Lecture 23 - Frequency Response of Amplifiers (I) Common-Source Amplifier. December 1, 2005

Transcription

1 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,

2 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?

3 6.012 Microelectronic Devices and Circuits Fall 2005 Lecture 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 MMDS 3G WE Datacom LMDS Teledesic Video WirelessMAN Skybridge DOM Radio 'V Band' Spacewav BW (MHz) Figure by MIT OCW.

4 6.012 Microelectronic Devices and Circuits Fall 2005 Lecture 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

5 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 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

7 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 )

8 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.

9 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

10 f t of different device technologies Cutoff Frequency [GHz] Fujitsu (02, EDL) UIUC (03, EL) IBM (03, IPRM) IBM (04, VLSI) IIIV HEMT IIIV HBT SiGe HBT Si CMOS Year

11 6.012 Microelectronic Devices and Circuits Fall 2005 Lecture 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

12 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}

13 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

14 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.

15 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??!!

16 6.012 Microelectronic Devices and Circuits Fall 2005 Lecture 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

17 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.

18 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.