IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMSII ANALOG AND DIGITAL SIGNAL PROCESSING VOL - PDF document

IEEETRANSACTIONSONCIRCUITSANDSYSTEMS—II:ANALOGANDDIGITALSIGNALPROCESSING,VOL.48,NO.10,OCTOBER2001937ALinearMOSTransconductorUsingSourceDegenerationandAdaptiveBiasingKo-ChiKuo,Member,IEEE,andAdrianLeuciuc,Member,IEEEThispaperpresentsanewconfigurationforlinearMOSvoltage-to-currentconversion(transconductance).Theproposedcircuitcombinestwopreviouslyreportedlinearizationmethods[1],[2].Thetopologyachieves60-dBlinearityforafullybalancedinputdynamicrangeupto1 -C.Active-configurationsuseop-amps,andresistorsandcapacitorsaspassivefrequency-determiningcomponents.Theypresentverygoodlinearity,butusuallyrequirelargedieareaforresistorsand/orcapacitors,thetuningcanbeachievedonlyinadiscretemannerbyusingarraysofpassivecomponents,andthelargevalueresistorscanintroducesubstantiallythermalnoise.Anotherclassofcontinuous-timefiltersisderivedfromclassicalactive-filtersandusesMOSfield-effecttransistors(MOSFETs),capacitors,andop-amps.TheyarethusreferredtoasMOSFET-Cactivefilters[3],[4].TheseimplementationshavepoorlinearityduetothenonlinearcharacteristicoftheMOStransistors.Althoughthelinearitycanbeimprovedby 40dBfor0.7 atasingle5-Vsupply.Theuseoftransconductorsandcapacitorstoimplementintegratorsisanothertechniquetorealizecontinuous-timeManuscriptreceivedOctober13,2000;revisedOctober12,2001.ThisworkwassupportedbytheCenterforDesignofAnalog-DigitalIntegratedCircuits(CDADIC).ThispaperwasrecommendedbyAssociateEditorG.Cauwen-berghs. -Cconfigurations[7],[8]havebetterfrequencyresponsecomparedtoactive-RCandMOSFET-Crealizationsduetotheabsenceoflocalfeedbackaroundtheactiveele-ments.Theyhavealsoelectronictuningcapability,butarecharacterizedbyaratherpoorlinearity.Therefore,additionalcircuitryisneededtolinearizethetransfercharacteristicofatransconductor.SinceG -Cconfigurationshavebetterfrequencyresponseandusuallywidertuningrange,theyarenowadaysamongthemostpopularapproachesforimplementingintegratedcontinuous-timefilters.SeveralcircuittechniqueshavebeenproposedinliteraturetoimprovethelinearityofbipolarandMOStransconductors.InthiscommunicationwewillreferonlytoMOStransconductors,agoodsurveyonmostofthelinearizationtechniquesbeinggivenin[9].Thelinearizationmethodsinclude:cross-couplingofmultipledifferentialpairs[2],[10],[11],adaptivebiasing[2],[12],sourcedegeneration(usingresistorsorMOStransistors)[1],[13],[14],shiftlevelbiasing[15],seriesconnectionofmultipledifferentialpairs[16],andpseudodifferentialstages(usingtransistorsinthetrioderegionorinsaturation)[17],[18].ThispaperpresentsanimprovedlinearMOStransconductorthatusesboththeadap- process,usingasingle3.3-Vsupplyvoltage.Experimentalresultsareincludedforcomparisontothesimulationresults.SomefinalconclusionsarepresentedinSectionIV.II.COPOLOGIESFORRANSCONDUCTORSInthissection,wewillfirstreviewthreelinearizationtech-niquespreviouslyreportedinliterature.ThefirstoneistheMOSdifferentialpairwithresistivesourcedegeneration.Thesecond – characteristicsfortheMOStransistorsinthesaturationre-1057–7130/01$10.00©2001IEEE 938IEEETRANSACTIONSONCIRCUITSANDSYSTEMS—II:ANALOGANDDIGITALSIGNALPROCESSING,VOL.48,NO.10,OCTOBER2001 Fig.1.(a)SimpledifferentialMOStransconductor.(b)MOStransconductorwithresistivesourcedegeneration.gionandthechannellengthmodulationeffectwillbeneglectedforsimplicity.Therefore,thedraincurrentisgivenby (1)where isthetransconductanceparameterand isthethresholdvoltageoftheMOStransistor.Using(1)thesimpledifferentialMOStransconductorshowninFig.1(a)hasatransfercharacteristicgivenby Betterlinearitycanbeachievedforlargeeffectivegate-to-sourcevoltages, .Forlow-voltageapplica-tionsthisconstitutesamajordrawback.Oneofthesimplesttopologiestolinearizethetransferchar-acteristicoftheMOStransconductoristheonewithsourcede-generationusingresistorsanddepictedinFig.1(b).Thedisad-vantageofthisconfigurationisthelargeresistorvalueneededtoachieveawidelinearinputrange.Sinceinthiscase ,theobtainedtransconductanceisrestrictedtosmallvalues.Moreover,thistechniqueeliminatestheelectronictuningcapa-bilityofthetransconductancebecauseitsvalueissetbythede-generationresistor.B.MOSTransconductorsWithSourceDegenerationUsingMOSTransistorsByreplacingthedegenerationresistorswithtwoMOStran-sistorsoperatinginthetrioderegion,thecircuitinFig.2isobtained.Consideringperfectlymatchedtransistors – , – ,andneglectingthebodyandchannellengthmodula-tioneffects,thetransfercharacteristicofthistransconductorisgivenby (3)where Usually,thenonlineartermunderthesquarerootcanbemademuchsmallerthanunityandimprovedlinearityandlargerinput Fig.2.MOStransconductorwithsourcedegenerationusingMOStransistors.dynamicrangecanbeobtained.However,increasedlinearitymeanssmallerequivalenttransconductanceandreducedtuningcapability.Thecircuithasbandwidthandnoiseperformancescomparabletothesimpledifferentialpair.Whentheinputvoltageincreasesbeyondacertainvalue oneofthetwodegenerationtransistorsentersinthesaturationregion( for ,respectively for ).Theoutputdifferentialcurrentinthiscaseisgivenby InFig.3(a)therelativeerrorofthetransconductance derivedfromeqs.(3)–(6)isplottedfordifferentvaluesofparameter .Itcanbeeasilyseenanditwasalsoshownin[1]thatonecanincreasetheinputlineardynamicrangebyappro-priatelysettingthevalueofparameter (somewherebetween2.5and2.75).However,thenonlinearityerrorisupto1%for %.InsomefilteringapplicationsitisrequiredtohavebetterlinearityinordertoachieveaTHDof 60dBorC.AdaptivelyBiasedMOSTransconductorsAnothertopologytoachievehighfrequencylinearMOStransconductorswasreportedin[2].Theideaistouseatailcurrentcontaininganinputdependentquadraticcomponenttocancelthenonlineartermin(2).Thus,if thetransfercharacteristicbecomeslinear Therequiredbiasingcurrentcanbeeasilyobtainedusingan-othertwoMOStransistors – havingidenticaltranscon-ductancecoefficientsastheonesinthedifferentialpair – andtwounit-gaincurrentmirrors – and – asitisshowninFig.4.Additionalcircuitryisneededforgeneratingthetuningvoltage .Thenoisegeneratedbythesquaringcir-cuitrydoesnotappearattheoutputofthetransconductorsinceitislikeacommonmodevoltageatthesourcesofthedifferential KUOANDLEUCIUC:LINEARMOSTRANSCONDUCTOR Fig.3.RelativetransconductanceerrorfortheMOStransconductors.(a)UsingsourcedegenerationwithMOStransistors.(b)UsingsourcedegenerationwithMOStransistorsandadaptivebiasing.Parameterisvariedwithastepof0.25. Fig.4.AdaptivelybiasedMOStransconductor.pair.Itwasshownin[9]thatduetotheeffectofmobilityreduc-tion,thesizeofthetransistorsinthesquaringcircuitryshouldbecomputedasafunctionofthevoltage inordertoob-tainthebestlinearity.Therefore,tuningthecircuitbymeans willworsenthelinearity.Theclassofinputsignals Fig.5.ProposedlinearMOStransconductor.whichcanbeprocessedislimitedsincetherequirementoffullybalancedsignalsisneededforthesquaringcircuittofunctionproperly[9].D.ALinearMOSTransconductorUsingSourceDegenerationandAdaptiveBiasingWeproposeanotherMOStransconductorthatcombinesthetwolinearizationapproachespresentedabove.Startingfromcir-cuitinFig.2andusingadaptivebiasingcurrentsources,thecir-cuitdepictedinFig.5isobtained.Totransformthenonlineartransfercharacteristic(3)intoalinearone,thetailcurrent shouldhavetheexpression Thetransfercharacteristicbecomeslinearandisgivenby Theadaptivebiascurrentis Comparing(9)and(11),thetransconductancecoefficientofthesquaringcircuitshouldbe (12)Since issmallerthan ,thedccomponentofthecurrentgeneratedbythesquaringcircuitryissmallcomparedtothenec-essaryvaluerequiredtobiasthedifferentialpair.Therefore,anadditionalcurrentsource isneededtotunethetranscon-ductor.Whentheinputvoltageincreasesabovethevalue (13) 940IEEETRANSACTIONSONCIRCUITSANDSYSTEMS—II:ANALOGANDDIGITALSIGNALPROCESSING,VOL.48,NO.10,OCTOBER2001oneofthetransistors , entersinthesaturationregionandtheoutputdifferentialcurrentisgivenby Fig.3(b)showsthecomputedrelativetransconductanceerrorforthecircuitinFig.5,assumingquadraticMOS – istics(1).Imposingacertainmaximumnonlinearityerror,thevalueofparameter canbecomputed.Inpractice,deviationsfromthequadraticMOS – characteristicduetomobilityre-ductionandthebodyeffectcauseincompletecancellationin(3).Therefore,thetransconductancecharacteristicpresentsacertaincurvatureevenforthecasewhenbothtransistors – areinthetrioderegion.SPICEsimulationsusingBSIM3v3MOSFETmodelshaveshownthatthebestlinearitycanbeachievedbysettingthevalueoftheparameter between1.5and1.75.III.SIMULATIONANDXPERIMENTALESULTSA.ComparisonofDifferentLinearizationTechniquesInordertocomparetheperformanceofdifferentlineariza-tiontechniques,numerouscomputersimulationshavebeenrun.Toobtainafairandaccuratecomparison,thecircuitspresentedinSectionIIhavebeenoptimizedtoachievethebestlinearitypossibleforagiventransconductancevalue.SPICEsimulatedtransconductanceasafunctionoftheinputdifferentialvoltageisplottedinFig.6.FromthedetailshowninFig.6(b)itcanbeeasilyseenthatthelinearityachievedbythenewlyproposedconfigurationisbetterthanalltheotherones.Thefigurealsoin-cludedtheresultsobtainedinthecaseofatransconductorwithresistivesourcedegenerationandadaptivebiasing,forcompar-isonpurposes.TheTHDoftheoutputdifferentialcurrentversustheampli-tudeoftheinputvoltageforthethreetransistor-onlylinearizedtransconductorsisdepictedinFig.7.ThetopologyinFig.4achievesTHDlessthan 57dBfor1.6 inputvoltage,10dBbetterthantheonewithoutadaptivebiasingand27dBbetterthantheoneusingonlyadaptivebiasing,forthesameinputrange.Forthesamedesignedtransconductancevalue,thenovelproposedconfigurationisthesecondbestasfarasthepowerconsumptionanddiearea.ItissurpassedonlybythecircuitinFig.4forwhichthelinearityisstronglydependentonthetuningvoltage.Fig.8illustratesthelinearityperformanceofthethreetran-sistor-onlytransconductorswhentunedforseveraltransconduc-tancevalues.ThetransconductorinFig.4istunedbychanging ,theoneinFig.2bychangingthetailcurrents ,andthenewlyproposedonebychanging .Ourapproachisagainthebestone.Sincethesquaringcircuitryusedinadaptivebiasingisprop-erlyfunctioningonlyforfullybalancedinputs,thebehavioroftheMOStransconductorshasbeenstudiedinthecaseofun-balancedinputaswell.Becausethequadraticcomponentofthe Fig.6.Simulatedtransconductanceforfivelinearizationtechniques.(a)Fullplot.(b)Detail.( )resistivesourcedegeneration;()resistivesourcedegenerationwithadaptivebiasing;()sourcedegenerationusingMOStransistors;( )adaptivebiasing;()sourcedegenerationusingMOStransistorsandadaptivebiasing. Fig.7.SimulatedTHDat1kHzforthethreeresistor-freelinearizationtechniques.( )sourcedegenerationusingMOStransistors;( )adaptivebiasing;()sourcedegenerationusingMOStransistorsandadaptivebiasing.adaptivebiasingcurrentfortheproposedcircuitissmallerthantheoneneededfortheconfigurationinFig.4[see(7)and(9)],thelinearityofthenewlyintroducedtransconductordegrades KUOANDLEUCIUC:LINEARMOSTRANSCONDUCTOR Fig.8.SimulatedtransconductanceofthreelinearizedMOStransconductorsundertuning.(a)SourcedegenerationusingMOStransistors.(b)Adaptivebiasing.(c)SourcedegenerationusingMOStransistorsandadaptivebiasing.lessforunbalancedinputs.TheobtainedsimulationresultsaredepictedinFig.9andtheyconfirmtheexpectedbehavior.B.ExperimentalResultsThelinearMOStransconductorhasbeenfabricatedusingthe mprocessfromTSMC.ThediagramoftheentirecircuitisshowninFig.10.Theactiveload – iscontrolledbythecommonmodefeedbackcircuitryforadjustingtheoutput Fig.9.Simulatedtransconductanceforthethreeresistor-freelinearizationtechniquesinthecaseofunbalancedinput.(a)SourcedegenerationusingMOStransistors.(b)Adaptivebiasing.(c)SourcedegenerationusingMOStransistorsandadaptivebiasing.( )fullybalanced;()20%unbalanced; )40%unbalanced;()60%unbalanced;()80%unbalanced;()100%commonmodevoltagetothedesiredvalue .Transistors – supplythevoltage and generates Tuningcanbeachievedbymeansofthetriodetransistor Thestart-upcircuitryneededforthebiasingparthasbeenomittedinFig.10.Thefabricatedprototypehasbeendesignedforuseinacon-tinuous-timelow-passdelta-sigmamodulator.Verylargearea 942IEEETRANSACTIONSONCIRCUITSANDSYSTEMS—II:ANALOGANDDIGITALSIGNALPROCESSING,VOL.48,NO.10,OCTOBER2001 Fig.10.Fullcircuitdiagramofthefabricatedtransconductor. Fig.11.Simulated(dottedlines)andmeasured(continuouslines)dcresponse.transfercharacteristic.(b)Transconductance.transistorsareusedintheoutputstagetominimize withanactiveareaof0.47mm fortheentiretransconductor.Asinglesupplyvoltageof3.3Vhasbeenusedandtheentiretransconductordissipates1mWfor and5-MHzbandwidth.Therelativelowvalueofthetransconductanceislimitedbytheapplication,andreducestheinputlinearrangecomparedtotheoptimalvaluesobtainedforthesimulationsintheprevioussection.ThesimulatedandmeasureddccharacteristicsareshowninFig.11.Thetransconductanceplothasbeenobtainedbydiffer-entiatingthemeasuredoutput – characteristic.Therippleiscausedbythesmallnumberofpointsandfiniteprecisionofthemeasurement.ThemeasuredTHDisapproximately6to10dBlargerthanthesimulatedone.Thisiscausedbythenonperfectmatchingofthetransistorsand,possibly,bytheadditionaldis-tortionsintroducedbythedifferentialtosingle-endedconver-sioncircuitryusedinthemeasurementsetup.IV.CAnimprovedlinearMOStransconductor,combiningtwolinearizationmethodshasbeenpresented.ThetopologycanachievebetterlinearitycomparedtootherapproachesanditcanbeusedinimplementingfullydifferentialG -Ccon-tinuous-timefilterswithseverelinearityrequirements.Theproposedcircuithasgoodtuningcapabilityanditfunctionsforbothfully-balancedandunbalancedinputsignals,withsomelinearitydepreciationinthelattercase.Inapracticalimplementation,thefinallinearityperformanceissetbythematchingprecisionoftheMOSFETs.Theproposedcircuithasbeenfabricatedandexperimentalresultsagreewithsimulatedlinearityperformance.[1]F.KrummenacherandN.Joehl,“A4-MHzCMOScontinuous-timefilterwithon-chipautomatictuning,”IEEEJ.Solid-StateCircuits,vol.23,pp.750–758,June1988.[2]A.NedungadiandT.R.Viswanathan,“DesignoflinearCMOStransconductanceelements,”IEEETrans.CircuitsSyst.,vol.CAS-31,pp.891–894,Oct.1984.[3]Y.TsividisandM.Banu,“Continuous-timeMOSFET-CfiltersinIEEEJ.Solid-StateCircuits,vol.SC-21,pp.15–30,Feb.1986.[4]M.BanuandY.Tsividis,“FullyintegratedactiveRCfiltersinMOStechnology,”IEEEJ.Solid-StateCircuits,vol.SC-18,pp.644–651,Dec.[5]Z.Czarnul,“ModificationofBanu–Tsividiscontinuous-timeinte-grator,”IEEETrans.CircuitsSyst.,vol.CAS-33,pp.714–716,July[6]G.Groenewold,“Thedesignofhighdynamicrangecontinuous-timeintegratablebandpassfilters,”IEEETrans.CircuitsSyst.,vol.38,pp.838–852,Aug.1991.[7]H.KhorramabadiandP.R.Gray,“High-frequencyCMOScon-tinuous-timefilters,”IEEEJ.Solid-StateCircuits,vol.SC-19,pp.939–948,Dec.1984. KUOANDLEUCIUC:LINEARMOSTRANSCONDUCTOR[8]F.Krummenacher,“Designconsiderationinhighfrequency,CMOSTransconductanceAmplifierCapacitor(TAC)filters,”inProc.IEEEInternationalSymp.CircuitsSyst.ISCAS’89,1989,pp.100–105.[9]S.T.DupuieandM.Ismail,“HighfrequencyCMOStransconductors,”AnalogueICDesign:TheCurrent-ModeApproach,C.Toumazou,F.J.Lidgey,andD.G.Haigh,Eds.London,U.K.:PeterPeregrinus,[10]H.Khorramabadi,“HighfrequencyCMOScontinuoustimefilter,”Ph.D.dissertation,Univ.California,Berkeley,1985.[11]E.SeevinckandR.F.Wassenaar,“AversatileCMOSlineartranscon-ductor/square-lawfunctioncircuit,”IEEEJ.Solid-StateCircuits,vol.SC-22,pp.366–377,June1987.[12]M.G.Degrauwe,J.Rijmenants,E.A.Vittoz,andH.J.DeMan,“Adap-tivebiasingCMOSamplifiers,”IEEEJ.Solid-StateCircuits,vol.SC-17,pp.522–528,June1982.[13]D.R.Welland,“Transconductanceamplifiersandexponentialvariablegainusingthesame,”U.S.Patent5451901,Sept.19,1995.[14]I.MehrandD.R.Welland,“ACMOScontinuous-time filterforPRMLreadchannelapplicationsat150Mb/sandbeyond,”IEEEJ.Solid-StateCircuits,vol.32,pp.499–513,Apr.1997.[15]Z.WangandW.Guggenbuhl,“Avoltage-controlledlinearMOStransconductorusingbiasoffsettechnique,”IEEEJ.Solid-StateCircuits,vol.25,pp.315–317,Feb.1990.[16]J.Silva-Martinez,M.S.J.Steyaert,andW.Sansen,“A10.7-MHz68-dBSNRCMOScontinuous-timefilterwithon-chipautomaticIEEEJ.Solid-StateCircuits,vol.27,pp.1843–1852,Dec.[17]R.Alini,A.Baschirotto,andR.Castello,“TunableBiCMOScontin-uous-timefilterforhigh-frequencyapplications,”IEEEJ.Solid-StateCircuits,vol.27,pp.1905–1915,Dec.1992.[18]S.L.Wong,“Noveldrain-basedtransconductancebuildingblocksforcontinuous-timefilterapplications,”Electron.Lett.,vol.25,no.2,pp.100–101,Jan.1989. Ko-ChiKuo(S’93–M’01)receivedtheDiplomainelectronicengineeringfromMingHsinEngineeringCollege,Hsin-Chu,Taiwan,R.O.C.,in1987,theM.S.degreefromTulaneUniversity,NewOrleans,LA,andthePh.D.degreefromtheStateUniversityofNewYorkatStonyBrook,bothinelectricalengineering,in1994and2001,respectivelyFrom1994and2001,hewaswiththeDepartmentofElectricalandComputerEngineering,theStateUniversityofNewYorkatStonyBrook.Currently,heisaStaffEngineerwiththeCommunicationRe-searchandDevelopmentCenter(CRDC),BostonDesignCenter,IBM,Lowell,MA.Hiscurrentresearchinterestsincludehighperformancedigitalcircuitdesign,lineartransconductors,mixedsignalcircuitdesign,andPLL/FrequencySynthesizersinwirelesscommunications.Dr.KuoisamemberofEtaKappaNu. AdrianLeuciuc(M’99)receivedtheDipl.Eng.(M.Sc.)andPh.D.DegreesinelectronicengineeringfromtheTechnicalUniversityofIasi,Romania,in1990and1996,respectively.From1991and1997,hewaswiththeDepartmentofElectronicsandTelecommunications,TechnicalUniversityofIasi,Romania.In1998,hewasaVisitingProfessorwiththeDepartmentofElectricalandComputerEngineering,theStateUniversityofNewYorkatStonyBrook,thenbecameanAssistantProfessorwiththesamedepartment.Hisresearchinterestsincludecontinuous-timefilters,dataconverters,nonlinearandchaoticcircuitsandtheirapplicationsincommunications.Dr.LeuciucisamemberofEtaKappaNu.