1EE105 - Fall 2005Microelectronic Devices and CircuitsLecture 21Time ConstantsFrequency Response of Common Drain/Common Source Amplifiers2AnnouncementsHomework 9 due todayHomework 10 due next TuesdayLab 8 this week (please read Chapter 9)Friday is a University holiday (no lab/discussion)Friday lab 8 on November 18No new lab next weekMidterm 2 next Thursday (Nov. 17)Review session on Tuesday, Nov. 15, 6:30-8pmReading: Chapter 10 (10.2, 10.3.2, 10.4.3-5 , 10.5-10.6)3Lecture MaterialLast lectureCommon source amplifier – frequency responseMiller effectThis lectureZero-order time constantsCommon drain, common gate frequency response4Miller Effect 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!5Method 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=++L6Equivalent 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…27Example CalculationRsRL+voutvsro||rocvgs+CgsCgdgmvgs8Higher-Order Time ConstantsGeneral two-pole transfer function:)1)(1()1)(1()(11210ppzzjjjjAjAωω+ωω+ωω+ωω+=ω()22101)()(ω+ω+ω=ωjajajNAjA21111ppaω+ω=2121ppaωω=9Higher-Order Time ConstantsCoefficient a1a1= R011C1+ R022C2Coefficient a2:a1= R211C1R022C2 =R011C1R122C2This is exact!If ωp1<< ωp2: 111paω≈212paaω≈10Example CalculationRsRL+voutvsro||rocvgs+CgsCgdgmvgs11Gain-Bandwidth ProductResult from Miller:Low-frequency gain:outmLRSRsoutvoRgvvA′−==,() ( ){}gdoutmgsSpCRgCR′++≈ω−11112Gain-Bandwidth ProductConsidering only the first pole(assuming zero and 2ndpole are at much higher frequencies):()1*=ωjAvω()dBvjAωvoA*ω()ωω=ωω≈ωω+≈ω1111pvopvopvovAAjAjA1*pvoA ω=ωÆ313Gain-Bandwidth ProductFor common-source amplifier:()gdoutmSgsSoutmpvoCRgRCRRgA′++′=ω11Special case: RS≈ RL< ro, rocTgdLmgsSLmpvoCRgCRRgA ω<<+≈ω)(1not that great!14Common-Drain AmplifierVDDRsRL+vOUT+vsVGS-VSSICS15Two-Port CD Model with CapacitorsIgnore gmbFind Miller capacitor for Cgs-- note that the gate-source capacitor isbetween the input and output16Voltage Gain AvCπAcross CπNote: this voltage gain is neither the two-port gain nor the “loaded” voltage gaingsgsvCgdMgdinCACCCC )1( −+=+=1≈+=outLoutgsvCRRRAgsLmgdinCRgCC++=11gdinCC ≈17Bandwidth of CC AmplifierInput low-pass filter’s –3 dB frequency:⎟⎟⎠⎞⎜⎜⎝⎛++=ω−LmgsgdSpRgCCR11Substitute favorable values of RS, RL:mSgR /1≈mLgR /1>>()mgdgdgdmpgCBIGCCg /1/11≈⎟⎟⎠⎞⎜⎜⎝⎛++≈ω−Model not valid at these high frequenciesTgdmpCg ω>≈ω /18Bandwidth of the Common-Gate Amplifier419Two-Port CB Model with CapacitorsNo Miller-transformed capacitor!Unity-gain frequency is on the order of ωTfor small RL+voutvsrovgs+CgsCgdgmvgsRsRL||roc20Summary of Single-Stage AmplifiersCS: suffers from Miller-magnified capacitor for high-gain caseCD: Miller transformation Æ nulled capacitor Æ“wideband stage”CG: no “Millerized” capacitor Æ wideband stage (for low load
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