Differential and Multistage Amplifiers - faculty.weber.edu · ... The analysis and design of MOS...

ECE 3120 Microelectronics II Dr. Suketu Naik

Chapter 8

Differential

Multistage

Amplifiers

Operational Amplifier Circuit Components

1. Ch 7: Current Mirrors and Biasing

2. Ch 9: Frequency Response

3. Ch 8: Active-Loaded Differential Pair

4. Ch 10: Feedback

5. Ch 11: Output Stages

Active-Loaded Differential Pair

Two Stage

Op Amp

(MOSFET)

Learning Objectives

1) MOS and the bipolar differential amplifiers: how

they reject common-mode noise or interference and

amplify differential signals

2) The analysis and design of MOS and BJT differential

amplifiers: utilizing passive resistive loads, current-

source loads, and cascodes

3) The structure, analysis, and design of amplifiers

composed of two or more stages in cascade

Why Differential?

0) What is a differential signal?

1) Differential circuits are less sensitive to noise and

interference

2) Differential configuration enables biasing the amplifier and

coupling of amplifier stages without bypass and coupling

capacitors

3) Useful in IC design because of good matching between the

transistors

MOS Differential Pair

8.1. The MOS Differential Pair

Differential Pair

Two matched transistors (Q1 and Q2) joined and biased by a constant current source I

FETs should not enter

triode region

Input Common Mode Range

8.1.1. Operation with a Common-Mode Input Voltage

Suppose that two gate terminals are joinedtogether and connected to a common-mode voltage(VCM)

vG1 = vG2 = VCM

Q1 and Q2 are matched

Current I will divide equally between the two transistors.

ID1 = ID2 = I/2,

VS = VCM – VGS; where VGS is the gate-to-source voltage.

Equations (8.2) through (8.8)

describe this circuit (channel-

length modulation is neglected)

Note the range (max and min)

of input common-mode voltage

(VCM): beyond this range the

diff pair leaves saturation

n GS t

OV GS t

D D DD D

CM t DD D

CM SS CS t OV

I Wk V V

LV V V

I Wk V

Iv v V R

IV V V R

V V V V V

8.1.1. Operation with a Common-Mode Input Voltage

8.1.2. Operation with a Differential Input Voltage

vid is applied to Q1 and Q2 is grounded:

vid = vGS1 – vGS2 > 0

iD1 > iD2

The opposite applies if Q1is grounded

The differential pair responds to a difference-mode or differential input signals.

The diff pair provides corresponding differential output signal between the two drains

Differential Input Voltage

Two input terminals

connected to a differntial

signal vid

Bias current I of a perfectly

symmetrical differential pair

divides equally

To steer the current

completely to one side of the

pair, a difference input voltage

vid of at least √2VOV is needed.

8.1.2. Operation with a Differential Input Voltage

8. 2 / /

n GS t

id GS S

WI k v V

v V I k W L

Large Signal Operation

8.1.3 Large-Signal Operation

Objective: derive expressions for drain current iD1 and iD2 in terms of differential signal vid = vG1 – vG2

Assumptions:

Perfectly matched transistors

Channel-length modulation is neglected

Load independence is present

Saturation region

Step #1: Expression drain

currents for Q1 and Q2.

Step #2: Take the square roots

of both sides of both (8.11)

and (8.12)

Step #3: Subtract (8.14) from

(8.15) and perform appropriate

substitution.

Step #4: Note the constant-

current bias constraint.

1 2 1 2

1(8.11)

(8.12)

(8.13)

(8.14)

D n GS t

GS GS G G id

Wi k v V

i k v VL

Wi k v V

v v v v v

Step #5: Simplify

(8.15).

Step #6: Incorporate

the constant-current

Step #7: Solve (8.16)

and (8.17) for the two

unknowns – iD1 and iD2.

(8.17)

(8.23)

(8.24) 12 2

D D n id

id idD

Wi i I k v

v vI Ii

Transfer characteristics of (8.23)

and (8.24) are nonlinear.

Linear amplification is desirable

and vid will be as small as possible.

For a given value of VOV, the only

option is to keep vid/2 much

smaller than VOV.

small-signal approximation

(8.25)

Figure 8.7: The linear range of operation of the MOS differential pair can be extended

by operating the transistor at a higher value of VOV .

VOV increases (smaller W/L): Gain will decrease, Linearity will increase

VOV decreases (larger W/L): Gain will increase, Linearity will decrease

Can increase the bias current to increase gm and gain

Small-signal Operation

8.2 Small-Signal Operation of the MOS Differential Pair

Virtual ground at the source

- Elimintates need for large

bypass capacitor

VCM = bias voltage at the gate

vid = differential small signal

For MOS pair, each device

operates with drain current

I/2 and corresponding

overdrive voltage (VOV).

gm = I/VOV

ro = |VA|/(I/2).

8.2.1 Differential Gain

2 2( /2)

(8.28)

(8.29)

(8.30)

(8.32)

(8.3 5)

G CM id

OV OV OV

ido m D

odd m D

I I Ig

vv g R

vA g R

8.2.1 Differential Gain

vi1 = VCM + vid/2 and vi2 = VCM – vid/2 causes a virtual signal ground to appear on the common-source (common-emitter) connection

Current in Q1 increases by gmvid/2 and the current in Q2 decreases by gmvid/2

Voltage amplitudes of gm(RD||ro)vid/2 develop at the two drains

8.2.2. The Differential Half-Circuit

Figure 8.9 (right): The

equivalent differential half-

circuit of the differential

amplifier of Figure 8.8

Here Q1 is biased at I/2 and

is operating at VOV

This circuit may be used to

determine the differential

voltage gain of the

differential amplifier Ad =

vod/vid.

8.2.3 The Differential Amplifier with Current-Source Loads

To obtain higher gain, the passive resistances (RD) can be

replaced with current sources.

Ad = gm1(ro1||ro3)

Figure 8.11: (a) Differential amplifier

with current-source loads formed by

Q3 and Q4. (b) Differential half-circuit

of the amplifier in (a).

8.2.4 Cascode Differential Amplifier

Gain can be increased via cascode configuration –discussed in Section 7.3

Ad = gm1(Ron||Rop)

Ron = (gm3ro3)ro1

Rop = (gm5ro5)ro7

Figure 8.12: (a) Cascode differential

amplifier; and (b) its differential half

circuit.

Common Mode Rejection Ratio (CMRR)

8.2.5 Common-Mode Gain and Common-Mode Rejection ratio (CMRR)

a) vin = VCM (DC common-mode signal) + vicm (common-mode noise

or interference)

b) current source with fininte output resistance RSS

c) T model without ro

d) common-mode half circuit

Equation (8.43) describes effect of common-mode signal (vicm) on vo1 and vo2.

(8.41)

(8.42)

(8.43)

(8.44)

icm SS

Do o icm

icm Do o

od o o

Rv v v

v Rv v

When the output is taken single-ended, magnitude of common-mode gain is defined in (8.46) and (8.47)

Taking the output differentiallyresults in the perfectly matched case, in zero Acm (infinite CMRR)

Mismatches between the drain resistances make Acm finite even when the output is taken differentially.

CMRR is the ratio of differential gain over common-mode gain

's aremismatched

(8.46)

(8.48)

(8.49) 2 2

Do icm

D Do icm

Dod o o icm

od D D Dcm

icm SS

R Rv v

Rv v v v

v R R RA

v R R R

( 8.50) d

8.4.1 Input Offset Voltage

Apply a small voltage of opposite polarity to cancel the offset

Device mismatches cause a finite dc voltage at the output

BJT Differential Pair

8.3 The BJT Differential Pair

Figure 8.15 shows the basic

BJT differential-pair

configuration

It is similar to the MOSFET

circuit – composed of two

matched transistors biased

by a constant-current source

– and is modeled by similar

expressions.

8.3.1 Basic Operation

Suppose that the two bases joined together and connected to a common-

mode voltage VCM

Since Q1 and Q2 are matched, and assuming an ideal bias current I with

infinite output resistance, this current will flow equally through both

transistors.

Input Common Mode Range

8.3.2 Input Common-Mode Range

The allowable range of VCM

is determined at the upper

end by Q1 and Q2 leaving

the active mode and

entering saturation.

Equations (8.66) and (8.67)

define the minimum and

maximum common-mode

input voltages.

0.4(8.66)

(8.67)

CM C CC C

CM EE CS BE

IV V V R

V V V V

Large Signal Operation

8.3.3 Large Signal Operation

(1) Note that the linear

range of BJT diff pair

is smaller than the

MOS diff pair

(2) It can be used for

fast switching (ECL

logic) by current

steering: e.g. current

flows entirely in one

branch then switches

to the other branch;

requires only 4VT

(3) The difference

input signal, vid should

be less than VT/2 to

linear amplification

How to increase the linear range?

Figure 8.18 The transfer characteristics of the BJT differential pair (a) can be linearized (b)

(i.e., the linear range of operation can be extended) by including resistances in the emitters.

Small Signal Operation

8.3.4 Small Signal Operation

)83.8....(2222 e

)80.8......(2 TT

Bias voltage

+ small

signal (ac)

8.3.4 Small Signal Operation: half-circuit

)95.8)......(||( oCmd rRgA

Virtual

Ground

8.3.4 Small Signal Operation: single-ended input

Note that we can apply

signal in the MOS diff

pair in similar fashion

(1) Emitter voltage is no longer at virtual

ground.

(2) Voltage at the emitters is appx.

Vid /2

8.3.5 Common-mode gain and CMRR

)99.8(),98.8......(22

)100.8......(2

ACMRR d

CMRR is the ratio of differential gain over common-mode gain

8.4.2 Input Offset Voltage

Apply a small voltage of opposite polarity to cancel the offset

Device mismatches cause a finite dc voltage at the output

VOS smaller than

MOS diff pair

List of Problems

MOS Diff Pair

p8.2: input common mode range of PMOS differential amplifier

ex8.4 MOS diff pair: differential gain

ex8.7 (simulate and verify) MOS diff pair: CMRR

p8.15: design of MOS differential amplifier

BJT Diff Pair

p8.34: input common mode range of npn differential amplifier

ex8.13: BJT diff pair: differential gain, CMRR

p8.49 (simulate): design of BJT differential amplifier

p8.62 (simulation only): npn differential amplifier

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