6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 24-1

Lecture 24 - Frequency Resp onse of Amplifiers (I I)

Other Amplifier Stages

May 8, 2003

Contents:

1. Frequency resp onse of common-drain amplifier

2. Frequency resp onse of common-gate amplifier

Reading assignment:

Howe and So dini, Ch. 10, §§10.5-10.6

6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 24-2

Key questions

• Do all amplifier stages suffer from the Miller effect?

• Is there something unique ab out the common-gate and common drain stages in terms of frequency re­sp onse?

• ⇒

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6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 24-3

1. Frequency resp onse of common-drain am­plifier

VDD

signal source

vs

VGG

RS

vOUT iSUP

+

-

signal� load

RL

VSS

Features:

• voltage gain 1

• high input resistance

• low output resistance

go o d voltage buffer

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6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 24-4

High-frequency small-signal mo del:

G Cgd D

RS

+ vs -

B

S

+

-

vgs

+

-

vbs

+

-

vout

gmvgs ro

RL roc

Cgs

Csb

gmbvbs

Cdb

vbs=0

Cgs

+ RS

+

+ -vgs

gmvgs Cgd Cdb ro//roc//RL=RL' vout

vs --

g R m L A = ≤ 1 v,LF 1 + g R m L

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6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 24-5

Compute bandwidth by op en-circuit time constant tech­nique:

1. shut-off all indep endent sources,

2. compute Thevenin resistance R seen by each C with Ti i

all other C ’s op en,

3. compute op en-circuit time constant for C as i

τ = R C i Ti i

4. conservative estimate of bandwidth:

1 ω H

Στ i

First, short v : s

Cgs

+

RS

+ -vgs

gmvgs Cgd Cdb RL' vout

-

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6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 24-6

Time constant asso ciated with C : gs

+ -vgs

gmvgs

1 2it + vt ­

+

RS RL' vout

-

no de 1:

v + v t out i − = 0 t

R S

no de 2:

v out g v − i − = 0 m gs t

R L

also

v = v gs t

Solve for v in 1 and plug into 2: out

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6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 24-7

v R + R t S LR = = Tgs i 1 + g R t m L

Time constant:

R + R S L τ = C gs gs 1 + g R m L

Time constant asso ciated with C : gd

-+ vgs

+

RS gmvgs +

-vt

it

RL' vout

-

R = R Tgd S

τ = C R gd gd S

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6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 24-8

Time constant asso ciated with C : db

-+ vgs it +

RS vt -

gmvgs RL'

it +

gm RL' vt -

1 R L R = //R = Tdb L g 1 + g R m m L

R L τ = C db db 1 + g R m L

Notice:

R = R //R Tdb out L

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6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 24-9

Bandwidth:

1 1 ωH

τgs + τdb =

Cgs R S +RL RL+ τgd

L+ Cgd RS + Cdb 1+g m R 1+g m RL

If back is not connected to source:

VDD

signal source

vs

VGG

RS

vOUT

VSS

iSUP

+

-

signal� load

RL

VSS

6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 24-10

Small-signal equivalent circuit:

G Cgd D

RS

+ vs

-

S

+

-

vgs

+

-

vbs

gmvgs ro

+

-

vout roc

Cgs

Csb

gmbvbs

Cdb

RL

B

Cgs

+ RS

+

+ -vgs

+

-

vbs gmvgs gmbvbs Cgd Csb ro//roc//RL=RL' vout

vs --

Cgs

+ RS

+

+ -vgs

gmvgs Cgd Csb RL'//(1/gmb)=RL'' vout

vs --

g R ” m L A = v,LF

1 + g R ” m L

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6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 24-11

C shows up at same lo cation as C b efore, then band­sb db

width is:

1ωH

Cgs R +R R S L L + C R + C gd S sb R R L L

” ”1+g m ” 1+g m ”

Simplify:

• CD amp is ab out driving low R L from high R S ⇒RS RL ”, and

1ωH

RS C gs

1+g R L ”( + C ) + C gd sb R L ” ”m R L 1+g m

• CD stage op erates as voltage buffer with A v,LF

1 ⇒ g m RL ” 1, and

ω1

H C sb g m

Cgd RS +

Since C gd and 1/g m are small, if R S is not to o high, ω H

can b e rather high (approach ω T ).

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6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 24-12

What happ ened to the Miller effect in CD amp?

1ω H C R ” gs L R ( + C ) + C S gd sb 1+g R ” 1+g R ” m m L L

Miller analysis of C : gs

g R ” 1 m L = C (1−A ) = C (1− ) = C gs v gs gs gs 1 + g R ” 1 + g R ” m L m L

agrees with ab ove result.

Note, since A → 1, C → 0. v gs

See in circuit:

iin C

+

vin

+ +

- -Avvin vout

-

C = C (1 − A ) M v

if A 1 ⇒ C 0: bootstrapping v M

C

• ⇒

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6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 24-13

2. Frequency resp onse of common-gate ampli­fier

VDD

is

iOUT

VSS

iSUP

IBIAS

signal source

RS

signal� load

RL

VSS

Features:

• current gain 1

• low input resistance

• high output resistance

go o d current buffer

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6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 24-14

Small-signal equivalent circuit mo del:

G

S

D +

-

vgs

+

-

vbs

gmvgs ro

roc

Cgs

Csb

gmbvbs

Cdb

is RS

Cgd iout

RL

B

vgs=vbs

(gm+gmb)vgs

is

+

-

vgs

ro

Cgs+Csb Cgd+Cdb RS roc//RL=RL'

Frequency analysis: first, op en i : s

(gm+gmb)vgs

RS

+

-

vgs

ro

C1=Cgs+Csb C2=Cgd+Cdb

RL'

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6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 24-15

Time constant asso ciated with C : 1�

(gm+gmb)vgs

RS RL'

(gm+gmb)vgs

it'

+ vt'

ro

RL' -

Don’t need to solve:

• test prob e is in parallel with R , S

• test prob e lo oks into input of amplifier ⇒ sees R ! in

R = R //R T 1 S in

And:

ro

+

-vt

it

τ = (C + C )(R //R ) 1 gs sb S in

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6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 24-16

Time constant asso ciated with C : 2

(gm+gmb)vgs

ro

roc +

-vt

it

RLRS

(gm+gmb)vgs

ro

roc

it' +

-' RS vt

Again, don’t need to solve:

• test prob e is in parallel with R L ,

• test prob e lo oks into output of amplifier ⇒ sees R out !

RT 2 = RL //R out

And:

τ2 = (Cgd + Cdb )(RL //R out )

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6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 24-17

Bandwidth:

1ω � H

(C + C )(R //R ) + ( C + C )(R //R ) gs sb S in gd db L out

No capacitor in Miller p osition → no Miller-like term.

Simplify:

• In a current amplifier, R � R : S in

1 1 R = R //R � R � � T 1 S in in

g + g g m mb m

• At output:

1 R = R //R = R //r //{r [1+ R (g +g + )] T 2 L out L oc o S m mb

r o or

R � R //r //[r (1 + g R )] � R T 2 L oc o m S L

Then:

1 ω � H 1 (C + C ) + (C + C )R gs sb gd db L g m

If R is not to o high, bandwidth can b e rather high (and L

approach ω ). T

6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 24-18

Key conclusions

• Common-drain amplifier:

– Voltage gain � 1, Miller effect nearly completely eliminates impact of C (bootstrapping) gs

– if R is not to o high, CD amp has high bandwidth S

• Common-gate amplifier:

– no capacitor in Miller p osition ⇒ no Miller effect

– if R is not to o high, CG amp has high bandwidth L

• R , R affect bandwidth of amplifier S L