small_signal_noise_simulation

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1、NoiseFigureCalculationExerciseUsingMicrowaveCADSoftware1.0DerivationofNoiseFigureExpressionforComputerSimulationAsimplenoiseanalysisoftheresistivenetworkiscarriedout.Linear2-portnetworkPort1R1Port2R2RLVoutRSVinFigure1–Atwo-portresistivenetwork.TheoutputvoltageatPo

2、rt2isgivenby:R//RL2V=V=A×V(1)outininR//R+R+RL21SInequation(1)Aistheeffectivevoltagegain.DeactivatingthesourcevoltageVinandconsideringthethermalnoisefromtheresistors,theequivalentcircuitofFigure2isobtained.Port1R1Port2R2RLVoutRSVn24kTRVn124kT(R+R)S1Figure2–Equivale

3、ntcircuitwiththermalnoisesource,signalsourcedeactivated.F.Kung1June2004ThenoisesourcesVn1andVn2arewhitenoise,andthePowerSpectralDensity(PSD)Sn1andSn2whichareassumedconstantwithrespecttofrequency.S(f)=4kT(R+R)(2a)n1S1S(f)=4kTR(2b)n222AssumingabandwidthofDf.Usingthe

4、factthatV=S(f)dfandn1òn12()V=Sfdf,thecontributionofthenoisesourcesindividuallyattheoutputnodeisn2òn2givenasfollows:R//R22L()V=V=4kTR+RDf(3a)out(n1)out(n1)S1R//R+R+R2L1S(R+R)//R21SLV=V=4kTRDf(3b)out(n2)out(n2)()2R+R//R+R1SL2TherandomprocessduetoVn1andVn2canbecombin

5、edusingSuperpositionTheoremforlinearcircuit.SincenoisesourcesVn1andVn2areuncorrelated,thetotalPSDatport2is(See[1],Section11.4):S(f)=S(f)+S(f)(4a)n1n2Or222V=V+V(4b)out(noise)out(n1)out(n2)Thisimplies:12[22]2V=V=V+Vout(noise)out(noise)out(n1)out(n2)1ì22ü2(5)ïéR2//RL

6、()ùé(R1+RS)//RLùï=íê4kTRS+R1Dfú+ê4kTR2DfúýR//R+R+R(R+R)//R+Rïîë2L1Sûë1SL2ûïþNotthatincomputingthetotalnoisevoltage,thecontributionfromtheterminationatport2,e.g.RLisnotconsidered.Thesignal-to-noiseratioattheinput,SNRinisgivenby:2VinSNR=(6)in4kTRSThesignal-to-noiser

7、atioattheoutput,SNRoutisgivenby:()2A×VinSNR=(7)out2Vout(noise)F.Kung2June2004Thusthenoisefactorofthenetwork,from(6)and(7)is:2SNRinVout(noise)NF==(8)2SNRoutA×4kTRsThenoisefigure(F)indBisthengivenbyéSNRùinF=10×log(9)10êúSNRëoutûEquations(8)and(9)areusuallyemployedby

8、computersimulationsoftwaretodeterminethenoisefigureFofalinearcircuit.2.0NumericalExampleo-23-1LetRS=RL=50,R1=50andR2=100.T=25Cor298K,k=1.380´10JK.Bandwi