Lecture 25 - Frequency Response of Amplifiers (III) Other Amplifier Stages. December 8, 2005

Transcription

1 6.012 Microelectronic Devices and Circuits Fall 2005 Lecture 251 Lecture 25 Frequency Response of Amplifiers (III) Other Amplifier Stages December 8, 2005 Contents: 1. Frequency response of commondrain amplifier 2. Cascode amplifier Reading assignment: Howe and Sodini, Ch. 9, 9.3.3; Ch. 10, 10.5, 10.7 Announcement: Final exam: December 19, 1:304:30 PM, dupont; open book, calculator required; entire subject under examination but emphasis on lectures #1926.

2 6.012 Microelectronic Devices and Circuits Fall 2005 Lecture 252 Key questions Do all amplifier stages suffer from the Miller effect? Is there something unique about the common drain stage in terms of frequency response? Can we make a transconductance amplifier with a large bandwidth?

3 6.012 Microelectronic Devices and Circuits Fall 2005 Lecture Frequency response of commondrain amplifier V DD signal source signal load i SUP v OUT V GG Features: voltage gain 1 high input resistance low output resistance good voltage buffer

4 6.012 Microelectronic Devices and Circuits Fall 2005 Lecture 254 Highfrequency smallsignal model: G C gd D v gs C gs g m v gs g mb v bs r o S C db B v bs C sb r oc v out v bs =0 C gs C gd v gs g m v gs C db r o //r oc // =RL' v out g m R 1 A v,lf = 1 gm L R L

5 6.012 Microelectronic Devices and Circuits Fall 2005 Lecture 255 Compute bandwidth by opencircuit time constant technique: 1. shutoff all independent sources, 2. compute Thevenin resistance R Ti seen by each C i with all other C s open, 3. compute opencircuit time constant for C i as τ i = R Ti C i 4. conservative estimate of bandwidth: 1 ω H Στi 2 First, short : C gs v gs C gd g m v gs C db RL' v out

6 6.012 Microelectronic Devices and Circuits Fall 2005 Lecture Time constant associated with C gs : 1 v i t t 2 v gs gmvgs RL' v out node 1: node 2: also v t v out i t =0 v out g m v gs i t R =0 L v gs = v t Solve for v out in 1 and plug into 2:

7 6.012 Microelectronic Devices and Circuits Fall 2005 Lecture 257 Time constant: R Tgs = = v t i t 1 g m R L R τ gs = C gs 1 g m L 2 Time constant associated with C gd : v gs i t v t g m v gs RL' v out R Tgd = τ gd = C gd

8 6.012 Microelectronic Devices and Circuits Fall 2005 Lecture Time constant associated with C db : v gs i t g m v gs RL' v t i t g m RL' v t R Tdb = 1 g m //R RL L = 1 g m R τ L db = C db 1 g m Notice: R Tdb = R out //

9 6.012 Microelectronic Devices and Circuits Fall 2005 Lecture Bandwidth: 1 1 ω H = τ R L R gs τ gd τ db C L gs 1gm R C gd C db 1gm R L L 2 If back is not connected to source: V DD signal source signal load i SUP v OUT V GG

10 6.012 Microelectronic Devices and Circuits Fall 2005 Lecture 2510 Smallsignal equivalent circuit: G C gd D v gs C gs g m v gs g mb v bs r o S B v bs C sb r oc v out C db C gs C gd v gs g m v gs g mb v bs v bs C sb r o //r oc // =RL' v out C gs C gd v gs gm v gs C sb '//(1/g mb )=RL'' v out g m A v,lf = 1 gm

11 6.012 Microelectronic Devices and Circuits Fall 2005 Lecture 2511 C sb shows up at same location as C db before, then bandwidth is: Simplify: 1 ω H C gs 1gm C gd C sb 1gm CD amp is about driving low from high, and 1 ω H Cgs ( 1g C gd) C sb 1gm m CD stage operates as voltage buffer with A v,lf 1 g m 1, and ω H 1 C sb C gd gm Since C gd and 1/g m are small, if is not too high, ω H can be rather high (approach ω T ).

12 6.012 Microelectronic Devices and Circuits Fall 2005 Lecture What happened to the Miller effect in CD amp? 1 ω H Cgs ( 1g C gd) C sb 1gm Miller analysis of C gs : m C g m 1 gs = C gs (1 A v )= C gs (1 )= C gs 1 g m 1 g m agrees with above result. Note, since A v 1, C 0. gs See in circuit: i in C Av v in v out v in C M = C(1 A v ) if A v 1 C M 0: bootstrapping

13 6.012 Microelectronic Devices and Circuits Fall 2005 Lecture Cascode amplifier Commonsource stage: excellent transconductance amplifier, but bandwidth hurt by Miller effect. What s a circuit designer to do? Consider CSCG stage: V DD V DD i SUP1 i SUP2 signal source v OUT1 V G2 i OUT VSS signal load V G1 i OUT1 I BIAS How does this address the problem? R in2 very small i OU T 1 can change a lot with v OU T 1 changing little small voltage gain in CS stage no Miller effect high bandwidth CG stage also has high bandwidth

14 6.012 Microelectronic Devices and Circuits Fall 2005 Lecture 2514 Before analyzing CSCG amp, notice that if we make i SUP1 = i SUP2 = i SUP, amplifier drastically simplified: V DD V DD i SUP i SUP signal source v OUT1 V G2 i OUT VSS signal load V G1 i OUT1 I BIAS V DD i SUP V G2 i OUT VSS signal load signal source V G1

15 6.012 Microelectronic Devices and Circuits Fall 2005 Lecture 2515 V DD i SUP V G2 i OUT VSS signal load signal source V G1 Smallsignal equivalent circuit model: (g m2 g mb2 )v gs2 C gd1 r o2 v gs1 Cgs1 gm1 v gs1 C db1 r o1 v gs2 C gs2 C sb2 C gd2 C db2 r oc // =RL ' Time constants associated with C gs1 and C gd2 C db2 have not changed. Time constant associated with C db1 C gs2 C sb2 small (looking into R in2 1/g m ).

16 6.012 Microelectronic Devices and Circuits Fall 2005 Lecture 2516 Focus on time constant associated with C gd1 : v t i t v gs1 g m1 v gs1 g m2 g mb2 From Lecture 24: 1 g m1 τ gd1 =[ (1 )]C gd1 g m2 g mb2 g m2 g mb2 If transistors identical (g m1 = g m2 ): τ gd1 2 C gd1 Much smaller than in single stage CS tansconductance amp: τ gd =[R (1 g m R out out)]c gd Cascode: excellent transconductance amplifier with high bandwidth.

17 6.012 Microelectronic Devices and Circuits Fall 2005 Lecture 2517 Key conclusions Commondrain amplifier: Voltage gain 1, Miller effect nearly completely eliminates impact of C gs (bootstrapping) if is not too high, CD amp has high bandwidth Cascode amplifier: effective sharing of current source Miller effect minimized by reducing voltage gain of CS stage as a result of low input impedance of CG stage transconductance amplifier with high bandwidth