6.012 Electronic Devices and Circuits-Fall 2000 Lecture 26 1

Lecture 26Differential Amplifiers (I)DIFFERENTIAL AMPLIFIERS

Outline

1. Introduction

2. Incremental analysis of differential amplifier

3. Common-source differential amplifier

Reading Assignment:Howe and Sodini, Chapter 11, Sections 11-1-11.3, 11.6

6.012 Electronic Devices and Circuits-Fall 2000 Lecture 26 2

Summary of Key Concepts

• In differential amplifiers, signals are represented by difference between two voltages

• Differential amplifier amplifies the difference between two voltages but rejects “common mode” signals– ⇒ Improved noise immunity

• Using “half-circuit” technique, small-signal operation of differential amplifiers is analyzed by breaking the problem into two simpler ones– Differential mode problem– Common mode problem

• Common-mode rejection ratio (CMRR) is an important figure of merit for differential amplifiers

• Differential amplifiers require good device matching

6.012 Electronic Devices and Circuits-Fall 2000 Lecture 26 3

1. Introduction

• Bias and gain sensitivity to device parameters (µCox, VT)– Sensitivity can be mitigated but often at a price in

terms of performance or cost (gain, power, device area, etc.)

• Vulnerability to ground and power supply noise– In dense IC’s there is cross-talk, 60 Hz coupling,

substrate noise, etc.

Two problems found in single-transistor amplifier stages are:

6.012 Electronic Devices and Circuits-Fall 2000 Lecture 26 4

Introduction (contd.)

Solution : represent relevant signal by the difference between two voltages

• Amplifies difference between two voltages• Rejects components common to both voltages

Differential Amplifier:

6.012 Electronic Devices and Circuits-Fall 2000 Lecture 26 5

MOSFET Differential AmplifierBasic Configuration

• vO responds to difference between vI’s– If vI1 = vI2 ⇒ symmetry ⇒ vO1 = vO2 ⇒ vO = 0

– If vI1 > vI2 ⇒ M1 conducts more than M2 ⇒ i1 > i2⇒ vO1 < vO2 ⇒ vO < 0

• vO insensitive to common mode signals:– If both vO1 and vO2 move in sync, symmetry is

preserved ⇒ vO unchanged

– If ground VDD or VSS have noise, symmetry preserved ⇒ vO unchanged

– If VT or µCox change, symmetry preserved ⇒ vOunchanged.

• Need precise device matching

6.012 Electronic Devices and Circuits-Fall 2000 Lecture 26 6

Differential-mode and Common-mode signals

Distinguish between common-mode and differential-mode:

2,

2 21ID

ICIID

ICI

vvv

vvv −=+=

Then:

2, 21

21II

ICIIID

vvvvvv

+=−=

Similarly at the output:

2,

2 21OD

OCOOD

OCO

vvv

vvv −=+=

Then:

2, 21

21OO

OCOOOD

vvvvvv

+=−=

6.012 Electronic Devices and Circuits-Fall 2000 Lecture 26 7

2. Incremental analysis of differential amplifierConsider generic differential amplifier:

Figures of Merit:

id

oddm v

va =

Differential-mode voltage gain (want it high):

ic

occm v

va =

Common-mode voltage gain (want it small):

cm

dm

aa

CMRR =

Common-mode rejection ratio (want it very high):

6.012 Electronic Devices and Circuits-Fall 2000 Lecture 26 8

Incremental analysis of differential amplifier (contd.)Two steps to simplify the problem:

1. Use superposition and break the problem into two:

2. Exploit symmetry:

Circuit broken into two “half circuits”.

6.012 Electronic Devices and Circuits-Fall 2000 Lecture 26 9

Incremental analysis of differential amplifier Differential-mode Analysis

No voltage relative to ground along axis of symmetry ⇒circuit identical to:

6.012 Electronic Devices and Circuits-Fall 2000 Lecture 26 10

Incremental analysis of differential amplifier Differential-mode Analysis (contd.)

Need to solve:

Differential-mode voltage gain:

12

12

ii

oo

id

oddm vv

vvvv

a−−

==

In differential –mode:

and 2 2121 ooid

ii vvv

vv −==−=

Then:

2

2 11

id

o

id

odm v

vvv

a ==

6.012 Electronic Devices and Circuits-Fall 2000 Lecture 26 11

Incremental analysis of differential amplifier Common-mode Analysis

No current across wires connecting the two half-circuits ⇒ circuit is identical to:

6.012 Electronic Devices and Circuits-Fall 2000 Lecture 26 12

Incremental analysis of differential amplifier Common-mode Analysis (contd.)

Common-mode voltage gain:

ic

oo

ic

occm v

vv

vv

a 212 +

==

In common–mode, vo1 = vo2, then:

ic

ocm v

va 1=

6.012 Electronic Devices and Circuits-Fall 2000 Lecture 26 13

3. Common-source differential amplifier (source-coupled pair)

Biasing Issues: must keep MOSFET’s in saturation

• Upper limit to VI1 and VI2: MI and M2 driven into linear regime:

21max,BIAS

DDDTTOIC

IRVVVVV −+=+=

• Lower limit to VI1 and VI2: set by circuit that implements IBIAS.

6.012 Electronic Devices and Circuits-Fall 2000 Lecture 26 14

Common-source differential amplifier (small-signal equivalent circuit model)

6.012 Electronic Devices and Circuits-Fall 2000 Lecture 26 15

Common-source differential amplifier Differential-mode half circuit

211id

Dmo

vRgv −=

Then the differential mode gain is

Dmid

odm Rg

vv

a 11

2

−==

6.012 Electronic Devices and Circuits-Fall 2000 Lecture 26 16

Common-source differential amplifier Common-mode half circuit

icobm

Dmo v

rgRg

v •+

−=1

11 21

Then the common-mode gain is

obm

obm

Dm

Dm

cm

dm rg

rgRgRg

aa

CMMR 1

1

1

1 21

21

+=

+−

−==

obm

Dm

ic

ocm rg

Rgvv

a1

11

21+−==

Common-mode Rejection Ratio (CMRR):

To get good CMRR, need good current source.

6.012 Electronic Devices and Circuits-Fall 2000 Lecture 26 17

Large-signal response of differential amplifier

• If vI1 = vI2 ⇒ vO1 = vO2 ⇒ vO = 0

• If vI1 > vI2 ⇒ M1 conducts more than M2 ⇒ i1 > i2⇒ vO1 < vO2 ⇒ vO < 0

• If vI1 >> vI2 ⇒ M1 conducts strongly, M2 turns off

⇒ i1 ≈ IBIAS, i2 ≈ 0 ⇒

• Symmetric behavior for vI1 < vI2 and vI1 << vI2

Examine large-signal transfer function:

DBAISOD

DDOODBAISDDOO

RIv

VvvRIVvv

−=

==−==

min,

max,12min,11 ,

6.012 Electronic Devices and Circuits-Fall 2000 Lecture 26 18

Large-signal response of differential amplifier (contd.)

Saturating behavior for large differential input signals:

vID that leads to amplifier saturation (vI1 >> vI2 ):

21, GSGSsatID vvv −=

With:

TGS

ox

BAISTGS

Vv

CL

WI

Vv

=

+=

2

1

2µµ

ox

BAISsatID

CL

WI

vµµ

2

, =

Then:

6.012 Electronic Devices and Circuits-Fall 2000 Lecture 26 19

Large-signal response of differential amplifier (contd.)

• For small vID, vO is linear in vI ⇒ differential amplifier

• For large vID, vO saturates: once vID is large enough, vO independent of vID ⇒ logic inverter

Can do logic with this:

• Logic 0 = -VID,sat, logic 1 = VID,sat

• Regenerative if VO (swing) >VID,sat

• Used in some MOSFET logic styles

• Used with Si BJTs: Emitter-Coupled Logic (ECL)

• And GaAs FETs: Source-Coupled FET Logic (SCFL)

6.012 Electronic Devices and Circuits-Fall 2000 Lecture 26 20

What did we learn today?

Summary of Key Concepts

• In differential amplifiers, signals are represented by difference between two voltages

• Differential amplifier amplifies the difference between two voltages but rejects “common mode” signals– ⇒ Improved noise immunity

• Using “half-circuit” technique, small-signal operation of differential amplifiers is analyzed by breaking the problem into two simpler ones– Differential mode problem

– Common mode problem

• Common-mode rejection ratio (CMRR) is an important figure of merit for differential amplifiers

• Differential amplifiers require good device matching

6.012 Electronic Devices and Circuits-Fall 2000 Lecture 26 21

Wrap-up of 6.012

• MICROELECTRONIC DEVICES– Semiconductor physics: electrons / holes and drift /

diffusion– Metal-oxide-semiconductor field-effect transistors

(MOSFETs): drift of carriers in inversion layer– Bipolar junction transistors (BJTs): minority carrier

diffusion• MICROELECTRONIC CIRCUITS

– Digital circuits (mainly CMOS): no static power dissipation; power ↓↓, delay ↓↓ & density ↑↑ as W & L ↓↓

– Analog circuits (BJT and CMOS): fττ ↑↑ and gm ↑↑ as L ↓↓: however, Avomax ↓↓ as L ↓↓

6.012: Introductory subject to microelectronic devices and circuits

Follow-on Courses

• 6.152J — Microelectronics Processing Technology• 6.720J — Integrated Microelectronic Devices• 6.301 — Solid State Circuits• 6.371 — Introduction to VLSI Systems• 6.374 — Analysis and Design of Digital ICs• 6.775 — Design of Analog MOS LSI