Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 20Lecture 20:Frequency Response: Miller EffectProf. NiknejadDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 20 Prof. A. NiknejadLecture OutlineFrequency response of the CE as voltage ampThe Miller approximationFrequency Response of Voltage BufferDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 20 Prof. A. NiknejadLast Time: CE Amp with Current InputCalculate the short circuit current gain of device (BJT or MOS)Can be MOSDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 20 Prof. A. NiknejadCS Short-Circuit Current Gain()1/()()( )mgdmmigs gd gs gdgjCggAjjC C jC Cωωωω−=≈++MOS Case0 dBMOSBJTTωzωNote: Zero occurs when all of “gm” current flows into Cgd:mgs gs gdgv v j Cω=Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 20 Prof. A. NiknejadCommon-Emitter Voltage AmplifierSmall-signal model:omit Ccsto avoid complicated analysisCan solve problem directlyby phasor analysis or using2-port models of transistorOK if circuit is “small”(1-2 nodes)Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 20 Prof. A. NiknejadCE Voltage Amp Small-Signal ModelTwo Nodes! EasySame circuit works for CS withrπ→∞Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 20 Prof. A. NiknejadFrequency 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+=>[]()()()[]|| || 1 0||||1010moocLSoutmoocLin SrgrrRjrRVrgrrRVjj rRππππ−−+=→−++ +Two PolesZeroNote: Zero occurs due to feed-forwardcurrent cancellation as beforeDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 20 Prof. A. NiknejadExact Poles()( ){}µµππωCRCRgCrRoutoutmSp′+′++≈1||11()()( ){}µµπππωCRCRgCrRrRRoutoutmSSoutp′+′++′≈1||||/2These poles are calculated after doing some algebraic manipulations on the circuit. It’s hard to get any intuition from the above expressions.Usually >> 1Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 20 Prof. A. NiknejadMiller ApproximationResults of complete analysis: not exact and little insightLook at how Zµaffects the transfer function: find ZinDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 20 Prof. A. NiknejadInput Impedance Zin(jωωωω)At output node:µZVVIouttt/)( −=outtmoutttmoutRVgRIVgV′−≈′−−= )(Why?µµZVAVItvCtt/)( −=µµvCttinAZIVZ−==1/Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 20 Prof. A. NiknejadMiller Capacitance CMEffective input capacitance:()[]µµµωωωµCAjCjACjZvCvCMin−=−==111111AV,Cx+─+─VinVoutCxAV,Cx+─+─Vout(1-Av,Cx)Cx(1-1/Av,Cx)CxDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 20 Prof. A. NiknejadSome ExamplesCommon emitter/source amplifier:=µvCANegative, large number (-100)Common collector/drain amplifier:=πvCASlightly less than 1,(1)100MVCCACCµµµ=− ,(1)0MVCCACππ=− Miller Multiplied Cap has Detrimental Impact on bandwidth“Bootstrapped” cap has negligible impact on bandwidth!Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 20 Prof. A. NiknejadCE Amplifier using Miller Approx.Use Miller to transform CµAnalysis is straightforward now … single pole!||SRrπDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 20 Prof. A. NiknejadComparison with “Exact Analysis”Miller result (calculate RC time constant of input pole):Exact result:()( ){}µµππωCRCRgCrRoutoutmSp′+′++=−1||11()( ){}11|| 1pS moutRrC gRCππµω−′=++Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 20 Prof. A. NiknejadMethod of Open Circuit Time Constants This is a technique to find the dominant pole of a circuit (only valid if there really is a dominant pole!)For each capacitor in the circuit you calculate an equivalent resistor “seen” by capacitor and form the time constant τi=RiCiThe dominant pole then is the sum of these time constants in the circuit,121p domωττ=++Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 20 Prof. A. NiknejadEquivalent Resistance “Seen” by CapacitorFor each “small” capacitor in the circuit:– Open-circuit all other “small” capacitors– Short circuit all “big” capacitors– Turn off all independent sources– Replace cap under question with current or voltage source– Find equivalent input impedance seen by cap– Form RC time constantThis procedure is best illustrated with an example…Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 20 Prof. A. NiknejadExample CalculationConsider the input capacitanceOpen all other “small” caps (get rid of output cap)Turn off all independent sourcesInsert a current source in place of cap and find impedance seen by source 1 MCCCπ=+||MSRrRπ=()( ){}1|| 1SmoutRrC gRCππµτ′=++Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 20 Prof. A. NiknejadCommon-Collector AmplifierProcedure:1. Small-signal two-port model2. Add device (andother) capacitorsDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 20 Prof. A. NiknejadTwo-Port CC Model with CapacitorsFind Miller capacitor for Cπ-- note that the base-emitter capacitor is between the input and outputGain ~ 1Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 20 Prof. A. NiknejadVoltage Gain AvCππππAcross Cππππ/()1vC out out LARRRπ≈+∼Note: this voltage gain is neither the two-port gain nor the “loaded” voltage gainπµµπCACCCCvCMin)1( −+=+=11inmLCC CgRµπ=++inCCµ≈1outmRg=1mLgR>>Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 20 Prof. A. NiknejadBandwidth of CC AmplifierInput low-pass filter’s –3 dB frequency:()++=−LminSpRgCCRR1||1πµωSubstitute favorable values of RS, RL:mSgR /1≈mLgR /1>>()mmpgCBIGCCg
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