Analysis and Design of Analog Integrated Circuits … ·  · 2013-08-11M.H. Perrott Differential...

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M.H. Perrott Analysis and Design of Analog Integrated Circuits Lecture 7 Differential Amplifiers Michael H. Perrott February 12, 2012 Copyright © 2012 by Michael H. Perrott All rights reserved.

Transcript of Analysis and Design of Analog Integrated Circuits … ·  · 2013-08-11M.H. Perrott Differential...

Page 1: Analysis and Design of Analog Integrated Circuits … ·  · 2013-08-11M.H. Perrott Differential Analysis Key observations-Inputs are equal in magnitude but opposite in sign to each

M.H. Perrott

Analysis and Design of Analog Integrated CircuitsLecture 7

Differential Amplifiers

Michael H. PerrottFebruary 12, 2012

Copyright © 2012 by Michael H. PerrottAll rights reserved.

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M.H. Perrott

Review Proposed Thevenin CMOS Transistor Model

RthgAvvgvg

isRths

Rthdisα

g

s

d

Proposed Small Signal Transistor Model

Av = 1

α = 1

RS

RG

RD

Rthd

Rths

Rthg

ID

Rthd= ro (1+gmRS)

Rthg= infinite

Rths=

1 + RD /ro

gm

Thevenin Resistances

Approximation(gmb << gm, gmro >> 1)

g

s

d

Rthd= ro (1+(gm+gmb)RS)+RS

Rthg= infinite

Exact

Rths= 1+RD /ro gm+gmb

1ro( )( )

Av = gm+gmbgmro

gm

ApproximationExact

α = 1+RD /Rthd

RD

RS

Rthd

Rths

Rthg

RG

-gmbvsvgs

vs

rogmvgs

Hybrid-π Model

g

s

d

1gm

gm 2μnCox(W/L)ID

2 2|ΦF| + VSB

γgmgmb

λID1ro

Key Small-Signal Parameters

qID nkT

(n-1)qID

nkT

Strong Inversion Weak Inversion

λID1

Parameter

(gmb<<gm, gmro>>1)

Note: gmb = 0if RS=0 or Vsb=0

(RD<< ro ) (RD<<Rthd

)

2

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M.H. Perrott

RthgAvvgvg

isRths

Rthdisα

g

s

d

Proposed Small Signal Transistor Model

Av = 1

α = 1

RS

RG

RD

Rthd

Rths

Rthg

ID

Rthd= ro (1+gmRS)

Rthg= infinite

Rths=

1 + RD /ro

gm

Thevenin Resistances

Approximation(gmb << gm, gmro >> 1)

g

s

d

Rthd= ro (1+(gm+gmb)RS)+RS

Rthg= infinite

Exact

Rths= 1+RD /ro gm+gmb

1ro( )( )

Av = gm+gmbgmro

gm

ApproximationExact

α = 1+RD /Rthd

1gm

(gmb<<gm, gmro>>1)

(RD<< ro ) (RD<<Rthd

)

Key Observations

For calculations focusing on signal flow from gate or source to the drain- Observe that current through Rd equals is

True since * Rthd/(Rd + Rthd) = 1 You can avoid doing calculations involving or Rthd

For calculations focusing on signal flow from the drain- Drain simply looks like impedance Rthd 3

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M.H. Perrott

Basic Single-Stage Amplifiers and Current Mirrors

SourceM1

W1L

Vout

ZL

idVin

M1

W1L

Vout

ZL

id

iin

Source

M1

W1L

Vout

ZL

VinSource

SourceM1

W1L

Vout

ZL

idVin

ZS

Common Source Common Gate Source Follower

Common Sourcewith Source Degeneration

M1

W1L

iout

M2

W2L

iin

Current Mirror

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M.H. Perrott

Today We Will Look At Differential Amplifiers

SourceM1

W1L

Vout

ZL

idVin

M1

W1L

Vout

ZL

id

iin

Source

M1

W1L

Vout

ZL

VinSource

SourceM1

W1L

Vout

ZL

idVin

ZS

Common Source Common Gate Source Follower

Common Sourcewith Source Degeneration

M1

W1L

iout

M2

W2L

iin

Current Mirror

M1 M2Vin+ Vin-

Vo+Vo-

Ibias

ZL ZL

DifferentialAmplifier

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M.H. Perrott

Differential and Common Mode Signals

Consider positive and negative input terminal signals Vi

+ and Vi-

Define differential signal as: Define common mode signal as: We can create arbitrary Vi

+ and Vi- signals from

differential and common mode components:

This also applies to differential output signals:

Vc

Vd/2

-Vd/2

Vic = (V+in + V

−in )/2

Vid = V+in − V −in

V +in = Vic +1

2Vid V −in = Vic −

1

2Vid

V +o = Voc +1

2Vod V −o = Voc −

1

2Vod

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M.H. Perrott

Differential Amplifier

Useful for amplifying signals in the presence of noise- Common-mode noise is rejected

Useful for high speed digital circuits- Low voltage swing allows faster gate/buffer

performance

M4

M1 M2

M3

Ibias1Vin+

RL

Vin-

RL

Vo+Vo-

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M.H. Perrott

First Steps in Small Signal Modeling

Small signal analysis assumes linearity- Impact of M4 on amplifier is to simply present its drain

impedance to the diff pair transistors (M1 and M2)- Impact of Vin+ and Vin- can be evaluated separately and then added (i.e., superposition) By symmetry, we need only determine impact of Vin+

Calculation of Vin- impact directly follows

M4

M1 M2

M3

Ibias1Vin+

RL

Rthd4= ro4

Vin-

RL

Vo+Vo-

M1 M2Vin+

RL

Vin-

RL

Vo+Vo-

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M.H. Perrott

Calculate Impact of Vin+ using Thevenin Models

Analysis follows fairly easily, but there is a simpler way!

ro4

M1 M2Vin+

RL RL

Vo+Vo-

Rthg1Av1vg1vg1

is1

Rths1

Rthd11is1α

M1

RL

Vo-

Rths2is2 Rthd2

is2

α2

RL

Vo+

ro4

M2

Common GateGeneral Model

Vin+

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M.H. Perrott

Method 2 of Differential Amplifier Analysis

Partition input signals into common-mode and differential components

By superposition, we can add the results to determine the overall impact of the input signals

ro4

M1 M2Vin+

RL

Vin-

RL

Vo+Vo-

ro4

M1 M2

RL RL

Vo+Vo-

Vic

Vid2

-Vid2

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M.H. Perrott

Differential Analysis

Key observations- Inputs are equal in magnitude but opposite in sign to each

other- By linearity and symmetry, is1 must equal -is2 This implies iR is zero, so that voltage drop across ro4 is zero

The sources of M1 and M2 are therefore at incremental ground and decoupled from each other!

Analysis can now be done on identical “half-circuits”

M1 M2

Vid

R1 R2

Vo+Vo-2

-Vid2

M1 M2

Vid

RL RL

Vo+Vo-2

-Vid2

ro4

is1

iR

is2

is1= is2iR = 0

M1 M2

Vid

R1 R2

Vo+Vo-2

-Vid2

What is the differential DC gain?11

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M.H. Perrott

Common Mode Analysis

Key observations- Inputs are equal to each other- By linearity and symmetry, is1 must equal is2

This implies iR = 2is1 = 2is2- We can view ro4 as two parallel resistors that have equal current running through them

Analysis can also be done on two identical half-circuits

ro4

M1 M2Vic

RL RL

Vo+Vo- Vic

is1

iR

is2

is1= is2iR = 2is1= 2is2

2ro4

M1 M2Vic

RL RL

Vo+Vo- Vic

is1

2ro4

is2idiff = 0

M1 M2Vic

RL RL

Vo+Vo- Vic

2ro42ro4

What is the common mode DC gain?12

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M.H. Perrott

Useful Metric for Differential Amplifiers: CMRR

Common Mode Rejection Ratio (CMRR)- Define: avd: differential gain, avc: common mode gain

- CMRR corresponds to ratio of differential to common mode gain and is related to received signal-to-noise ratio

Vinput VodVid=VsigVnoise

Vod = avdVsig + avcVnoise

⇒ Signal

Noise=

µavdavc

¶µVsigVnoise

¶= CMRR

µVsigVnoise

CMRR =

µavdavc

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M.H. Perrott

Another Useful Metric for Differential Amplifiers: PSRR

Power Supply Rejection Ratio (PSRR)- avd: differential gain- avp+: positive power supply gain- avp-: negative power supply gain

Vinput VodVid=VsigVnoise

Vsup+

Vsup-

PSRR+ =

µavdavp+

¶PSRR− =

µavdavp−

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M.H. Perrott

Example: Calculate CMRR and PSRR

First determine avd, avc, avp+, and avp-

Then calculate CMRR and PSRR- Note that CMRR and PSRR are often expressed in dB

Example: CMRR = 20log(avd/avc)

ro4

M1 M2Vin+

RL

Vin-

RL

Vo+Vo-

ro4

M1 M2

RL RL

Vo+Vo-

Vic

Vid2

-Vid2

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M.H. Perrott

Common Mode Voltage Range of Differential Amplifier

While keeping all devices in saturation:- What is the maximum common mode output range?

Assume Vid = 0- What is the maximum common mode input range?

Assume Vod = 0

M4

M1 M2

M3

Ibias

RL

Vin-

RL

Vo+Vo-Id1 Id2

VTH+ΔV2

Vin+

VTH+ΔV1 Iss

ΔV4

ΔV1 ΔV2

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M.H. Perrott

Large Signal Behavior of Differential Mode Operation

Note: above analysis assumes strong inversion

M4

M1 M2

M3

Ibias

Vid = Vin+-Vin-

RL

Vin-

RL

Vo+Vo-

Id1 Id2

Iss

-Iss

Iod = Id1-Id2

VTH+ΔV2

Vin+

VTH+ΔV1

Vid = Vin+-Vin-= (VTH+ΔV1) - (VTH+ΔV2) = ΔV1-ΔV2

Id1where k =

μnCoxW2Lk

Iss

Id2

kVid =

Iss+Iod/2k

Iss-Iod/2k

Vid =

square and solve for Iod

where Iod = Id1-Id2

2Iss

k-Vid

2Iod = KVid for Vid <Iss

k

Iss

k

Iss

k

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