R. T. HoweEECS 105 Spring 2002 Lecture 31Dept. of EECSUniversity of California at BerkeleyLecture 31• Last time:– Short-circuit current gain of CE and CS amps– Unity-gain frequency ωT• Today :– Frequency response of the CE as voltage amp– The Miller approximationR. T. HoweEECS 105 Spring 2002 Lecture 31Dept. of EECSUniversity of California at BerkeleyCommon-Emitter Voltage AmplifierSmall-signal model:omit Ccsdue to avoid complicated analysisR. T. HoweEECS 105 Spring 2002 Lecture 31Dept. of EECSUniversity of California at BerkeleyCE Voltage Amp Small-Signal ModelR. T. HoweEECS 105 Spring 2002 Lecture 31Dept. of EECSUniversity of California at BerkeleyFrequency ResponseKCL at input and output nodes; analysis is made complicated due to Zµbranch ! see H&S pp. 639-640.[]()()()21/1/1/1||||ppzLocoSminoutjjjRrrRrrgVVωωωωωωππ++−+−=Low-frequency gain: Zero:µπωωCCgmTz+=>R. T. HoweEECS 105 Spring 2002 Lecture 31Dept. of EECSUniversity of California at BerkeleyPoles()( ){}µµππωCRCRgCrRoutoutmSp′+′++≈1||11()()( ){}µµπππωCRCRgCrRrRRoutoutmSSoutp′+′++′≈1||||/2R. T. HoweEECS 105 Spring 2002 Lecture 31Dept. of EECSUniversity of California at BerkeleyDecoupling Input and Output:the Miller ApproximationResults of complete analysis: not exact and little insightLook at how Zµaffects the transfer function: find ZinR. T. HoweEECS 105 Spring 2002 Lecture 31Dept. of EECSUniversity of California at BerkeleyInput Impedance Zin(jω)At output node:µZVVIouttt/)(−=outtmoutttmoutRVgRIVgV′−≈′−−=)(Why?µµZVAVItvCtt/)(−=µµvCttinAZIVZ−==1/R. T. HoweEECS 105 Spring 2002 Lecture 31Dept. of EECSUniversity of California at BerkeleyMiller Capacitance CMEffective input capacitance:()[]µµµωωωµCAjCjACjZvCvCMin−=−==111111 Cx AvCx + - - + Vin Vout What about the role of Cxwhen viewed from the output port?R. T. HoweEECS 105 Spring 2002 Lecture 31Dept. of EECSUniversity of California at BerkeleySome ExamplesCommon emitter/source amplifier:=µvCANegative, large number (-100)Common collector/drain amplifier:=πvCASlightly less than 1R. T. HoweEECS 105 Spring 2002 Lecture 31Dept. of EECSUniversity of California at BerkeleyCE Amplifier using Miller Approx.Use Miller to transform CµAnalysis is straightforward now … single pole!R. T. HoweEECS 105 Spring 2002 Lecture 31Dept. of EECSUniversity of California at BerkeleyComparison with “Exact Analysis”Miller result:Exact result:=−11pω()(
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