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1、Close-inphasenoiseinelectricaloscillatorsRezaNavid*a,ChristophJungemannb,ThomasH.LeeaandRobertW.DuttonaaCenterforIntegratedSystems,StanfordUniversity420ViaPalou,Stanford,CA94305-4070USA;bNST,TechnicalUniversityBraunschweig,Postfach3329,38023Braunschweig,Germany
2、ABSTRACTUnderstandingthepropertiesofclose-inphasenoiseiscrucialforanalyzingtheeffectsoflow-frequency,colorednoiseonthefrequencystabilityofelectricaloscillators.Thispapershowsthesepropertiesaredistinctlydifferentfromthoseoffar-outphasenoise,whicharecommonlystudi
3、edintheliterature.Unlikefar-outphasenoise,thespectrumofclose-inphasenoisecausedbyseveraluncorrelatednoisesourcesisnotthesameasthesumofthephasenoisespectracausedbyindi-vidualsources.Furthermore,intheabsenceofcolorednoise,thisspectrumisnotnecessarilyLorentzianasg
4、enerallybelieved.Weshowthatthephasenoisespectrumofaperiodicsignalwithzerocycle-to-cyclejitterisalwaysLorentziananddemonstratetheappearanceof1/f4phasenoiseduetoaLorentziannoisesource.Wealsostudytwomethodsforsup-pressingtheeffectsoflow-frequency,colorednoiseonpha
5、senoise:signalsymmetrizationandnoise-sourceswitching.Weshowthatthesuppressionof1/f3phasenoiseinsingle-endedringoscillatorsisduetoswitchingandnotbecauseofsymmetrization.Symmetrizationiseffectiveonlyforthenoisesourceswhichareconstantly“on”,suchasthetailcurrentsou
6、rceindifferentialringoscillators.Thesefindingsprovideeffectiveguidelinesfordesigninglow-phase-noiseoscilla-tors.Keywords:electricaloscillator,jitter,phasenoise,ringoscillator,relaxationoscillator,frequencystability1.INTRODUCTIONDespiteitspracticalimportanceinco
7、mmunications,theformaldefinitionofphasenoiseremainsamatterofcontroversy.Atleasttwodistinctdefinitionsareintroducedbyvariousauthors.Oneofthesedefinitionsinvolvesthepowerspectraldensity(PSD)ofphase1,theotheroneisbasedonthePSDofthesignalitself2.Thechoiceofdefiniti
8、onisirrelevantatlargeoffsetfrequencies(hereafterreferredtoasfar-outphasenoise)becausethePSDofphasecanbeapproximatedbythePSDofthesignalatfar-outfrequencies3.However,thenumeri
