A-Study-of-Phase-Noise-in-CMOS-Oscillatorsvi

IEEEJOURNALOFSOLID-STATECIRCUITS,VOL.31,NO.3,MARCH1996331AStudyofPhaseNoiseinCMOSOscillatorsBehzadRazavi,Member,IEEEAbstract-ThispaperpresentsastudyofphasenoiseintwoinductorlessCMOSoscillators.First-orderanalysisofalinearoscillatorysystemleadstoanoiseshapingfunctionandanewdefinitionofQ.AlinearmodelofCMOSringoscillatorsisusedtocalculatetheirphasenoise,andthreephasenoisephenomena,namely,additivenoise,high-frequencymultiplicativenoise,andlow-frequencymultiplicativenoise,areidentifiedandformulated.Basedonthesameconcepts,aCMOSrelaxationoscillatorisalsoanalyzed.Issuesandtechniquesrelatedtosimulationofnoiseinthetimedomainaredescribed,andtwoprototypesfabricatedina0.5-pmCMOStechnologyareusedtoinvestigatetheaccuracyofthetheoreticalpredictions.Comparedwiththemeasuredresults,thecalculatedphasenoisevaluesofa2-GHzringoscillatoranda900-MHzrelaxationoscillatorat5MHzoffsethaveanerrorofapproximately4dB.I.INTRODUCTIONOLTAGE-CONTROLLEDoscillators(VCO’s)areanVintegralpartofphase-lockedloops,clockrecoverycir-cuits,andfrequencysynthesizers.RandomfluctuationsintheoutputfrequencyofVCO’s,expressedintermsofjitterandphasenoise,haveadirectimpactonthetimingaccuracywherephasealignmentisrequiredandonthesignal-to-noiseratiowherefrequencytranslationisperformed.Inparticular,RFoscillatorsemployedinwirelesstranceiversmustmeetstringentphasenoiserequirements,typicallymandatingtheuseofpassiveLCtankswithahighqualityfactor(Q).However,thetrendtowardlarge-scaleintegrationandlowcostmakesitdesirabletoimplementoscillatorsmonolithically.Thepaucityofliteratureonnoiseinsuchoscillatorstogetherwithalackofexperimentalverificationofunderlyingtheorieshasmotivatedthiswork.Thispaperprovidesastudyofphasenoiseintwoinduc-torlessCMOSVCO’s.Followingafirst-orderanalysisofalinearoscillatorysystemandintroducinganewdefinitionofQ,weemployalinearizedmodelofringoscillatorstoobtainanestimateoftheirnoisebehavior.Wealsodescribethelimitationsofthemodel,identifythreemechanismsleadingtophasenoise,andusethesameconceptstoanalyzeaCMOSrelaxationoscillator.Incontrasttopreviousstudieswheretime-domainjitterhasbeeninvestigated[l],[2],ouranalysisisperformedinthefrequencydomaintodirectlydeterminethephasenoise.Experimentalresultsobtainedfroma2-GHzringoscillatoranda900-MHzrelaxationoscillatorindicatethat,despitemanysimplifyingapproximations,lackofaccurateMOSmodelsforRFoperation,andtheuseofsimplenoiseManuscriptreceivedOctober30,1995;revisedDecember17,1995.TheauthorwaswithAT&TBellLaboratories,Holmdel,NJ07733USA.PublisherItemIdentifierS0018-9200(96)02456-0.HeisnowwithHewlett-PackardLaboratories,PaloAlto,CA94304USA.models,theanalyticalapproachcanpredictthephasenoisewithapproximately4to6dBoferror.Thenextsectionofthispaperdescribestheeffectofphasenoiseinwirelesscommunications.InSection111,theconceptofQisinvestigatedandinSectionIVitisgeneralizedthroughtheanalysisofafeedbackoscillatorysystem.TheresultingequationsarethenusedinSectionVtoformulatethephasenoiseofringoscillatorswiththeaidofalinearizedmodel.InSectionVI,nonlineareffectsareconsideredandthreemechanismsofnoisegenerationaredescribed,andinSectionVII,aCMOSrelaxationoscillatorisanalyzed.InSectionVIII,simulationissuesandtechniquesarepresented,andinSectionIXtheexperimentalresultsmeasuredonthetwoprototypesaresummarized.11.PHASENOISEINWIRELESSCOMMUNICATIONSPhasenoiseisusuallycharacterizedinthefrequencydo-main.ForanidealoscillatoroperatingatWO,thespectrumassumestheshapeofanimpulse,whereasforanactualoscillator,thespectrumexhibits“skirts”aroundthecenteror“carrier”frequency(Fig.1).Toquantifyphasenoise,weconsideraunitbandwidthatanoffsetAwwithrespecttoWO,calculatethenoisepowerinthisbandwidth,anddividetheresultbythecarrierpower.Tounderstandtheimportanceofphasenoiseinwire-lesscommunications,consideragenerictransceiverasdepictedinFig.2,wherethereceiverconsistsofalow-noiseamplifier,aband-passfilter,andadownconversionmixer,andthetransmittercomprisesanupconversionmixer,aband-passfilter,andapoweramplifier.Thelocaloscillator(LO)providingthecarriersignalforbothmixersisembeddedinafrequencysynthesizer.IftheLOoutputcontainsphasenoise,boththedownconvertedandupconvertedsignalsarecorrupted.ThisisillustratedinFig.3(a)and(b)forthereceiveandtransmitpaths,respectively.ReferringtoFig.3(a),wenotethatintheidealcase,thesignalbandofinterestisconvolvedwithanimpulseandthustranslatedtoalower(andahigher)frequencywithnochangeinitsshape.Inreality,however,thewantedsignalmaybeaccompaniedbyalargeinterfererinanadjacentchannel,andthelocaloscillatorexhibitsfinitephasenoise.WhenthetwosignalsaremixedwiththeLOoutput,thedownconvertedbandconsistsoftwooverlappingspectra,withthewantedsignalsufferingfromsignificantnoiseduetotailoftheinterferer.Thiseffectiscalled“reciprocalmixing.”ShowninFig.3(b),theeffectofphasenoiseonthetransmitpathisslightlydifferent.Supposeanoiselessreceiveristo0018-9200/96$05.0001996IEEE332IEEEJOURNALOFSOLID-STATECIRCUITS,VOL.31,NO.3,MARCH1996-AiwFig.1.Phasenoiseinanoscillator.Low-NoiseAmplifiercBand-PassFilterFrequencySynthesizer.AmplifierBand-PassFig.2.Genericwirelesstransceive