6.0 Microelectronic Devices and Circuits Spring 003 Lecture 3 Lecture 3 Frequency Resp onse of Amplifiers (I) CommonSource Amplifier May 6, 003 Contents:. Intro duction. Intrinsic frequency resp onse of MOSFET 3. Frequency resp onse of commonsource amplifier 4. Miller effect Reading assignment: Howe and So dini, Ch. 0, 0.0.4
6.0 Microelectronic Devices and Circuits Spring 003 Lecture 3 Key questions How do es one assess the intrinsic frequency resp onse of a transistor? What limits the frequency resp onse of an amplifier? What is the Miller effect?
6.0 Microelectronic Devices and Circuits Spring 003 Lecture 33. Intro duction Frequency domain is a ma jor consideration in most analog circuits. Data rates, bandwidths, carrier frequencies all pushing up. Motivation: Pro cessor sp eeds Traffic volume data rates More bandwidth available at higher frequencies in the sp ectrum [from Agilent Technologies]
6.0 Microelectronic Devices and Circuits Spring 003 Lecture 34. Intrinsic frequency resp onse of MOSFET How do es one assess the intrinsic frequency resp onse of a transistor? f shortcircuit currentgain cutoff frequency [GHz] t Consider MOSFET biased in saturation regime with smallsignal source applied to gate: V DD i G =i in i D =I D i out v s V GG v s at input i i out in : transistor effect due to gate capacitance i out i in Frequency dep endence: f i in iout f frequency at which = t iin
6.0 Microelectronic Devices and Circuits Spring 003 Lecture 35 Complete smallsignal mo del in saturation: i in G C gd i out v s v gs S Cgs g m v gs g mb v bs r o C db D v bs C sb B v bs =0 i in C gd i out v s v gs C gs gm v gs no de : iin v gs jω Cgs v gs jω Cgd = 0 iin = v gs jω (Cgs Cgd ) no de : iout g m v gs v gs jω Cgd = 0 iout = v gs (g m jω Cgd )
6.0 Microelectronic Devices and Circuits Spring 003 Lecture 36 Current gain: i out g m jω C gd h = = i jω (C C ) in gs gd Magnitude of h : h = g ω Cgd m ω (C gs C gd ) g m C gd For low frequency, ω, h g m ω (C gs C gd ) g m C gd For high frequency, ω, Cgd h < C C gs gd
6.0 Microelectronic Devices and Circuits Spring 003 Lecture 37 log h C gd C gs C gd ω T log ω h b ecomes unity at: ω T =πf T = C gs g m C gd Then: f = T g m π (C gs C gd )
6.0 Microelectronic Devices and Circuits Spring 003 Lecture 38 Physical interpretation of f : T Consider: C C C = πf g g gs gd gs T m m Plug in device physics expressions for C gs and g m : or C gs LW C ox L = 3 = πf g µc (V V ) µ W V V T m L ox GS T L 3 GS T L L = = τt πf µ< E > <v > T chan chan Then: τ transit time from source to drain [s] t f T πτ t f T gives an idea of the intrinsic delay of the transistor: go o d firstorder figure of merit for frequency resp onse.
6.0 Microelectronic Devices and Circuits Spring 003 Lecture 39 To reduce τ t and increase f T : L : tradeoff is cost (V V ) I : tradeoff is p ower GS T D µ : hard to do note: f T indep endent of W Impact of bias p oint on f : T W m L ox GS T L W g µc (V V ) µc ox I D f T = = = π (C C ) π (C C ) π (C C ) gs gd gs gd gs gd f T f T 0 0 V T VGS 0 I D In typical MOSFET at typical bias p oints: f 5 GH z T
6.0 Microelectronic Devices and Circuits Spring 003 Lecture 30 3. Frequency resp onse of commonsource amp V DD i SUP signal source R S v s V GG v OUT signal load R L V SS Smallsignal equivalent circuit mo del (assuming current source has no parasitic capacitance): R S C gd v s v gs C gs gm v gs C db r o r oc R L v out R out ' Lowfrequency voltage gain: Av,LF = v out v s = g m (r o //r oc //RL) = g m Rout
6.0 Microelectronic Devices and Circuits Spring 003 Lecture 3 R S C gd v s v gs C gs g m v gs C db R out ' v out no de : v s v gs R S v gs jω Cgs (v gs v out )jω Cgd = 0 v out R out no de : (v gs v out )jω Cgd g m v gs v out jω Cdb =0 Solve for v gs in : v gs = v out jω (Cgd Cdb )R out jω C gd g m Plug in and solve for v out /v s : with A = v (g jωc )R DEN m gd out DEN = jω{r C R C [ R ( g )] R C } S gs S gd out m out db R S S out gs gd db ω R R C (C C ) [check that for ω =0, A v,lf = g m R out]
6.0 Microelectronic Devices and Circuits Spring 003 Lecture 3 Simplify: g m gs. Op erate at ω ω = T C C g ω (C C ) >ω C,ω C m gs gd gs gd. Assume g high enough so that m RS gd g g 3. Eliminate ω term in denominator of Av worstcase estimation of bandwidth Then: m m Av g R m out jω [R S Cgs RS Cgd ( g m Rout) R outcdb ] This has the form: Av Av,LF (ω ) = j ω ω H
6.0 Microelectronic Devices and Circuits Spring 003 Lecture 33 log A v g m R out ' ω H log ω At ω = ω : H A v (ω H ) = A v,lf ω H gives idea of frequency b eyond which A v starts rolling off quickly bandwidth For commonsource amplifier: ω = H R C R C ( g R ) R S gs S gd m out out C db Frequency resp onse of commonsource amplifier limited by C gs and C gd shorting out the input, and C db shorting out the output.
6.0 Microelectronic Devices and Circuits Spring 003 Lecture 34 Can rewrite as: f = H π {R [C C ( A )] R S gs gd v,lf out C db } Compare with: f = T g m π (C gs C gd ) In general: f f due to H T typically: g m R S C db enters f H but not f T presence of A v,lf in denominator To improve bandwidth, C,C,C A but... gs gd db v,lf small transistor with low parasitics don t want more gain than really needed why is it that effect of C on f app ears to b eing amgd H plified by A??!! v,lf
6.0 Microelectronic Devices and Circuits Spring 003 Lecture 35 4. Miller effect In commonsource amplifier, C it really is. gd lo oks much bigger than Consider simple voltagegain stage: i in C v in A v v in v out What is the input imp edance? i =(v v )jω C in in out But v out = A v v in Then: i = v ( A )C in in v
6.0 Microelectronic Devices and Circuits Spring 003 Lecture 36 or v in Z in = = i jω ( A )C in From input, C, lo oks much bigger than it really is. This is called the Miller effect. When a capacitor is lo cated across no des where there is voltage gain, its effect on bandwidth is amplified by the voltage gain Miller capacitance: v Why? C M iller = C( A v ) v v = A v (v v ) i in out v in in out in In amplifier stages with voltage gain, it is critical to have small capacitance across voltage gain no des. As a result of the Miller effect, there is a fundamental gainbandwidth tradeoff in amplifiers.
6.0 Microelectronic Devices and Circuits Spring 003 Lecture 37 Key conclusions f (shortcircuit currentgaincutoff frequency): fig T ure of merit to assess intrinsic frequency resp onse of transistors. In MOSFET, to first order, f = t πτ t where τ is transit time of electrons through channel. t In commonsource amplifier, voltage gain rolls off at high frequency b ecause C gs and C gd short out input and C shorts out output. db In commonsource amplifier, effect of C gd on band width is magnified by amplifier voltage gain. Miller effect: effect of capacitance across voltage gain no des is magnified by voltage gain tradeoff between gain and bandwidth.