6.012 Microelectronic Devices and Circuits Fall 2005 Lecture 231 Lecture 23 Frequency Response of Amplifiers (I) CommonSource Amplifier December 1, 2005 Contents: 1. Introduction 2. Intrinsic frequency response of MOSFET 3. Frequency response of commonsource amplifier 4. Miller effect Reading assignment: Howe and Sodini, Ch. 10, 10.110.4
6.012 Microelectronic Devices and Circuits Fall 2005 Lecture 232 Key questions How does one assess the intrinsic frequency response of a transistor? What limits the frequency response of an amplifier? What is the Miller effect?
6.012 Microelectronic Devices and Circuits Fall 2005 Lecture 233 1. Introduction Frequency domain is a major consideration in most analog circuits. Data rates, bandwidths, carrier frequencies all pushing up. Motivation: Processor speeds Traffic volume data rates More bandwidth available at higher frequencies in the spectrum Frequency 60 50 40 25 20 4 0 0 MMDS 3G WE Datacom LMDS Teledesic Video WirelessMAN Skybridge DOM Radio 'V Band' Spacewav 2 8 20 40 45 100 155 500 BW (MHz) Figure by MIT OCW.
6.012 Microelectronic Devices and Circuits Fall 2005 Lecture 234 2. Intrinsic frequency response of MOSFET 2 How does one assess the intrinsic frequency response of a transistor? f t shortcircuit cuit currentgain cutoff frequency [GHz] 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 out : transistor effect i in due to gate capacitance Frequency dependence: f i in i out i in i out f t frequency at which = 1 i in
6.012 Microelectronic Devices and Circuits Fall 2005 Lecture 235 Complete smallsignal model 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 iin C gd 1 2 i out v s v gs C gs gm v gs node 1: i in v gs jωc gs v gs jωc gd =0 i in = v gs jω(c gs C gd ) node 2: i out g m v gs v gs jωc gd =0 i out = v gs (g m jωc gd )
6.012 Microelectronic Devices and Circuits Fall 2005 Lecture 236 Current gain: i out g m jωc gd h 21 = = i in jω(c gs C gd ) 2 Magnitude of h 21 : h 21 = g 2 ω 2 C 2 m gd ω(c gs C gd ) For low frequency, ω g m, C gd g m h 21 ω(cgs C gd ) For high frequency, ω g m, C gd h 21 C gd < 1 C gs C gd
6.012 Microelectronic Devices and Circuits Fall 2005 Lecture 237 log h 21 1 C gd 1 C gs C gd ω T log ω h 21 becomes unity at: g m ω T =2πf T = Cgs C gd Then: g m f T = 2π(Cgs C gd )
6.012 Microelectronic Devices and Circuits Fall 2005 Lecture 238 Physical interpretation of f T : Consider: 1 2πf T = C gs C gd g m C gs g m Plug in device physics expressions for C gs and g m : or 1 2πf T C gs g m = 2 3 LW C ox L µc ox(v GS V T ) = W L µ 3 V GS V T 2 L 1 2πf T L µ<e chan > = L <v chan > = τ t τ t transit time from source to drain [s] Then: f T 1 2πτ t f T gives an idea of the intrinsic delay of the transistor: good firstorder figure of merit for frequency response.
6.012 Microelectronic Devices and Circuits Fall 2005 Lecture 239 To reduce τ t and increase f T : L : tradeoff is cost (V GS V T ) I D : tradeoff is power µ : hard to do note: f T independent of W Impact of bias point on f T : W g m L µc oxi D f T = = L µc ox(v GS V T ) 2 W = 2π(C gs C gd ) 2π(C gs C gd ) 2π(C gs C gd ) f T f T 0 0 V T VGS 0 I D In typical MOSFET at typical bias points: f T 5 50 GH z
f t of different device technologies Cutoff Frequency [GHz] 600 500 400 300 200 100 Fujitsu (02, EDL) UIUC (03, EL) IBM (03, IPRM) IBM (04, VLSI) IIIV HEMT IIIV HBT SiGe HBT Si CMOS 0 1985 1990 1995 2000 2005 Year
6.012 Microelectronic Devices and Circuits Fall 2005 Lecture 2310 3. Frequency response 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 model (assuming current source has no parasitic capacitance): R S C gd v s v gs Cgs g m v gs C db r o r oc R L v out ' R out Lowfrequency voltage gain: A v,lf = v out = g m (r o //r oc //R L )= g m R out v s
6.012 Microelectronic Devices and Circuits Fall 2005 Lecture 2311 C gd RS 1 2 v s v gs C gs g m v gs C db R out ' v out node 1: v s v gs v gs jωc gs (v gs v out )jωc gd =0 R S node 2: (v gs v out )jωc gd g m v gs v out jωc db v out =0 R out Solve for v gs in 2: 1 jω(c gd C db ) R v gs = v out jωc gd g m out Plug in 1 and solve for v out /v s : with A v = (g m jωc gd )R DEN out DEN = 1 jω{r S C gs R S C gd [1 R 1 gm )] R ω 2 R S R outc gs (C gd C db ) out ( R S [check that for ω = 0, A v,lf = g m R out] out C db}
6.012 Microelectronic Devices and Circuits Fall 2005 Lecture 2312 Simplify: g m 1. Operate at ω ω T = Cgs C gd g m ω(c gs C gd ) > ωc gs,ωc gd 2. Assume g m high enough so that 1 gm g m R S 3. Eliminate ω 2 term in denominator of A v worstcase estimation of bandwidth Then: A v g m R out 1 jω[r S C gs R S C gd (1 g m R out ) R out C db] This has the form: A v (ω) = A v,lf 1 j ω ω H
6.012 Microelectronic Devices and Circuits Fall 2005 Lecture 2313 log A v g m R out ' 1 ω H log ω At ω = ω H : A v (ω H ) = 1 2 A v,lf ω H gives idea of frequency beyond which A v starts rolling off quickly bandwidth For commonsource amplifier: ω H = 1 R S C gs R S C gd (1 g m R out)r outc db Frequency response of commonsource amplifier limited by C gs and C gd shorting out the input, and C db shorting out the output.
6.012 Microelectronic Devices and Circuits Fall 2005 Lecture 2314 Can rewrite as: 1 f H = 2π{RS [C gs C gd (1 A v,lf )] R outc db } Compare with: g m f T = 2π(Cgs C gd ) 2 In general: f H f T due to typically: g m R 1 C db enters f H but not f T presence of A v,lf in denominator 2 To improve bandwidth, S C gs,c gd,c db small transistor with low parasitics A v,lf don t want more gain than really needed but... why is it that effect of C gd on f H appears to being amplified by 1 A v,lf??!!
6.012 Microelectronic Devices and Circuits Fall 2005 Lecture 2315 4. Miller effect In commonsource amplifier, C gd looks much bigger than it really is. Consider simple voltagegain stage: i in C v in Av v in v out What is the input impedance? i in =(v in v out )jωc But Then: v out = A v v in i in = v in (1 A v )C
6.012 Microelectronic Devices and Circuits Fall 2005 Lecture 2316 or v in 1 Z in = = i in jω(1 A v )C From input, C, looks much bigger than it really is. This is called the Miller effect. When a capacitor is located across nodes where there is voltage gain, its effect on bandwidth is amplified by the voltage gain Miller ler ca pacitance: : Why? C M iller = C(1 A v ) v in v out = A v v in (v in v out ) i in In amplifier stages with voltage gain, it is critical to have small capacitance across voltage gain nodes. As a result of the Miller effect, there is a fundamental gainbandwidth andwidth tradeoff in amplifiers.
6.012 Microelectronic Devices and Circuits Fall 2005 Lecture 2317 Key conclusions f T (shortcircuit currentgain cutoff frequency): figure of merit to assess intrinsic frequency response of transistors. In MOSFET, to first order, 1 f t = 2πτt where τ t is transit time of electrons through channel. In commonsource amplifier, voltage gain rolls off at high frequency because C gs and C gd short out input and C db shorts out output. In commonsource amplifier, effect of C gd on bandwidth is magnified by amplifier voltage gain. Miller effect: effect of capacitance across voltage gain nodes is magnified by voltage gain tradeoff between gain and bandwidth.