartransistors,inwhichbothelectronandholecurrentsexist.

Page28

Figure2.12Symbolsfordepletionmodetransistors.

thedevicebytheSiO2layerunderit.Henceitisoftencalledaninsulatedgatefieldeffecttransistor(IGFET).Also,thevoltagevGinducesandenhancesthedraincurrent.Thusthedevicesdescribedoperateintheenhancementmode.

ItisalsopossibletofabricateanMOStransistorthatconductsdraincurrentwhenvG=0.Forexample,anntypelayercanbeintroducedbydoping,whichconnectsthesourceanddrainofanNMOSdevice.Withsuchadopedchannel,thefieldofthegateisnotneededtoproduceaninversionlayertheregionR(Fig.2.7)nowhasa''builtin"conductingntypechannel.

However,ifanegativegatevoltageisapplied,thefieldthuscreatedwillrepelelectronsandcreateadepletionlayerinthechanneladjacenttotheSiO2surface,therebyreducingtheconductivityandthusthedraincurrent.Ifthemagnitudeofthenegativegatevoltageissufficientlylarge,thechannelbecomescompletelydepletedandiD 0results.ThevaluevGatwhichthisoccursisagaincalledthresholdvoltageandisdenotedbyVT.Now,however,VT0,byestablishingaptypedopedchannel.

Therelations(2.6)to(2.11)remainvalidfordepletionmodedevicesifthevalueandsignofVTischosenappropriately,asdescribedabove.TwosymbolsoftenusedtodenotedepletionmodeMOSFETsareshowninFig.2.12.

Atotallydifferentstructurecanalsobeusedtoproduceadepletionmodefieldeffecttransistor(Fig.2.13).Here,alightlydopedntypelayer(channel)connectsthen+sourceanddrainregionsandthegateisap+regionimplantedinthislayer.Hence,forvS=vG=0andvGD>0,adraincurrentwillflow.IfvGismadenegative,thep+implantactingasthegatewillbesurroundedbyadepletionlayerthegreater|vG|,thedeeperthelayer.Themobileelectronsinthechannelcannot

Figure2.13Junctionfieldeffecttransistor.

Page29

enterthisdepletionlayer,ortheonealongthepnjunctionbetweenthechannelandthesubstrate.Hencetheeffectivecrosssectionofthechannelisreducedas|vG|isincreased.AtsomevaluevG=VP(VP

Page30

TABLE2.1.KeyUnitsandConstantsforMOSTransistors

Thisphenomenon,thebodyeffect,isamajorlimitationofMOSdevicesoperatedwithvS vBitsevilinfluencewillbelamentedrepeatedlylaterinthebook.AsEqs.(2.12)and(2.13)show,toreducethebodyeffect,Nimpshouldbemadesmall.However,forverysmallNAvalues(say,NA

Page31

TABLE2.2.DrainCurrentRelationsforMOSFETsinLargeSignalLowFrequencyOperation

Page32

Inthefollowingdiscussion,weconcentrateonthelinearizedapproximationandmodelingprocessforMOSFETsoperatingintheirsaturationregions,whichistheusualconditionforlinear(analog)operation.Afterward,wegiveabriefoverviewofthelinearizationandmodelingfordevicesthatoperateintheirtriode(nonsaturated)orcutoffregion.AssuminganNMOStransistor,andcombiningEqs.(2.9)and(2.12),therelation

results.Hereweused wecanwrite

Here( iD/ vGS)0andsoondenotethepartialderivativesevaluatedatthebiaspoint. iDisthedeviation(increment)ofiDfromitsbiasvalue vGS, vDS,and vSBaretheincrementsofvGS,vDS,andvSB.AlldeviationsmustbesmallforEq.(2.15)tohold.Ifonlytheincremental(smallsignalac)componentsareofinterest,Eq.(2.15)canbewrittenas

Figure2.14LowfrequencyequivalentcircuitofaMOSFET.

Page33

where

Heregdisthe(incremental)drainconductancegmandgmbaretransconductancesthatcanberepresentedbyvoltagecontrolledcurrentsources(VCCSs).Henceanequivalentcircuitmodel,showninFig.2.14,canbeconstructed.Thevaluesofgm,gmb,andgdcanbefoundfromEq.(2.14):

Hence,toagoodapproximation,gmandgmbareproportionalto

TheotherimportantcomponentsofthecompletesmallsignalmodeloftheMOSFETarethecapacitorsrepresentingtheincrementalvariationsofstoredchargeswithchangingelectrodevoltages.Theseplayanimportantroleinthehighfrequencyoperationofthedevice.TheintrinsiccomponentsoftheterminalcapacitancesoftheMOSFETdevices(associatedwithreversebiasedpnjunctionsandwithchannelanddepletionregions)arestronglydependentontheregionofoperation,whiletheextrinsiccomponents(duetolayoutparasitics,overlappingregions,etc.)arerelativelyconstant.Assumingagainthatthetransistoroperatesinthesaturationregion,itcanbeassumedthatthechannelbeginsatthesourceandextendsovertwo

Page34

thirdsofthedistancetothedrain.Inthisregionofoperation,themostimportantcapacitancesarethefollowing:

1.Cgd:GatetoDrainCapacitance.Thisisduetotheoverlapofthegateandthedraindiffusion.Itisathinoxidecapacitance,andhencetoagoodapproximationcanberegardedasbeingvoltageindependent.

2.Cgs:GatetoSourceCapacitance.Thiscapacitancehastwocomponents:Cgsov,thegatetosourcethinoxideoverlapcapacitance,and isnearlyvoltageindependentinthesaturationregion.

3.Csb:SourcetoSubstrateCapacitance.Thiscapacitancealsohastwocomponents:Csbpn,thepnjunctioncapacitancebetweenthesourcediffusionandthesubstrate,and whichcanbeestimatedastwothirdsofthecapacitanceofthedepletionregionunderthechannel.TheoverallcapacitanceCsbhasavoltagedependencewhichissimilartothatofanabruptpnjunction.

4.Cdb:DraintoSubstrateCapacitance.Thisisapnjunctioncapacitanceandisthusvoltagedependent.

5.Cgb:GatetoSubstrateCapacitance.Thiscapacitanceisusuallysmallinthesaturationregionitsvalueisaround0.1COX.

Figure2.15illustratesthephysicalstructureofanNMOStransistorandthelocationsofthecapacitancesinthecutoff(Fig.2.15a),saturation(Fig.2.15b),andnonsaturationortriode(Fig.2.15c)regions.Table2.3liststheterminalcapacitorsoftheNMOSdeviceandtheirestimatedvaluesinthethreeregionsofoperation.ThenotationsusedarethoseshowninFig.2.15atoc.Figure2.16depictsthecompletehighfrequency(ac)smallsignalmodeloftheMOSFET.InanalyzingthesmallsignalbehaviorofMOSFETs,themodelofFig.2.14canbeusedifonlylowfrequencysignalsarepresentifthecapacitivecurrentsarealsoofinterest,thecircuitofFig.2.16mustbeapplied.

FromthemodelsofFigs.2.14and2.16andaccompanyingdiscussions,anumberofgeneralstatementscanbemadeaboutthedesirableconstructionofaMOSFET:

1.Forhighacgain,gmshouldbelarge.Thiswillbethecase,byEq.(2.18),if shouldbeaslargeastheallowabledcpowerdissipationpermits.

2.AsthenegativesigninEq.(2.19)indicates,thebodyeffectreducesthegain.Tominimizegmb,byEqs.(2.19)and(2.13),weneedlargeCOX,smallNimp(i.e.,lightlydopedsubstrate),andalargebiasvoltage forthesource.

Page35

Figure2.15ParasiticcapacitancesinMOSFETinthe(a)cutoffregion,(b)saturationregion,and(c)trioderegion.

(Ofcourse,ifvSBisconstant,noincrementalbodyeffectoccursandtheserequirementsareirrelevant.)

3.Ideally,theMOSFETinsaturationshouldbehaveasapurecurrentsource.Hence,asFig.2.14illustrates,gdshouldbesmall.ByEq.(2.20)thisrequiresasmallbiascurrent andasmall .Since isintroducedbychannellengthmodulation,itcanbereducedbyincreasingLandalso[1,Sec.8.4]byincreasingNimp.AsummaryoftheformulasderivedinthissectionisgiveninTable2.4.

Page36

TABLE2.3.TerminalCapacitancesofaMOSFETintheThreeMainRegionsofOperationa

Page37

Figure2.16HighfrequencyequivalentcircuitofaMOSFET.

Next,wediscussbrieflythelinearmodelofaMOSFETthatisbiasedinitsnonsaturated(triode)region.Usually,suchadeviceisusedasaswitchthatisopenedorclosed(turnedonoroff)byalargegatevoltageorasafairlylinearlargevaluedvariableresistor.Hence,herewederiveitsmodelonlytoanalyzeitsbehaviorinsuchapplications.WeassumethatvGSisconstantandthat andhencenegligible.UndertheseconditionsitcanbeseenfromEq.(2.7)thatwhenthedeviceconductsdraincurrent,itbehaveslikearesistorconnectedbetweenthedrainandsourceterminals.TheequivalentsmallsignaldraintosourceresistanceforthecaseofvDSnearzeroisgivenby

andisthuscontrolledbythegatevoltageoverdrive

Inhighfrequencyapplication,thedevicecapacitancesmustalsobeincludedinthemodel.AsimpleequivalentcircuitisshowninFig.2.17.Sincenowacontinuouschannelextendsfromthesourcetothedrain,thegatetochannelcapacitanceC'gsisconnectedtoboththedrainandthesource.Anaccuratehighfrequencyrepresentationofthechannelshouldincludeadistributedresistivelineextendingfromthesourcetothedrainandcapacitivelycoupledtoboththegateandthesubstrate.However,asafirstapproximation,C'gscanbetreatedasalumpedcapacitancepartitionedequallybetweenCgsandCgd,asindicatedinthelastrowofTable2.3.

Finally,ifthedeviceiscutoff,nochannelexistsandthemodelcontainsonly

Figure2.17HighfrequencymodelofaMOSFETinitstrioderegion.

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TABLE2.4.SmallSignalParametersofMOSFETSinSaturationa

aSeeFig.2.16.| vDS| 1isassumedinallformulas.

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Figure2.18HighfrequencymodelofaMOSFETinitscutoffregion.

thecapacitances,withthevalueslistedinthefirstrowofTable2.3.AsimplifiedmodelofaMOSFETinthecutoffregionisshowninFig.2.18,wherethedrainsourceresistanceisinfinityandCgsandCdscapacitorsareduetogateoverlapandfringingcapacitances.ThegatetosubstratecapacitanceCgdinthecutoffregionis,however,highlynonlinear,andforthegatetosourcevoltagearoundzeroitsvalueisapproximatelyequaltoWL'Cox,whereL =L2LovandLovisthelengthoftheoverlapbetweenthegateandthesourcedraindiffusionregions.

2.5WeakInversion

ThetriodeandsaturationregionsofoperationdiscussedearlierinthischapterassumethatthedeviceisoperatedinstronginversionandVGSVT 100mV(foranNMOStransistor).IfVGSVT

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2.6ImpactIonization[4]

OneofthesevereproblemsinsubmicronMOStechnologiesoperatingatsupplyvoltagesaround5Visimpactionization.Figure2.19illustratesannchannelMOSdevicecrosssectionshowingtheimpactionizationcurrentflowandtheIVcharacteristicasaresultofimpactionization.Asdepictedinthefigure,whenthedraintosourcevoltageisincreased,thestrengthoftheelectricfieldatthedrainendofthechanneleventuallybecomeshighenoughtoinducesignificantimpactionizationcurrentwhichoriginatesfromthedraindepletionregionandflowsintothesubstrate.Oncethishappensthecurrentthatflowsintothedrainterminalhastwocomponents.OnecomponentistheMOStransistorchannelcurrentthatflowsfromthedraintothesource,andtheotheristheimpactionizationcurrentthatflowsfromthedraintothesubstrate.Theimpactionizationcurrentisnotafunctionofthetransistorchannellength,andthemagnitudeofthecurrentisnotreduceddramaticallysimplybymakingthelengthlonger.Thecurrentislargelydeterminedbythepeakelectricfield,whichinturnisafunctionofthegateoxidethickness,drainjunctiondepth,dopingconcentrationinthesubstrate,thevoltagebetweenthedrainterminalandthedrainendofthechannelregion,andthegatetodrainvoltage.Intechnologieswithfeaturesizesintherangeof2m,forannchannelMOSdevice,theimpactionizationcurrentequals1%ofthedraincurrentwhenthevoltagebetweenthedrainandthedrainendofthechannelisintherange4to9V,andthedeviceisbiased

Figure2.19(a)AnnchannelMOSdevicecrosssectionshowingimpactionizationcurrentflow(b)IVcharacteristic

observedasaresultofimpactionization.

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inthesaturationregion.InpchannelMOSdevicestheeffectoccursatsubstantiallyhigherfieldstrengths.

Theimpactionizationhasseveralpotentiallydamagingsideeffects.OneseriousnegativeconsequenceshowninFig.2.19bisdegradationofthetransistoroutputimpedance,whichresultsinreducedgaininamplifierstagesthatusetransistorsasactiveloads.Onewaytodealwiththisproblemisthroughcircuittechniques,whereashieldingnchanneldeviceisplacedinserieswiththetransistor,preventingitfromhavingaVdSgreaterthanhalfthesupplyvoltage[4].Theseconddamagingeffectisthepossibilityoftriggeringlatchupduetotheohmicdropinducedbytheionizationcurrentthatflowsintothesubstrate.Latchupisaphenomenoncausedbytheparasiticlateralpnpandnpnbipolartransistorscreatedonthechip.Thecollectorsofeachtransistorfeedtheother'sbase,andthiscreatesanunstabledevicesimilartoapnpnthyristor[5].Thiscausesasustaineddccurrentthatmaycausethechiptostopfunctioningandmayevendestroyit.Latchupmaybepreventedbypropersubstratestrappingandusingguardringstosurroundsomecriticaltransistorsonthechip.Anotherstrategyistoreducethesubstrateresistance.Inthismethodthepandnchanneltransistorsareformedinalightlydopedepitaxiallayerthatisgrownonalowresistivitysubstrate.Finally,thethirdserioussideeffectofimpactionizationisthethresholdshiftoftheMOSdeviceduetothecontinuousoperationintheimpactionizationmode.Thisphenomenonisduetothehighelectricfieldwhichcreateshighenergycarriesthatcanbetrappedinthegateoxide,resultinginlongtermthresholdshift.Severalprocessmodificationshavebeenproposedthatareeffectiveatraisingthevoltageatwhichimpactionizationbecomesaproblem.Onetechniqueistolowertheimpuritygradientinthedrainjunctionusinglightlydopeddrain(LDD)structures.

2.7NoiseinMOSFETs

Therearethreedistinctsourcesofnoiseinsolidstatedevices:shotnoise,thermalnoise,andflickernoise.

ShotNoise

Sinceelectriccurrentsarecarriedbyrandomlypropagatingindividualchargecarriers(electronsorholes),superimposedonthenominal(average)currentI,thereisalwaysarandomvariationinS.Thisisduetofluctuationinthenumberofcarrierscrossingagivensurfaceintheconductorinanytimeinterval.ItcanbeshownthatthemeansquareofinSisgivenby

whereq=1.61019Cisthemagnitudeoftheelectronchargeand fisthebandwidth.Thisformulaonlyholds,however,ifthedensityofthechargecarriersissolowandtheexternalelectricfieldissohighthattheinteractionbetweenthe

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Figure2.20Thermalnoiseinaresistor:(a)noisyresistor

(b)and(c)equivalentcircuits.

carriersisnegligible.Otherwise,therandomnessoftheirdensityandvelocityisreducedduetothecorrelationintroducedbytherepulsionoftheircharges.ThenoisecurrentisthenmuchsmallerthanpredictedbyEq.(2.24).

InaconductingMOSFETchannel,thechargedensityisusuallyhighandtheelectricfieldislow.Therefore,Eq.(2.24)doesnothold.Thenoisecurrentduetorandomcarriermotionsishencebetterdescribedasthermalnoise,whichisdiscussednext.

ThermalNoise

InarealresistorR,theelectronsareinrandomthermalmotion.Asaresult,afluctuatingvoltagevnTappearsacrosstheresistorevenintheabsenceofacurrentfromanexternalcircuit(Fig.2.20a).ThustheThveninmodelofthereal(noisy)resistoristhatshowninFig.2.20b.Clearly,thehighertheabsolutetemperatureToftheresistor,thelargervnTwillbe.Infact,itcanbeshownthatthemeansquareofvnTisgivenby

HerekistheubiquitousBoltzmann'sconstant,and fisthebandwidthinwhichthenoiseismeasured,inhertz.(Thevalueof4kTatroomtemperatureisabout1.661020VC.)

IfEq.(2.25)wastrueforanybandwidth,theenergyofthenoisewouldbeinfinite.Infact,however,forveryhighfrequencies( 1013Hz)otherphysicalphenomenaenter,whichcause todecreasewithincreasingfrequencysothattheoverallnoiseenergyisfinite.

Theaveragevalue(dccomponent)ofthethermalnoiseiszero.Sinceitsspectraldensity isindependentoffrequency(atleastforlowerfrequencies),itisawhitenoise.Clearly,Fig.2.20bmayberedrawnintheformofaNortonequivalentthatisasa(noiseless)resistorRinparallelwithanoisecurrentsourceinT(Fig.2.20c).Thevalueofthelatterisgivenby

whereG=1/R.

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Figure2.21Equivalentmodelsofthe

thermalnoiseinaMOSFET.

SincethechannelofaMOSFETinconductioncontainsfreecarriers,itissubjecttothermalnoise.Therefore.Eqs.(2.25)and(2.26)willhold,withRgivenbytheincrementalchannelresistance.Thenoisecanthenbemodeledbyacurrentsource,asshowninFig.2.21a.Ifthedeviceisinsaturation,itschanneltapersoff(Fig.2.8)andtheapproximationR 3/2gmcanbeusedinEq.(2.26).

InmostcircuitsitisconvenienttomodeltheeffectofinTcausedbyavoltagesourceconnectedtothegateofan(otherwisenoiseless)MOSFET(Fig.2.21b).This''gatereferred"noisevoltagesourceisthengivenby

BothinTandvnTdependthusonthedimensions,biasconditions,andtemperatureofthedevice.Asanexampleoftheirordersofmagnitude,foratransistorwithW=200m,L=10m,andCox=4.34108F/cm2(correspondingtoanoxidethicknessof800)whichisoperatedinsaturationatadraincurrentiD=200A,thegatereferrednoisevoltageatroomtemperatureisabout

Ifthedeviceisswitchedoff,Rbecomesveryhigh,andtheequivalentnoisecircuitwillbeacurrentsourcewithavaluegivenbyEq.(2.26).Clearly, isverysmallhenceforusual(lowormoderate)externalimpedancelevels,theMOSFETcanberegardedasanoiselessopencircuitifitisturnedoff.

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Flicker(1/f)Noise

InanMOStransistor,extraelectronenergystatesexistattheboundarybetweentheSiandSiO2.Thesecantrapandreleaseelectronsfromthechannel,andhenceintroducenoise[6,7].Sincetheprocessisrelativelyslow,mostofthenoiseenergywillbeatlowfrequencies.Asbefore,apossiblemodelofthisnoisephenomenonisacurrentsourceinparallelwiththechannelresistance.Thedcvalueofnoisecurrentisagainzero.ItsmeansquarevalueincreaseswithtemperatureandthedensityofthesurfacestatesitdecreaseswiththegateareaWLandthegateoxidecapacitanceperunitareaCox.Fordevicesfabricatedwitha"clean"process,thegatereferrednoisevoltageisnearlyindependentofthebiasconditionsandisgivenbytheapproximatingformula

HereKdependsonthetemperatureandthefabricationprocessatypicalvalue[8,p.31]is31024V2F.Forthetransistordescribedintheprecedingexample,theformulagivesanoisevoltageof

Thenoiseprocessdescribedisusuallycalledflickernoiseor(inreferencetothe1/ffactorin 1/fnoise.Astheexamplegivenillustrates,atlowfrequencies(say,below1kHz)itisusuallythedominantnoisemechanisminaMOSFET.

Inconclusion,thechannelnoiseinaMOSFETcanbemodeledbyanequivalentnoisecurrentgenerator,asinFig.2.21a.InthesmallsignalmodelthisgeneratorwillbeinparallelwiththecurrentsourcesgmvGSandgmbvBS(Fig.2.16).Itsvaluecanbechosenastherootmeansquare(RMS)noisecurrent,whichfromEqs.(2.26)(2.28)is

Notethatthemeansquaresofthenoisecurrentsareadded,sincethedifferentnoisemechanismsarestatisticallyindependent.Alternatively,thenoisecanberepresentedbyitsgatereferredvoltagesource(Fig.2.21b),inserieswiththegateterminal.Thevalueofthesourceisin/gm,withingivenbyEq.(2.29).

2.8CMOSProcess

TheCMOSprocessprovidesthemostflexibilitytothecircuitdesigner,duetotheavailabilityofcomplementaryMOSdevicesonthesamechip.TheoriginalmotivationfordevelopingtheCMOStechnologywastheneedforlowpowerandhighspeedlogicgatesfordigitalcircuits.Therequiredisolationbetweenthetwodifferentdevicetypesisaccomplishedbytheuseof"wells,"thatis,large,lowdopingleveldeepdiffusions,whichserveasthesubstratesforoneofthetwodevicetypes.Asanexample,Fig.2.22showspartofannwellCMOSchip,wherehighresistivityptypesubstrateisusedforthenchanneldevices,anddiffusednwellsforthepchanneldevices.

Page45

Figure2.22Devicestructurefabricatedinahighperformance

nwellCMOSprocess.

Aswillbeshowninlaterchapters,aCMOScircuitcanbeoperatedwithasinglepowersupply,anditcanbeusedtorealizehighspeed,highgain,lowpoweranalogamplifierstages.Anadditionaladvantageisthatforthedevicesinthewell(inFig.2.22,thePMOStransistor),thesourcecanbeconnectedtothewell,therebyeliminatingthebodyeffect,andifthedeviceisusedinanamplifier,increasingthegainofthecircuit.This,however,resultsinalargestraycapacitancebetweenthesourceandthesubstrate,duetothelargesizeofthewelltobodyinterface.AnotherimportantadvantageoftheCMOSprocessistheavailabilityoftransmissiongatesmadeofaparallelconnectionofcomplementarytransistorsthatcanbeusedasswitches.Whensuchtransmissiongatesareused,thesignalisnolongerlimitedtoalevel,whichisathresholdvoltagebelowthatofthehighclocksignal,asisthecasewhensinglechannelswitchesareused.Inaddition,inCMOSchipsabipolartransistorcanbefashionedfromasourcediffusion,thewell,andthesubstrate.Thiscanbeusedinanemitterfollowerbufferstage(describedlater),inabandgapvoltagereferencecircuit,andsoon.

Inadditiontotransistors,analogMOScircuitsusuallyrequireonchipcapacitors,andsometimesalsoonchipresistors.Inasilicongate"doublepoly"process,asecondlayeroflowresistivitypolysiliconisavailableforuseasaninterconnectorfortheformationofafloatinggateformemoryapplications.Thesetwolayersofpolysiliconcanalsobeusedasthetopandbottomelectrodesofamonolithiccapacitor.Figure2.22showstheconstructionofacapacitorwithtwopolysiliconelectrodes.ResistorscanbecreatedonanMOSchipusingadiffusedorimplantedlayeronthesurfaceofthesubstrate.Sincethesheetresistanceoftheseresistivelayersisrelativelylow(typically25to70 forasquarelayer),thesizeoftheresistorsobtainableonareasonablysmallareaislimitedtoabout100k .Thehigherresistivitywelldiffusionisalsoavailableasaresistor.Thisresistor,however,hasmuchhighervoltageandtemperaturecoefficientscomparedtodiffusedorimplantedones.

Problems

2.1.Apnjunctiondiodeisconnectedtoanexternalvoltagevintheforwarddirection(Fig.2.3).Reversingthepolarityofthevoltagereducesthecurrentbyafactor

Page46

Figure2.23CircuitforProblem2.8.

106.AssumethatthediodesatisfiesEq.(2.1)andisatroomtemperature.Whatisv?

2.2.Forapnjunction(Fig.2.3),NA=ND=1016ions/cm3,|v|=5V,A=0.34mm2,andthemeasuredvalueofCis27pF.Howmuchisxd,thewidthofthedepletionlayer?Howmuchis i?

2.3.UsingthedefinitionR=1/( iD/ VDS),calculatethechannelresistanceofanNMOStransistorfrom(a)Eq.(2.6),(b)Eq.(2.7),and(c)Eq.(2.9).

2.4.ForanNMOStransistor,n=103cm2/Vs,thethicknessofthegateoxideis103(1=108cm),W=25m,andL=5m.Thethresholdvoltageis4V.CalculateiDforvS=vB=0VandvG=6V,and(a)vD=0.1V,(b)vD=2V,and(c)vD=4V.

2.5.RepeatthecalculationsofProblem2.4ifvS=0,vB=3V,and p=0.3V.Whatconclusionscanyoudrawfromyourresultsregardingthebodyeffect?

2.6.ForanNMOStransistor,k =2A/V2,W=30m,L=10m, p=0.3V, =1.5V,and =0.03V1.Findtheincrementalconductancesgm,gd,andgmbforvSB=0V,v0DS=5V,andi0D=10A.RepeatyourcalculationsforvSB=2V!

2.7.AnNMOSswitchtransistorhasagatetosourcevoltagevGS>VT.Itsdrainisopencircuited.HowmuchisvDS?Why?

2.8.InthecircuitofFig.2.23,theswitchSisopenedatt=0.(a)Isthetransistoroperatinginitslinearorsaturationregion?(b)Neglectingbodyeffectandchannellengthmodulation,findv(t)bysolvingtheappropriatedifferentialequationforthecircuit.

2.9.InthecircuitofFig.2.24anoisevoltagevnisgeneratedduetothermaland

Figure2.24CircuitforProblem2.9.

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Figure2.25CircuitforProblem2.10.

shotnoiseeffects.ForwhatvalueofRwillthetwonoisevoltagesvnTandvnSbeequal?

2.10.Calculatetheincrementalimpedance v/ iseenatnodeAofthecircuitsshowninFig.2.25.

2.11.ShowthatthetransconductancegminthesaturationregionisequaltothedrainconductanceinthetrioderegionforagivendeviceandafixedVG.

References

1.R.S.MullerandT.I.Kamins,DeviceElectronicsforIntegratedCircuits,Wiley,NewYork,1977.

2.A.S.Grove,PhysicsandTechnologyofSemiconductorDevices,Wiley,NewYork,1967.

3.Y.P.TsividisandR.W.Ulmer,ACMOSvoltagereference,IEEEJ.SolidStateCircuits,SC13(6),774778(1978).

4.C.A.Laber,C.F.Rahim,S.F.Dryer,G.T.Uehara,P.T.Kwoh,andP.R.Gray,IEEEJ.SolidStateCircuits,SC22(2),181189(1987).

5.S.M.Sze(Ed.),VLSITechnology,McGrawHill,NewYork,1983.

6.M.B.DasandJ.M.Moore,IEEETrans.Electron.Devices,ED21(2),247257(1974).

7.P.R.GrayandR.G.Meyer,AnalysisandDesignofAnalogIntegratedCircuits,Wiley,NewYork,1977.

8.P.R.GrayandD.A.Hodges,andR.W.Brodersen(Eds.),AnalogMOSIntegratedCircuits,IEEEPress,NewYork,1980.

Page48

Chapter3BasicAnalogCMOSSubcircuits

InthischaptersomeofthebasicsubcircuitscommonlyutilizedinanalogMOSintegratedcircuitsareexamined.Theseblocksincludeavarietyofbiascircuits,currentmirrors,singlestageamplifiers,sourcefollowers,anddifferentialstages.Thesesubcircuitsaretypicallycombinedtosynthesizeamorecomplexcircuitfunction.Theoperationalamplifierandcomparator,coveredinlaterchapters,areexamplesofhowsimplesubcircuitsarecombinedtoformmorecomplexfunctions.

ThefirstpartofthischaptercoversthesubjectofthebiascircuitsinCMOStechnologyandthecurrentmirrors.Next,theCMOSgainstageisintroduced,withparticularemphasisontheuseofactivedevicesasactiveloads.Thecurrentmirrorsubcircuitcoveredasabiasingelementisutilizedasadynamicloadtoobtainveryhighvoltagegainsfromasinglestageamplifier.Thedifferentialamplifier,whichrepresentsabroadclassofcircuits,isdiscussednext.Thedifferentialamplifierisoneofthemostwidelyusedgainstages,whosebasicfunctionistoamplifythedifferencebetweentwoinputsignals.Finally,thelastpartofthechapterdealswiththesmallsignalanalysisandfrequencyresponseofCMOSamplifierstages.AgoodunderstandingofthetopicspresentedinthischapterisessentialfortheanalogCMOSdesigner,asmostdesignsstartatthesubcircuitlevelandprogressupwardtorealizeamorecomplexfunction.

3.1BiasCircuitsinMOSTechnology

Opampandamplifierstages,describedindetaillater,needvariousdcbiasvoltagesandcurrentsfortheiroperation.Anidealvoltageorcurrentbiasisindependentofthedcpowersupplyvoltages(VDD>0andVSS 0)andoftemperature.

ToobtainthedcbiasvoltagesVo1,Vo2,...,Von,whereVSS

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Figure3.1(a)DiodeconnectedNMOStransistor(b)currentvoltage

characteristicofdiodeconnectedtransistor.

Von

Page50

andVSS=0ischosen.SinceVGS=VDShereforbothdevices,theconditionforsaturation,

issatisfied.Hencethecommonvalueofthedraincurrentsisgivenapproximatelyby

HereIbiasisusuallyspecifiedthenVo1andVo2canbeselectedandEq.(3.3)usedtofindtheW/LratiosofthedevicesandthevalueRoftheresistor.

AnundesirablefeatureofthisconfigurationisthatthebiasvoltagesandcurrentdependonthesupplyvoltagesVDDandVSS.Infact,thebiascurrentincreasesrapidlywithincreasingpowersupplyvoltage.Sincesuchbiasstringsareusedtoprovidebiasforotherdevicesinthecircuit,thedcpowerconsumptionoftheoverallcircuitbecomesheavilydependentonthesupplyvoltages.

ACMOScircuitwith(theoretically)perfectsupplyindependenceisshowninFig.3.3.IfQ3andQ4arematchedtransistorssothat(W/L)3=(W/L)4,theyideallycarryequalcurrents.Choosing(W/L)1=(W/L)2willthenresultinVGS1=VGS2,

Figure3.3VTreferencedsupplyindependentCMOS

biassource.

Page51

andthevoltageacrosstheresistor,IbiasR,willbeequaltoVGS0.Thisequilibriumconditionleadstotheequation

Equation(3.4),whichisindependentofVDD,canbesolvedtoobtainIbias.Notethatinthisanalysisweneglectedtheeffectsofchannellengthmodulation(i.e.,weassumedthatIDisindependentofVDS).

AnalternativeversionofthebiascircuitshowninFig.3.3thatusesthebaseemittervoltage(VBE)ofabipolartransistorasthereferencevoltageisshowninFig.3.4a.InaCMOSprocess,thesubstrate,well,andthesourcedrainjunctioninsidethewellcanbeusedtoformaverticalbipolartransistor.Forexample,Fig.3.4b

Figure3.4(a)VBEbasedsupplyindependentbiascircuit(b)verticalpnpbipolartransistorinannwell

CMOSprocess.

Page52

showsaverticalpnpdevicethatisformedinannwellprocess.Thecollectorofthispnpdeviceisthepsubstratethatispermanentlyconnectedtothemostnegativevoltageonthechip.Forthebipolartransistor,thecollectorcurrentisgivenby

whereVBEisthebaseemittervoltage,VT=kT/q,andIsisaconstantcurrent,whichisproportionaltothecrosssectionalareaoftheemitter,whichisusedtodescribethetransfercharacteristicofthetransistorintheforwardactiveregion.

InFig.3.4a,asinFig.3.3,if(W/L)1=(W/L)2and(W/L)3=(W/L)4,equalcurrentsareforcedthroughthetwobranchesofthebiascircuitandthevoltagedropacrossresistorRequalsVBE.Thusthebiascurrentisgivenby

CombiningEqs.(3.5)and(3.6),wehave

ThisequationcanbesolvediterativelyforIbias.

Bothsupplyindependentbiascircuitshaveasecondtrivialsteadystatecondition,cutoffwhenIbias=0.Topreventthebiascircuitfromsettlingtothewrongsteadystatecondition,astartupcircuitisnecessaryinallpracticalapplications.ThecircuittotherightofthedashedlineinFig.3.5functionsasastartupcircuit.IfIbias=0,Q5isoffandthevoltageatnodeAishigh,causingQ6toturnonanddrawacurrentthroughQ3,forcingthecircuittomovetoitsotherequilibriumstate.Oncethecircuitsettlesinthedesiredstate,Q5turnsonandnodeAgoeslow,turningoffQ6.Atthisstatethestartupcircuitisessentiallyoutofthepicture.

Figure3.5Supplyindependentbiascircuitwithstartup.

Page53

Anotherimportantperformanceaspectofthebiascircuitsistheirtemperaturedependence.Unfortunately,supplyindependentbiascircuitsarenotnecessarilytemperatureindependent,becausethebaseemittervoltage(VBE),andgatetosourcevoltage(VGS)arebothtemperaturedependent.IfthetemperaturecoefficientTCFisdefinedastherelativechangeofthebiascurrentperdegreeCelsiustemperaturevariation,wehave[1]

UsingthedefinitionaboveandEq.(3.6),therelativetemperaturecoefficientoftheVBEbasedbiasgeneratorcanbecalculated:

Sincethetemperaturecoefficientofthebaseemitterjunctionvoltageisnegative(2mV/C)whileresistorstypicallyhaveapositivetemperaturecoefficient,thetwotermsinEq.(3.9)add,resultinginanetTCFthatisquitehigh.ThetemperaturebehaviorofthethresholdbasedbiasgeneratorofFig.3.3issimilartotheVBEbasedcircuit.

Analternativesupplyindependentbiasgeneratoristhe VBEbasedcircuitshowninFig.3.6a.Theoperationofthiscircuitisbasedonthedifferencebetweenthebaseemittervoltagesoftwotransistorsoperatedatdifferentcurrentdensities.InFig.3.6a,asinFigs.3.3and3.4,(W/L)1=(W/L)2and(W/L)3=(W/L)4.Therefore,equalcurrentsflowthroughthetwobranchesofthecircuitandVGS1=VGS2.Also,thepnptransistorM1,hasanemitterareathatismtimestheemitterareaof,M0.ThevoltageacrosstheresistorRis VBE=VBE0VBE1.FromEq.(3.5),

VBEappearsacrossRandproducesacurrentofvalue

Obviously,theresultingbiascurrentisindependentofthepowersupplyVDD.Thiscircuitalsohastwooperatingstates:oneatthedesiredoperatingcurrentgivenbyEq.(3.13)andtheotheratzero.Topreventthecircuitfromoperatinginthecutoffstate,astartupcircuitsimilartotheoneshowninFig.3.5isrequired.

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Figure3.6(a) VBEbasedsupply

independentbiasgenerator(b)highperformance VBEbased

supplyindependentbiasgenerator.

ThetemperaturecoefficientofthebiascurrentcanbecalculatedfromEq.(3.13):

Page55

Since VT/ Tand R/ Tarebothpositive,thetwotermsinthetemperaturecoefficientstendtocanceleachother.ThuscomparedtoVBEorthresholdbasedbiascircuits,the VBEbasedbiascircuitcanproduceamuchsmallertemperaturecoefficient.

Onedrawbackofthe VBEbasedbiasgeneratoristhestrongdependenceofIbiasonthemismatchesbetweenQ3Q4andQ1Q2devicepairs.ThemismatchbetweenQ3Q4willresultindifferentcurrentstoflowinthetwobranchesofthecircuit.If1+ representstheratioofthetwocurrents, VBEwillbecome

whichisequivalenttomodifyingm,theratiooftheemitterareas,by1+ .ThemismatchbetweenQ1andQ2andthecurrentdifferenceduetothemismatchofQ3andQ4willmaketheVGSvaluesofQ1andQ2different.ThisisequivalenttoadcoffsetvoltageVos= VGS,whichmodifiesEq.(3.13)to

Assumingthatm=8, =0.01,andVT=26mVatroomtemperature, VBE=261n[8(1+0.01)]=54.3mVresults.Fora VGS=5mVoffsetvoltage,fromEq.(3.17),Ibiaswillchangeby10%.ToreducethisvariationspecialcareshouldbetakeninthelayoutofQ1Q4.Forbettergeometricalmatching,thesedevicesshoulduseacommoncentroidlayoutstrategy[2].

ThecurrentmatchingaccuracyofthebiasgeneratorofFig.3.6aisfurtherdegradedduetothemismatchbetweenthedraintosourcevoltagesofQ3Q4andQ1Q2transistorpairs.Thecircuitcanbemadesymmetrical,andthedraintosourcevoltagedropsequalized,byaddingtransistorsQ5toQ8tothetwobranchesofthecircuit(Fig.3.6b).Theimprovedconfigurationalsousesthecascodecurrentmirrorprinciple,describedinSection3.2,toimprovethepowersupplyrejection.Ontheotherhand,theminimumpowersupplyvoltageisincreasedcomparedtothecircuitofFig.3.6a,duetotheextravoltagedropsrequiredbythetwocascodedevices.Thisbecomesamajorshortcominginadvancedsubmicronprocesstechnologies,orinlowpower/lowvoltageapplicationswherethepowersupplyvoltageislimitedto3.3V.

3.2MOSCurrentMirrorsandCurrentSources

Aswillbeseeninlatersections,constantcurrentsourcesandcurrentmirrorsareimportantcomponentsinMOSamplifiers.TheMOScurrentsourcesarequitesimilartothebipolarsources[1,3],wherethecurrentmirrorsworkontheprinciplethatidenticaldeviceswithequalgatetosourceanddraintosourcevoltagescarryequal

Page56

Figure3.7(a)nchannelcurrentmirror(b)outputvoltagecurrentrelationship

andusefuloutputrangeofthecurrentsource.

draincurrents.AnNMOSrealizationofacurrentmirrorisshowninFig.3.7a.InthiscircuitQ1isforcedtocarryacurrentI1,sinceitsinputresistanceatitsshortedgatedrainterminalsislow(muchlowerthanr0),anditsgatepotentialVD1adjustsaccordingly.IfQ1andQ2areinsaturation,theirdraincurrentsI1andI2aredeterminedtoalargeextentbytheirVGSvalues.SinceVGS1=VGS2=VG,thecondition

willthereforehold.Moreaccurately,sincedrainsaturationcurrentisgivenby

ifthetransistorshavethesame ,k andVT,then

ThecurrentI1isthus''mirrored"inI2.

UsingEq.(3.19)andignoringtheeffectof ,thegatevoltageVGisgivenby

Forthetransistorstooperateinthesaturationregion,VD VGVTmusthold.UsingEq.(3.21),therefore,thedrainsaturationvoltageis

whereVDsatistheminimumdrainvoltagethatkeepsthetransistorsinsaturation.

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Figure3.8SmallsignalequivalentcircuitoftheMOScurrentmirror.

FortheMOScurrentsourceofFig.3.7a,theoutputvoltagevouthastobegreaterthanVDsattokeepQ2inthesaturationregion.Figure3.7bshowstheoutputvoltagecurrentrelationshipofthecurrentsourceofFig.3.7a.

Forsmallsignalanalysis,theequivalentcircuitofFig.2.14canbeusedtomodelQ1andQ2.TheresultingcircuitisshowninFig.3.8.Herer0istheincrementalresistanceofthecurrentsourceI1andv inisthetestvoltageconnectedtothedrainofQ2formeasuringtheoutputimpedanceofthecircuit.Thesmallsignaloutputimpedanceissimply

whereEq.(3.19)wasused.

Clearly,thecurrentsourceofFig.3.7ahasanoutputimpedancethatisnotbetter(i.e.,higher)thantheoutputimpedanceofasimpleMOStransistor,alsoinaccuratecurrentmatchingduetothevariationofthedrainvoltageofQ2withtheoutputvoltage,andfinallyareasonablywideoutputvoltagerange,whichislimitedatthelowerendbyVDsat.

Theoutputimpedanceroutcanbeincreased,andthusthecircuitmadetoperformmorelikeanidealcurrentsource,byaddingonemoredeviceandmodifyingtheconnectionsslightly.Theresultingcircuit(Fig.3.9)istheMOSequivalentofWilson'scurrentsource[1,3].Inthiscircuit,ifI2increases,Q2causesv1tobecomelarger.Thisresultsinadropofv3whichthencounteractstheincreaseofI2.Thusanegativefeedbackloopexists,whichtriestoholdI2constant.Thesmallsignal

Figure3.9MOSversionofWilson's

currentsource.

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Figure3.10SmallsignalequivalentcircuitofWilson'scurrentsource.

equivalentcircuitisshowninFig.3.10asimplifiedcircuitisshowninFig.3.11.Thelatterwasobtainedbycombiningr0andrd1into byreplacingtheselfcontrolledcurrentsourcegm2v2byaresistor1/gm2,andbyneglectingrd2,whichisnowparallelwiththe(usuallymuchsmaller)resistor1/gm2.SolvingforiininFig.3.11gives

Typicalvaluesforgmarearound1mA/V,whilerdisontheorderofhundredsofkiloohms.Hence Then,fromEq.(3.24),

Here,ontherighthandsidethevalueofthefirstfactorisaround100,whilethatofthesecondisaround1.Hencetheoutputimpedanceroutistwoordersofmagnitudelargerthanrd3.TheoutputimpedanceofthecurrentsourcedropsassoonastransistorQ3entersthelinear(triode)region.TheminimumleveloftheoutputvoltageswingoftheWilson'scurrentsourceisthuslimitedtoVmin=VGS2+VDsat3.Insummary,thecharacteristicsofWilson'scurrentsourcearethefollowing:highoutputimpedance,restrictedoutputvoltageswing,andpoorcurrentmatchingaccuracy,duetothemismatchbetweenthedraintosourcevoltagesoftransistorsQ1andQ2.

Figure3.11Simplifiedsmallsignalequivalentcircuitof

Wilson'scurrentsource.

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Figure3.12ImprovedMOSWilson's

currentsource.

Thecircuitcanbemadesymmetrical,andthedrainsourcevoltagedropsofQ1andQ2equalized,byaddinganothertransistor,Q4(Fig.3.12).ItcaneasilybeshownthattheoutputimpedanceoftheresultingimprovedMOSWilson'scurrentsourceisagaingivenbyEq.(3.25).Thedetailedanalysisofthecircuitislefttothereader(Problem3.6a).

AslightlybetterversionofthecircuitofFig.3.12(oftencalledcascodecurrentsource)isshowninFig.3.13a.ItssmallsignalequivalentcircuitisshowninFig.3.13bandinasimplifiedforminFig.3.13c.ThiscircuitalsousesfeedbacktomaintainI2constant,anditalsoequalizesthedrainpotentialsofQ1andQ2,thusimprovingthecurrentmatchingpropertiesofthecurrentmirror.Itcaneasilybeshown(Problem3.6b)thatnow

Hencethereisagaina100foldincreaseoverthesingleMOSFEToutputresistance.Inaddition,nowtheinternalimpedanceroofthecurrentsourceI1isinparallelwith1/gm1+1/gm4,alowinputimpedance,ratherthanwithrd1.Henceitsloadingeffectismuchreduced.

ThecascodecurrentsourceissimilartotheimprovedWilson'scurrentsource:Itischaracterizedbyhighoutputimpedanceandaccuratecurrentmirroringcapability.However,acommondisadvantageofbothcircuitsisthattheminimumleveloftheoutputvoltageswingishigherthanthatofthesimplecurrentmirrorofFig.3.7.Thisreducestheavailablevoltageswingofthestage(s)drivenbythemirror.ForthecircuitofFig.3.13,theminimumvoltageswingbeforeQ3makesthetransitionfromthesaturationregiontothelinearregionis

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Figure3.13(a)Cascodecurrentsource(b)equivalentsmallsignalcircuitofthecascodecurrentsource(c)simplifiedsmallsignalcircuit

ofthecascodecurrentsource.

TheoutputvoltagecurrentplotforthecascodecurrentsourceisshowninFig.3.14.Theplotshowsthreeoperatingregions.IntheregionwherebothQ2andQ3areinsaturation(VD VT+2VDsat)theoutputimpedancehasthehighestvalue.IntheregionwhereQ2isinsaturationandQ3isthelinearregion(2VDsat VD

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Figure3.14Outputvoltagecurrentrelationshipforcascode

currentsource.

Asmentionedearlier,amajordrawbackofthecascodecurrentsourceisitslimitedoutputvoltageswing.AsEq.(3.27)shows,theminimumvoltageattheoutputofthecurrentsourcethatkeepsbothQ2andQ3insaturationisnowVT+2VDsat.Thislossofvoltageswingisespeciallyimportantwhenthecurrentsourceisusedastheloadofagainstage.Toreducethelossandincreasetheoutputswing,wecanbiasthedrainofthelowertransistorQ2attheedgeofthesaturationregion.TheresultinghighswingcascodecurrentsourceisshowninFig.3.15[4].

Inthiscircuitasourcefollower(Q5andQ6)hasbeeninsertedbetweenthegatesofQ3andQ4inFig.3.13a,andtheW/LratioofQ3hasbeenreducedbyafactorof4.UsingthesimplifiedMOSIVequationID=k W/L(VGSVT)2forthesaturationregion,andtheW/LratiosgiveninFig.3.15,wehave

Figure3.15Highswingcascodecurrentsource.

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Figure3.16Highswingimprovedcurrentsource.

where FromFig.3.15,thenodevoltagesVA,VB,andVDS2canbefound:

Q2isthereforebiasedattheedgeofsaturation.Thelowestleveloftheoutputvoltageswingisnowlimitedto2VDsat,whichisamajorimprovementcomparedtothatofthecircuitofFig.3.13a.Thehighswingcascodecurrentsourceexhibitsahighoutputimpedance,similartothatofthecascodecurrentsource,andanimprovedoutputvoltageswing.Thecurrentmatching,however,suffersduetothemismatchinthedraintosourcevoltagesofthemirrortransistorsQ1andQ2.ForQ1,VDS1=VT+VDsat,whileforQ2,VDS2=VDsat.

Animprovedhighswingcascodecurrentsource,alongwithitsbiasingcircuit,isshowninFig.3.16.Herenisapositiveintegernumber[5,p.560].Onceagain,usingthesimplifiedMOSIVequationresultsin

where(VDsat)W/ListheminimumdraintosourcevoltagerequiredtokeepdevicesQ1andQ3withacurrentIandaspectratioW/Linsaturation.FordevicesQ3andQ5wehave

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UsingEq.(3.31)yields

Clearly,sinceVDS1=VDS2=(VDsat)W/L,bothQ1andQ2arebiasedattheedgeoftheirsaturationregions.Also,assumingthatVDS3=VT VDsat3=n(VDsat)W/L,Q3willbebiasedinthesaturationregion.Asaresult,thecircuitwillhaveahighoutputimpedance.Noticethattheoutputnodevouthashighswingcapability.Actually,aslongasvoutisgreaterthan(n+1)(VDsat)W/L,theoutputwillmaintainitslargeoutputimpedance.FortheimprovedcurrentmirrorthedevicesQ1andQ2haveequalVGSaswellasequalVDSvaluesandthereforegoodcurrentmatchingcapability.

Theformulasandnumericalestimatesgivenforthecurrentsourcesaresomewhatoptimisticsincetheyneglectthebodyeffectofthefloatingdevices(transistorsQ3andQ4inFigs.3.13to3.16).Also,realMOStransistorsdonotdisplayanabrupttransitionfromthesaturationtolinearregion.Therefore,itisnecessarytobiasthedrainvoltagesofthemirrordevicesQ1andQ2slightlyabovetheidealsaturationvoltageproducedby toachievethehighoutputimpedancederivedearlier.

3.3MOSGainStages[68]

AsimpleNMOSgainstagewithresistiveloadisshowninFig.3.17.Q1isbiasedsothatitoperatesinitssaturationregion.ThelowfrequencysmallsignalequivalentcircuitisshowninFig.3.18.Thevoltagegainofthestageisclearly

Inintegratedcircuitrealization,theresistorRLisundesirablesinceitoccupiesalargeareaandintroducesalargevoltagedropandhenceisusuallyreplacedbya

Figure3.17ResistiveloadMOS

gainstage.

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Figure3.18Smallsignallowfrequencyequivalentcircuitoftheresistiveloadgainstage.

secondMOSFET.IfanNMOSenhancementmodedeviceisusedasaload,thecircuitofFig.3.19results.ThedrainandgateofQ2areshortedtoensurethatvds>vgsVT,andhencethedeviceisinsaturation.ThesmallsignalequivalentcircuitoftheloaddeviceQ2aloneisshowninFig.3.20.Herethevoltagecontrolledcurrentsourcegmvdsisacrossthevoltagevdshenceitbehavessimplyasaresistorofvalue1/gm.Similarly,sincevsb=vout,thesourcegmbvsbcorrespondstoaresistor1/|gmb|[recallthatbyEq.(2.19),gmb

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Figure3.20Smallsignalequivalentcircuitofthe

enhancementloaddeviceQ2.

Includingbodyeffect(butstillneglectingchannellengthmodulation),usingEqs.(2.12),(2.19),and(3.34),

results.For| p|=0.3V, ,and =1,thedenominatoris1.21hencethegainisreducedfrom10to8.26.

Inconclusion,theNMOSenhancementloadgainstageprovidesalowgain.Thisstageisnonethelessoftenusefulinwidebandamplifiers,wherealowbutpredictablegaincanbetoleratedandthegainstageexhibitsawidebandwidthduetothelowresistanceoftheload.Forhighgainapplications,however,thestageneedsalargesiliconareaandsincetheloaddevicehasahighresistance(smallW/Lratio),ithasalargedcvoltagedropacrossitwhichreducesthesignalhandlingcapabilityandhencethedynamicrangeofthestage.

ToimprovetheperformanceandincreasethegainoftheMOSamplifiers,acurrentsourceloadcanbeused.Anyofthecurrentsourcesdescribedintheearliersectionscanserveasaload.AcommonsourceMOSgainstagethatusesanNMOSinputdeviceandthepchannelversionofthesimplecurrentsourceofFig.3.7aisshowninFig.3.21.TheoperationofthiscircuitissimilartotheresistiveloadgainstageofFig.3.17,buttheresistiveloadisreplacedbythesmallsignaloutputimpedancerd2ofthePMOScurrentsource.UsingEq.(3.33),thegainoftheCMOSamplifiesstageis

Forgm1=0.2mA/Vandrd1=rd2=1M ,thesmallsignallowfrequencygainisAv=100.Obviously,thegainisproportionaltothetransconductanceofthe

Figure3.21CommonsourcegainstagewithNMOSinputandpchannelcurrentsourceasactiveload.

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Figure3.22Enhancementloadgainstage

withcapacitiveload.

inputdeviceandthesmallsignaloutputresistanceofthestager0=rd1||rd2.Since foragivensizeoftheloaddevice,largevaluesofgaincanbeachievedinamoderatelysmallsiliconarea.Usingacascodecurrentsourcewithsignificantlyhigheroutputimpedancewillnotincreasethegainoftheamplifierdirectly,becausetheoutputresistanceofthestageislimitedbytheoutputimpedanceoftheinputdevice.

ForthegainstageofFig.3.21tooperateproperly,bothinputandloaddevicesshouldoperateintheirsaturationregions.TheoutputsignalswingisthuslimitedtoVDD|VDsat2|andVDsat1onthepositiveandnegativeside,respectively.Theoutputsignalmustthereforeremainintherange

andthetotaloutputswingis

Forhighfrequencyapplications,allgainstagesdiscussedsofarhaveacommonshortcoming.ConsiderthecircuitofFig.3.22,whichincludesthesourceresistanceRSandthecapacitiveloadCLofthegainstage.Includingtheparasiticcapacitancesinthesmallsignalequivalentcircuit,thediagramshowninFig.3.23aisobtained.Combiningparallelconnectedelements,thecircuitofFig.3.23bresults,where

ThenodeequationsfornodesAandBare

whereallvoltagesareLaplacetransformedfunctions.

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Figure3.23(a)EquivalentcircuitoftheMOSgainstage

(b)simplifiedequivalentcircuitoftheMOSgainstage.

SolvingEq.(3.41)gives

Toobtainthefrequencyresponse,smustbereplacedbyj .Formoderatefrequencies, hold.Thenagoodapproximationis

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Figure3.24Approximateequivalentcircuitofthe

MOSgainstage.

HereA0v=gm1/GLeqisthedcvalueofAv(j ),and

Av(j )inEq.(3.43)canberecognizedasthetransferfunctionofthecircuitshowninFig.3.24.ThusthecapacitorCgd1whichisconnectedbetweentheinputandoutputterminalsofthegainstage(Fig.3.23a)behaveslikeacapacitance thehighfrequencygainwillbeseriouslyaffectedandthebandwidthconsiderablyreducedbythisphenomenon.

TopreventtheMillereffect,thecascodegainstageofFig.3.25canbeused.HereQ2isusedtoisolatetheinputandoutputnodes.Itprovidesalowinputresistance1/gm2atitssourceandahighoneatitsdraintodriveQ3.Ignoringthebodyeffect,thelowfrequencysmallsignalequivalentcircuitisintheformshowninFig.3.26.Neglectingthesmallgdadmittances,clearly

Hence,forlowfrequencies,

Figure3.25Cascodegainstagewith

enhancementload.

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Figure3.26Lowfrequencysmallsignalcircuitof

cascodegainstage.

ThegatetodraingainofQ1isgm1/gm2,andthereforetheCgd1ofthedrivertransistorQ1isnowmultipliedby(1+gm1/gm2).Choosinggm1=gm2,thisfactorisonly2.Theoverallvoltagegaingm1/gm3,however,canstillbelarge,withoutintroducingsignificantMillereffect,sincethereisnoappreciablecapacitancebetweentheinputandoutputterminals.

Asbe