mismatch-distortion匹配失真习题讲解

Noise,[e-mail]@esat.kuleuven.beKULeuvenESAT-MICASAnalogbuildingblocksforsignalprocessing11NoiseNoiseAnalogbuildingblocksforsignalprocessing22Theoryy-Bothintime-andfrequencydomain:x(t)andX(f)mean=0:00iv-mean=0:-power≠0!!0,0nniv-Expressedas:=meanpowerofanoisesignalvninabandwidthof1Hzaroundfrequencyf][)(2)(22/HzVfSfdvnvninabandwidthof1Hzaroundfrequencyf-Totalnoisepowerp=totalintegratedoutputnoise][)(202,2,VdffdvVoutnoutnrmsAnalogbuildingblocksforsignalprocessing33AnalogbuildingblocksforsignalprocessingTheoryy-Noisebandwidth:totalintegratedoutputnoise=DCvalueofnoise*noisebandwidthBNnoise:1storderbehavior:220,0()NvnoutvBdfdf02NfB-2kindsofnoise:Whitenoise:ctefdvn)(2Pinknoise:Cfffn)(2()nctedvffAnalogbuildingblocksforsignalprocessing44CornerfrequencyfcAnalogbuildingblocksforsignalprocessingNoise:circuitelements-Noisedensitycausedbycircuitelements:Analogbuildingblocksforsignalprocessing55-Capacitors&inductors:nonoiseinjection!AnalogbuildingblocksforsignalprocessingNoise:circuitelementsCalculationmethodfortotal,equivalentinputnoise:1.Foreachnoisesourceinthecircuit:-determinenoisequantityofthesource:)(2fdiv)(fH-determinetransferfunctionfromnoisesourcetocircuitoutput:(smallsignalmodel!!)2.Totaloutputnoise:)(fHi)()()(222fdvfHfdvp3.Total,equivalentinputnoise:)()()(,fdvfHfdviiitotout2221()()intotvdvfdf,,2()()()outtotintotvffHfAnalogbuildingblocksforsignalprocessing66AnalogbuildingblocksforsignalprocessingNoise:systemlevely-Signal-to-NoiseRatio:2,10210log[dB]srmsVSNRV-NoisefactorF=measureoftheSNRdegradationwhenasignalpropagatingthroughasystem2,nrmsVsystemoutinSNRSNRF-Noisefigure:NF[dB]=10*log10(F)=SNRin[dB]–SNRout[dB]-Cascadeofcircuits:totalinputnoisefactor:32122211211TotFFFFAAAwhereA1andA2arethevoltagegain(inabsolutenumbers)Analogbuildingblocksforsignalprocessing77Analogbuildingblocksforsignalprocessing12gg()Exercise1:assignmentgAreceiverconsistsofafilterandamixer.Thefilterattenuates3.75dBandhasanoisefigureof3.75dB.Themixerhasanoisefigureof16dB.(a)Calculatetheequivalentnoisefigureattheinputofthefilter.(b)Togetabetternoiseperformance,anamplifierwithagainof20dBandanoisefigureof3dBisaddedtothecircuit.DeterminethebestpositionforthisamplifierandcalculateDeterminethebestpositionforthisamplifierandcalculatetheequivalentnoisefigure.Analogbuildingblocksforsignalprocessing8Exercise1:solutionIEquivalentnoisefigureattheinput:with:21211totFFFAA1=10(-3.75/20)=0,649F1=10(3.75/10)=2,371F2=10(16/10)=39,811→noisefactorFtot=94,5noisefigureNF=10log(945)=1975dBAnalogbuildingblocksforsignalprocessing9→noisefigureNFtot=10log10(94,5)=19,75dBExercise1:solutionIIAddamplifier:A=20dB,NF=3dB.Option1:Equivalentnoisefigureattheinput:2222,371139,81111,992,3910100,649totF,10log(2,39)4,66totNFdBAnalogbuildingblocksforsignalprocessing10Exercise1:solutionIIIAddamplifier:A=20dB,NF=3dB.Option2:Equivalentnoisefigureattheinput:2221,99139,81112,3715,650,649100,64910log(565)752totFNFdB→Placethecomponentwithhighestgainatthefrontoftheiithiththbtif!!10log(5,65)7,52totNFdBAnalogbuildingblocksforsignalprocessing11circuitchaintohavethebestnoiseperformance!!Exercise2:assignmentgCalculatethetotalequivalentinputCalculatethetotal,equivalentinputnoiseforthecascodestageshownontheright.Theoutputresistanceand1/fnoiseofthetransistorscanbeand1/fnoiseofthetransistorscanbeneglected.WhdthifthdWhendoesthenoiseofthecascodetransistorbecomeimportant?Analogbuildingblocksforsignalprocessing1212AnalogbuildingblocksforsignalprocessingExercise2:solutionICalculationmethodfortotal,equivalentinputnoise:1.Foreachnoisesourceinthecircuit:-determinenoisequantityofthesource:)(2fdiv)(fH-determinetransferfunctionfromnoisesourcetocircuitoutput:(smallsignalmodel!!)2.Totaloutputnoise:)(fHi)()()(222fdvfHfdvp3.Total,equivalentinputnoise:)()()(,fdvfHfdviiitotout2221()()intotvdvfdf,,2()()()outtotintotvffHfAnalogbuildingblocksforsignalprocessing1313AnalogbuildingblocksforsignalprocessingExercise2:solutionIINoiseexpressionsforeachnoisesource:24)(DRRkTfdi2,382)(2mMDkTgfdiR1,3821)(mMkTgfdiAnalogbuildingblocksforsignalprocessing1414AnalogbuildingblocksforsignalprocessingExercise2:solutionIIITransferfunctionnoisesource–circuitoutput:(lt)(neglectrout)1.RD:xmoutvgiRv02DoutRxxxmxmDRvjHvCjvgR)(0222.M2:DRRijHD)(20outmxDvigvR2220()DxxmxDxMmxjCvigvjRCHjgjCAnalogbuildingblocksforsignalprocessing15152mxgjAnalogbuildingblocksforsignalprocessingExercise2:solutionIV3.M1:xxxmxmDoutvCjivgvgRv2204.in-out(total):xmDmMCjgRgjH22)(1()20outmxDvgvR1212()DminxxmxmmDRgvjCvgvggHjRgjCAnalogbuildingblocksforsignalprocessing16162mxgjCAnalogbuildingblocksforsignalprocessingExercise2:solutionVTotaloutputnoise:Totalequivalentinputnoise11222222222,()()()()()()()DDouttotRRMMMMdvfHjdifHjdifHjdifTotalequivalentinputnoise11222222222,21()()()()()()()()DDineqRRMMMMdvfHjdifHjdifHjdifHj22