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

Transcription

1 6.02 Microelectronic Devices and Circuits Fall 2005 Lecture 23 Lecture 23 Frequency Response of Amplifiers (I) Common Source Amplifier December, 2005 Contents:. Introduction 2. Intrinsic frequency response of MOSFET 3. Frequency response of common source amplifier 4. Miller effect Reading assignment: Howe and Sodini, Ch. 0,

2 6.02 Microelectronic Devices and Circuits Fall 2005 Lecture 23 2 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 6.02 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 2 8 LMDS Teledesic Video WirelessMAN Skybridge BW ( MHz) WE Datacom DOM Radio 'V Band' Spacewav Figure by MIT OCW.

4 6.02 Microelectronic Devices and Circuits Fall 2005 Lecture Intrinsic frequency response of MOSFET How does one assess the intrinsic frequency response of a transistor? f t short circuit current gain cut off 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 i out Frequency dependence: f i in iin i out f t frequency at which = iin

5 6.02 Microelectronic Devices and Circuits Fall 2005 Lecture 23 5 Complete small signal 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 2 i out v s v gs C gs gm v gs node : 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 6.02 Microelectronic Devices and Circuits Fall 2005 Lecture 23 6 Current gain: i out g m jωc gd h 2 = = i in jω(c gs C gd ) Magnitude of h 2 : h 2 = g 2 ω 2 C 2 m gd ω(c gs C gd ) For low frequency, ω g m, C gd g m h 2 ω(cgs C gd ) For high frequency, ω g m, C gd Cgd h 2 Cgs C gd <

7 6.02 Microelectronic Devices and Circuits Fall 2005 Lecture 23 7 log h 2 C gd C gs C gd ω T log ω h 2 becomes unity at: ω T =2πf T = g m C gs C gd Then: f T = g m 2π(C gs C gd )

8 6.02 Microelectronic Devices and Circuits Fall 2005 Lecture 23 8 Physical interpretation of f T : Consider: C gs C gd C gs = 2πf T g m g m Plug in device physics expressions for C gs and g m : or 2 3 C gs LW C ox L = W = 2πf T g m L µc ox(v GS V T ) µ3 V GS V T 2 L L L = = τ t 2πf T µ<echan > <v chan > τ t transit time from source to drain [s] Then: f T 2πτt f T gives an idea of the intrinsic delay of the transistor: good first order figure of merit for frequency response.

9 6.02 Microelectronic Devices and Circuits Fall 2005 Lecture 23 9 To reduce τ t and increase f T : L : trade off is cost (V GS V T ) I D : trade off is power µ : hard to do note: f T independent of W Impact of bias point on f T : W 2 W L µc oxi D g m L µc ox(v GS V T ) f T = = = 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 GHz

10 6.02 Microelectronic Devices and Circuits Fall 2005 Lecture Frequency response of common source amp V DD i SUP signal source R S v s V GG v OUT signal load R L V SS Small signal 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 Low frequency voltage gain: ' R out A v,lf = v out v s = g m (r o //r oc //R L )= g m R out

11 6.02 Microelectronic Devices and Circuits Fall 2005 Lecture 23 v s R S v gs C gs g m v gs C db R out ' v out C gd 2 node : v s v gs R vgs jωc gs (v gs v out )jωc gd S =0 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: jω(c gd C db ) R v gs = v out jωc gd g m Plug in and solve for v out /v s : with A v = (g m jωc gd )R DEN DEN = jω{r S C gs R S C gd [ R g m )] R ω 2 R S R outc gs (C gd C db ) out out ( R S [check that for ω =0, A v,lf = g m R out] out out C db}

12 6.02 Microelectronic Devices and Circuits Fall 2005 Lecture 23 2 Simplify:. Operate at ω ω T = g m C gs C gd g m ω(c gs C gd ) >ωc gs,ωc gd 2. Assume g m high enough so that R S g m g m 3. Eliminate ω 2 term in denominator of A v worst case estimation of bandwidth Then: g m R out A v jω[rs C gs R S C gd ( g m R ] out ) R out C db This has the form: A v,lf A v (ω) = j ω ω H

13 6.02 Microelectronic Devices and Circuits Fall 2005 Lecture 23 3 log A v g m R out ' ω H log ω At ω = ω H : A v (ω H ) = A v,lf 2 ω H gives idea of frequency beyond which A v off quickly bandwidth starts rolling For common source amplifier: ω H = R S C gs R S C gd ( g m R out) R out C db Frequency response of common source amplifier limited by C gs and C gd shorting out the input, and C db shorting out the output.

14 6.02 Microelectronic Devices and Circuits Fall 2005 Lecture 23 4 Can rewrite as: f H = 2π{R S [C gs C gd ( A v,lf )] R outc db } Compare with: f T = g m 2π(C gs C gd ) In general: f H f T due to typically: g m R C db enters f H but not f T presence of A v,lf in denominator 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 A v,lf??!!

15 6.02 Microelectronic Devices and Circuits Fall 2005 Lecture Miller effect In common source amplifier, C gd looks much bigger than it really is. Consider simple voltage gain 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 ( A v )C

16 6.02 Microelectronic Devices and Circuits Fall 2005 Lecture 23 6 or v in Z in = = i in jω( 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 capacitance: Why? C Miller = C( 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 gain bandwidth tradeoff in amplifiers.

17 6.02 Microelectronic Devices and Circuits Fall 2005 Lecture 23 7 Key conclusions f T (short circuit current gain cut off frequency): figure of merit to assess intrinsic frequency response of transistors. In MOSFET, to first order, f t = 2πτ t where τ t is transit time of electrons through channel. In common source amplifier, voltage gain rolls off at high frequency because C gs and C gd short out input and C db shorts out output. In common source 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 trade off between gain and bandwidth.