DesignofAnalogIntegratedCircuitsnoise2/1/20231Outline7.1StatisticalCharacteristicsofNoise7.2TypesofNoise7.3RepresentationofNoiseinCircuits7.4NoiseinSingle-stageAmplifiers7.5NoiseinDifferentialPairs7.6NoiseBandwidth2/1/202327.1StatisticalCharacteristicsofNoiseTheaveragepowerofnoiseispredictable.sincethesignalsarenotperiodic,themeasurementmustbecarriesoutoveralongtime:Forcalculationsimply,PavisexpressedinV2ratherthanW.Wecanalsodefinearoot-mean-square(rms)voltagefornoiseas2/1/202337.1.1NoiseSpectrumSpectrum:Alsocalledthe“powerspectraldensity”(PSD),itshowshowmuchpowerthesignalcarriesateachfrequency..ThePSD,Sx(f),ofanoisewaveformx(t)isdefinedastheaveragepowercarriedbyx(t)inaone-hertzbandwidtharoundf.Sx(f)isexpressedinV2/Hz,itisalsocommontotakethesquarerootofSx(f),expressingtheresultin2/1/202347.1.1NoiseSpectrum(cont.)Theorem7-1:IfasignalwithspectrumSx(f)isappliedtoalineartime-invariantsystemwithtransferfunctionH(s),thentheoutputspectrumisgivenbyWhereH(f)=H(s=j2πf)2/1/202357.1.2CorrelatedandUncorrelatedSourcesInnoiseanalysis,ultimatelytheaveragenoisepowerisofinterest,weaddtwonoisewaveformsandtaketheaverageoftheresultingpower:Ifgeneratedbyindependentdevices,thenoisewaveformsareusually“uncorrelated”andtheintegralitemvanishes.Wesaysuperpositionholdsforthepowerofuncorrelatednoisesources.2/1/202367.2TypesofNoiseinDevices7.2.1ThermalNoiseResistorThermalNoiseExample:a50ΩresistorheldatT=300Kexhibits8.28×10-19V2/Hzofthermalnoise.i.e.0.91nV/Hz1/2.

k=1.38×10-23J/K,Boltzmannconstant.Canbemodeledbyaseriesvoltagesource2/1/202377.2.1ThermalNoise(cont.)RCcircuitsThetransferfunctionfromVRtoVout:Fromthetheorem7-1,wehaveThetotalnoisepowerattheoutput,2/1/202387.2.1ThermalNoise(cont.)Thethermalnoiseofaresistorcanberepresentedbyaparallelcurrentsource.Expressedin為A2/HzExample:2/1/202397.2.1ThermalNoise(cont.)ThermalNoiseinMOSFETNoiseinchannelwithWhere,γ（nottobeconfusedwiththebodyeffectcoefficient）Forlong-channel,γ＝2/3Forshot-channel,γ＝2,3orlarger.ThermalnoiseintheohmicsectionsofMOSFETsForawidetransistor,thesourceanddrainresistanceisnegligible;LumpedresistorR1representsthedistributedgateresistanceRG,R1＝RG/3※2/1/2023107.2.2FlickerNoiseFlickerNoise“dangling”bondsModeledasavoltagesourceinserieswiththegate:Kisaprocess-dependentconstantontheorderof10-25V2FFlickernoisecornerfrequency

2/1/2023117.3RepresentationofNoiseinCircuitsInput-referenceNoiseFirst,gettotaloutputnoise;Theideaistorepresenttheeffectofallnoisesourcesinthecircuitbyasinglesourceatinput.Letinputstozero,calculatethetotaloutputnoiseofgenerationofallnoiseincircuits.However,theoutputnoiseisdependencetothegain,thenoiseisdifficultytocompare.Generally,representationofnoisebyvoltageandcurrentsources.Accordinginputimpedanceofsignalsourceandthecircuits,thevoltageorcurrentsourceisused.Mustconsiderthecorrelationbetweentwotypesofnoisesource.2/1/202312GDSSCGDCGSgmvGSrovGSVDSIf↓thermalnoise,↑ID、↑W、↓LGDSSCGSgmvGSrOvGSvDSCGDIf↓flickernoise,↑WLTradeoff？example:noisecalculationofMOS2/1/2023134、Noiseinsingle-stageAmplifier4.1NoiseinCommon-sourceStageThinkabout:designoflownoiseCSstage？Tradeoff？2/1/2023144.2NoiseinCommon-gateStageOwingthelowinputimpedance,theinput-referencenoisecurrentisnotnegligible.Neglectingchannel-modulation,onlyconsideringthermalnoisehere,1/fsimilarCurrentnoiseVoltagenoiseDrawback:CGdirectlyreferthenoisecurrentproducedbytheloadtotheinput.2/1/2023154.3NoiseinCommon-drainstage(SourceFollower)Sincetheinputimpedance,theinput-referrednoisecurrentisneglected.onlyconsideringthermalnoisehere,1/fsimilarTheoutput-referencenoisecomingfromM2Sincesourcefollowersaddnoisetotheinputsignalwhileprovidingavoltagegainlessthanunity,theyareusuallyavoidinlow-noiseamplification.2/1/2023164.4NoiseincascodeM2doesnotaffectVn,outAtlowfrequencies,thenoisecurrentofM1andRDflowthroughRD,thenoisecontributedbyM1andRDisquantifiedasinacommon-sourceM1M2的電流噪聲In2折算到M2的柵端的電壓噪聲，然后按帶源極負(fù)反饋的共源級(jí)電路計(jì)算到Vnout的值，若M1的輸出電阻非常大，則增益很小，可以忽略其影響。Sincetheinputimpedance,theinput-referrednoisecurrentisneglected.Neglectingchannel-modulation,onlyconsideringthermalnoisehere,1/fsimilar2/1/2023175.NoiseinDifferentialPairsAdifferentialpaircanbeviewedasatwo-portcircuit.Sincetheimpedanceofthecircuitislarge,forlow-frequencyoperation,istypicallynegligible2/1/202318Input-referenceNoiseofDifferentialPairSincenoisesareuncorrelated,superpositionofpowerispossibleNeglectingchannel-modulation,2/1/2023196.NoiseBandwidthConsideramulti-polecircuithavingtheoutputnoisespectrumasBnisdefinedas“NoiseBandwidth”.Thenoisebandwidthofaone-polesystemisequaltoπ/2timesofthepolefreq