1EE105 - Fall 2005Microelectronic Devices and CircuitsLecture 20Common Source AmplifierFrequency Response2AnnouncementsHomework 9 due next TuesdayLab 7 this weekLab 8 next week (please read Chapter 9)Reading: Chapter 10 (10.2, 10.3.2, 10.4.3-5 )3Lecture MaterialLast lectureSecond-order circuitsStarted frequency response of amplifiersThis lectureCommon source amplifier – frequency responseMiller effectZero-order time constants5Common Source Amplifer: Ai(jω)DC Bias is problematic: what sets VGS?6CS Short-Circuit Current GainTransfer function:())(/1)(gdgsmgdmiCCjgCjgjA+ωω−=ω7Magnitude Bode Plot ωT Transition frequency:Current gain = 128MOS Unity Gain FrequencySince the zero occurs at a higher frequency than pole, assume ithas negligible effect:1()migs gdgAjC Cω≈=+()mTgsgdgCCω=+2()()3223ox GS TmGSTTgsoxWCVVgVVLCLWLCμμω−−≈= =Performance improves with L2for long channel devices!For short channel devices the dependence is ~ L12()3~2GS TeffGS TTLVVEVVvLLLLLμμμωτ−−≈===Time to cross channel9Common-Source Voltage AmplifierSmall-signal model:omit Ccsdue to avoid complicated analysisVDDRsRL+vOUT+vsVGS-VSSICS10CS Voltage Amp Small-Signal ModelRsRL+voutvsro||rocvgs+CgsCgdgmvgs11Frequency ResponseKCL at input and output nodes; analysis is made complicated due to Zgdbranch Æ see H&S pp. 639-640 (for common emitter)[]()()( )21/1/1/1||||ppzLocominoutjjjRrrgVVωω+ωω+ωω−−=Low-frequency gain: Zero:gdgsmTzCCg+=ω>ω12Poles(){}gdoutgdoutmgsSpCRCRgCR′+′++≈ω111(){}gdoutgdoutmgsSSoutpCRCRgCRRR′+′++′≈ω1/213Miller ImpedanceConsider the current flowing through an impedance Z hooked up to a “black-box” where the voltage gain from one terminal to the other is fixedZ1v2v21vvAv=I111211vvvAv AvvIvZZZ−−−== =314Miller ImpedanceNotice that the current flowing into Z from terminal 1 looks like an equivalent current to ground where Z is transformed down by the Miller factor:From terminal 2, the situation is reciprocal1,111vMvAZIv ZZA−=→=−11222121vvvAv AvvIvZZZ−−−−−−= = =,211MvZZA−=−15Miller Equivalent CircuitWe can decouple these terminals if we can calculate the gain Av across the impedance ZOften the gain Avis weakly depedendent on ZThe approximation is to ignore Z, calculate Av, and then use the decoupled Miller impedances,11MvZZA=−,111MvZZA−=−Note:,1 ,2MMZZZ+=16CE Amplifier using Miller Approx.Use Miller to transform CgdRsRL+voutvsro||rocvgs+CgsCgdgmvgs17Comparison with “Exact Analysis”Miller result:Exact result:=ω−11p()( ){}μμππ−′+′++=ω CRCRgCrRoutoutmSp1||1118Some ExamplesCommon source amplifier:=gdvCAnegative, large number (-100)Common drain amplifier:=gdvCAslightly less than 1Miller multiplied cap has detrimental Impact on bandwidth“Bootstrapped” cap has negligible impact on bandwidth!19Method 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,121pdomωττ=++L420Equivalent Resistance “Seen” by CapacitorFor each “small” capacitor in the circuit:Open-circuit all other “small” capacitorsShort circuit all “big” capacitorsTurn off all independent sourcesReplace cap under question with current or voltage sourceFind equivalent input impedance seen by capForm RC time constantThis procedure is best illustrated with an example…21Example
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