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Chapter 6

Differential and Multistage Amplifiers

The most widely used circuit building block in analog integrated

circuits.

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Differential pair circuits are one of the most

widely used circuit building blocks. The input

stage of every op amp is a differential amplifier

Basic Characteristics

Two matched transistors with emitters

shorted together and connected to a current

source

Devices must always be in active mode Amplifies the difference between the two

input voltages but there is also a common

mode amplification in the non!ideal case

"et#s first understand how this circuit works.

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Assume the inputs are shorted together to a common voltagevCM called the common mode voltage

e$ual currents flow through Q1and Q2

emitter voltages e$ual and at vCM!%.& in order for the

devices to be in active mode collector currents are e$ual and so collector voltages are

also e$ual for e$ual load resistors

difference between collector voltages ' %

(hat happens when we vary vCM)

As long as devices in active mode e$ual currents flow

through Q1and Q2 *ote+ current through Q1and Q2always add up toI

current through the current source

,o collector voltages do not change and difference is still-ero.

Differential pair circuits thus re/ect common mode signals

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Q2base grounded and Q1base at 01 2

All current flows through Q1

*o current flows through Q2 3mitter voltage at %.42 and Q2#s 3B5 not 6B

vC1= VCC-IRC

vC2= VCC

Q2base grounded and Q1base at !1 2

All current flows through Q2

*o current flows through Q1

3mitter voltage at !%.&2 and Q1#s 3B5 not 6B

vC2' VCC-aIC

vC1' VCC

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Apply a small signal vi

Causes a small positive!Ito flow in Q1 7e$uires small negative!Iin Q2

sinceI"10I"2'I

Can be used as a linear amplifier for smallsignals 8!I is a function ofvi9

Differential pair responds to differences in theinput voltage

Can entirely steer current from one side ofthe diff pair to the other with a relativelysmall voltage

"et#s now take a $uantitative look at the large!signal operation of the differential pair

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"arge!,ignal :peration

6irst look at the emitter currents when the emitters are tied together

,ome manipulations can lead to the following e$uations

and there is the constraint+

Given the exponential relationship, small differences in vB1,2can cause all of the current to flow through

one side

T

"#V

Vv$

" eI

i

=

1

1

T

"#

V

Vv

$" e

Ii

=

;

;

T

##

Vvv

"

" ei

i ;1

;

1

=

T

##

V

vv

""

"

eii

i1;

1

1

;1

1

+

=

+T

##

V

vv

""

"

eii

i;1

1

1;1

;

+

=

+

Iii "" =+ ;1

T

##

V

vv"

e

Ii

1;

1

1

+

=

T

##

V

vv"

e

Ii

;1

1

;

+

=

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*otice vB1!vB;

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,mall!,ignal :peration

"ook at the small!signal operation+ small

differential signal vdis applied

e>pand the e>ponential and keep the first

two terms

T

d

V

vC

e

Ii

+

=

1

1

d## vvv = ;1

T

d

T

d

T

d

V

v

V

v

V

v

C

ee

Iei

;;

;

1

+

=

( )

( ) ( ) ;;;;1;1;1

1d

TTdTd

TdC

v

V

II

VvVv

VvIi

+=

++

+

;;;

;d

T

C

v

V

IIi

;;

d

T

c

v

V

Ii

=

TT

Cm

V

I

V

Ig

;==

;dmc vgi =

multiply top

and bottom

byT

d

V

v

e ;

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Differential 2oltage ain

For small differential input signals, vd

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Differential alf Circuit

(e can break apart the differential pair circuit into two half circuits which

then looks like two common emitter circuits driven by 0vd@; and vd@;

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We can then analye the small!signal operation with the half

circuit, but must remember

parameters r,gm, and roare biased at I"2

input signal to the differential half circuit is vd"2

#oltage gain of the differential amplifier $output ta%en

differentially& is e'ual to the #oltage gain of the half circuit

( )oCmd

cd rg

v

v% ==

;

1

#d"2 r

#

gm

#

r

()

#c*

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Common!ode ain

When we dri#e the differential pair with a common!mode signal,

vCM, the incremental resistance of the bias current effects circuitoperation and results in some gain $assumed to be + when (

was infinite&

v

r

vv CCM

e

CCMC

;;1

+

=

vv C

CMC ;;

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f the output is ta%en differentially, the output is ero since both sides mo#etogether. -owe#er, if ta%en of the single circuit, the common!mode gain is finite

f we loo% at the differential gain of the circuit, we get

hen, the common re/ection ratio $)0((& will be

which is often e1pressed in d

% Ccm

;

=

Cmd g% =

g%

%CM m

cm

d

;

1=

cm

d

%

%CM 1%log;%=

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C and Differential ain 3$uation

nput signals to a differential pair usually consists of two

components3 common mode $vCM& and differential$vd&

hus, the differential output signal will be in general

;

;1 vvvCM+

=;1 vvvd =

( );

;1;1

vv%vv%v cmdo

++=

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The B5T Differential air

Ese CD

Fmplemented by a

transistor circuit

Connection to 7C not

essential to the operation

3ssential that G1

and G; never enter

saturation

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Different odes of :peration

Differential pair with a common!mode input

Common voltage

F@;

v3 ' vC!2B3

vC1 ' 2CC 8 H9 F 7C

vC; ' 2CC 8 H9 F 7C

vC1 vC; ' )

2ary vC 8what happens)9

7e/ects common!mode

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Differential pair with a large differential input


vB1 ' 01

G1

G;

v3 ' %.4

Ieeps G; off

vC1 ' 2CC ! F 7C

vC; ' 2CC

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Differential pair with a large differential input o opposite polarity

To that of 8b9


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Differential pair with a small differential input


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