Lecture 24 ­ Frequency Response of amp PDF

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Lecture 24 ­ Frequency Response of amp...

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6.012 - Microelectronic Devices and Circuits - Fall 2005

Lecture 24-1

Lecture 24 - Frequency Response of Amplifiers (II) Open-Circuit Time-Constant Technique December 6, 2005 Contents: 1. Open-circuit time-constant technique 2. Application of OCT to common-source amplifier 3. Frequency response of common-gate amplifier Reading assignment: Howe and Sodini, Ch. 10, §§10.4.4-10. 4.5. 10.6

6.012 - Microelectronic Devices and Circuits - Fall 2005

Lecture 24-2

Key questions • Is there a fast way to assess the frequency response of an amplifier? • Do all amplifiers suffer from the Miller effect?

6.012 - Microelectronic Devices and Circuits - Fall 2005

Lecture 24-3

1. Open-Circuit Time-Constant Technique Simple technique to estimate bandwidth of an amplifier. Method works well if amplifier transfer function has: • a dominant pole that dominates the bandwidth • no zeroes, or zeroes at frequencies much higher than that of dominant pole Transfer function of form: Vout Avo = ω + jω2ω)(1 + jω3ω)... Vs (1 + ωj1 )(1 with ω1 � ω1 , ω2 , ω3, ... log |Av| Avo

-1

-2

1

2

log

6.012 - Microelectronic Devices and Circuits - Fall 2005

Lecture 24-4

Vout Avo = ω + jω2ω)(1 + jω3ω)... Vs (1 + ωj1 )(1 Multiply out the denominator: Vout Avo = Vs 1 + jωb1 + (jω)2 b2 + (jω)3 b3... where: b1 =

1 1 1 + + + ... ω1 ω2 ω3

If there is a dominant pole, the low frequency behavior well described by: Vout Avo = � Vs 1 + jωb1 Bandwidth then: ωH �

1 b1

Avo 1 + ωHj ω

6.012 - Microelectronic Devices and Circuits - Fall 2005

log |Av|

Lecture 24-5

log |Av|

Avo

Avo

-1

-1

-2

1

log

2

H

log

It can be shown (see Gray & Meyer, 3rd ed., p. 502) that coefficient b1 can be found exactly through: b1 =

n� i=1

τi =

n�

i=1

RT i Ci

where: τi is open-circuit time constant for capacitor Ci RT i is Thevenin resistance across Ci (with all other capacitors open-circuited) Bandwidth then: ωH �

1 = b1

1 �n

i=1

τi

=

�n

i=1

1 RT i Ci

6.012 - Microelectronic Devices and Circuits - Fall 2005

Lecture 24-6

Summary of open-circuit time constant technique: 1. shut-off all independent sources 2. compute Thevenin resistance RT i seen by each Ci with all other C ’s open 3. compute open-circuit time constant for Ci as τi = RT i Ci 4. conservative estimate of bandwidth: ωH �

1 Στi

Works also with other transfer functions:Vs

Iout Vout

,

Iout Is ,

Is

.

6.012 - Microelectronic Devices and Circuits - Fall 2005

Lecture 24-7

2. Application of OCT to evaluate bandwidth of common source amplifier VDD

iSUP signal source RS

+ vOUT

vs

signal฀ load RL

VGG

VSS

Small-signal equivalent circuit model (assuming current source has no parasitic capacitance): Cgd

RS +

+

vgs

vs -

+

Cgs

gmvgs

Cdb

-

Three capacitors ⇒ three time constants

Rout'

vout -

6.012 - Microelectronic Devices and Circuits - Fall 2005

Lecture 24-8

� First, short vs: Cgd +

vgs

RS

Cgs

gmvgs

Cdb

Rout'

-

� Time constant associated with Cgs it

vgs

+

RS

+

-

vt

gmvgs

-

Clearly: RT gs = RS and time constant associated with Cg s is: τgs = RS Cg s

Rout'

6.012 - Microelectronic Devices and Circuits - Fall 2005

Lecture 24-9

� Time constant associated with Cdb : it

+

vgs

+

RS

gmvgs

vt

-

-

Note: vgs = 0 Then: RT db = Rout� and time constant associated with Cg s is: τgs = Rout�Cdb

Rout '

6.012 - Microelectronic Devices and Circuits - Fall 2005

Lecture 24-10

Time constant associated with Cgd : + +

RS

vgs

vt

-

it gmvgs

Rout'

-

Note: vgs = itRS Also: vt = vg s + (gm vgs + itout )R� Putting it all together, we have: � (1 + gm RS )] vt = it[RS + Rout

Then: RT gd = RS + Rout� (1 + gm RS ) = Rout� + RS (1 + gm Rout� ) and time constant associated with Cgd: τgd = [Rout� + RS (1 + gm Rout� )]Cgd

6.012 - Microelectronic Devices and Circuits - Fall 2005

Lecture 24-11

The bandwidth is then: ωH �

1 = � Στi RS Cgs + [R out

1 � C + RS (1 + gout R�gd + R m)]C out db

Identical result as in last lecture. Open circuit time constant technique evaluates bandwidth neglecting −ω 2 term in the denominator of Av ⇒conservative estimate of ωH .

6.012 - Microelectronic Devices and Circuits - Fall 2005

Lecture 24-12

3. Frequency response of common-gate amplifier VDD

iSUP iOUT VSS signal source is

RS

IBIAS

VSS

Features: • current gain � 1 • low input resistance • high output resistance • ⇒ good current buffer

signal฀ load RL

6.012 - Microelectronic Devices and Circuits - Fall 2005

Lecture 24-13

Small-signal equivalent circuit model: Cgd

G

iout

D

+

vgs S is

RS

Cgs

gmbvbs

gmvgs

ro

-

vbs

roc

Cdb Csb

+

B

vgs=vbs

(gm+gmb)vgs

ro

-

is

RS

vgs

Cgs+Csb

Cgd+Cdb

roc//RL=RL'

+

� Frequency analysis: first, open is: (gm+gmb)vgs

-

RS

vgs +

ro C1=Cgs+Csb C2=Cgd+Cdb

RL'

RL

6.012 - Microelectronic Devices and Circuits - Fall 2005

Lecture 24-14

� Time constant associated with C1 : (gm+gmb)vgs

it

ro

+

RL'

vt

RS

-

(gm+gmb)vgs

ro

it' +

vt '

RL'

-

Don’t need to solve: • test probe is in parallel with RS , • test probe looks into input of amplifier ⇒ sees Rin! RT 1 = RS //Rin And: τ1 = (Cgs + Csb )(RS //Rin)

6.012 - Microelectronic Devices and Circuits - Fall 2005

Lecture 24-15

� Time constant associated with C2 : (gm+gmb)vgs

ro

it + vt -

RS

roc

RL

(gm+gmb)vgs

ro

it' roc

RS

+ -

vt'

Again, don’t need to solve: • test probe is in parallel with RL , • test probe looks into output of amplifier ⇒ sees Rout ! RT 2 = RL //Rout And: τ2 = (Cgd + Cdb )(RL //Rout )

6.012 - Microelectronic Devices and Circuits - Fall 2005

Lecture 24-16

� Bandwidth: ωH �

(Cgs

1 + Csb )(RS //Rin ) + (Cgd + Cdb )(RL //Rout )

No capacitor in Miller position → no Miller-like term. Simplify: • In a current amplifier, RS � Rin: 1 1 � RT 1 = RS //Rin � Rin � gm + gmb gm • At output: 1 RT 2 = RL //Rout = RL //roc //{ro [1+RS (gm +gmb + ro or

)]

RT 2 � RL //roc //[ro (1 + gm RS )] � RL Then: ωH �

(Cgs

1 + Csb1m) g + (Cgd + Cdb )RL

If RL is not too high, bandwidth can be rather high (and approach ωT ).

6.012 - Microelectronic Devices and Circuits - Fall 2005

Lecture 24-17

Key conclusions • Open-circuit time-constant technique: simple and powerful method to estimate bandwidth of amplifiers. • Common-gate amplifier: – no capacitor in Miller position ⇒ no Miller effect – if RL is not too high, CG amp has high bandwidth • RS , RL affect bandwidth of amplifier...