1

Opamps

Part 2

Dr. David W. Graham

West Virginia UniversityLane Department of Computer Science and Electrical Engineering

© 2009 David W. Graham

2

High Gain

• Goal of opamp design – High gain

• Previous opamps do not have very high gain

• Example – 5T Opamp

– Gain = -gm1ro2||r04

– Subthreshold operation – |Gain| ≈ 650

– Above threshold operation – |Gain| ≈ 50

• Need much higher gain

– Cascode structures provide high gain

– Cascade of multiple amplifiers

3

Telescopic Opamps

MbVb

Vi1

Vo2

Vi2M1 M2

Vo1

Vb1

Vb2

Vb3

M5 M6

M7 M8

M3 M4

( )6684421

|| oxooxomv rgrrgrgA =

Approximately the square of the original gain

This is a high-speed opamp design

Major Drawback

• Very limited allowable signal swing

• Must ensure all transistors stay in saturation

• Limited signal swing at both the input and the output

4

Telescopic Opamps – Single-Ended Output

MbVb

Vi1

Vout

Vi2M1 M2

Vb1

M5 M6

M7 M8

M3 M4

MbVb

Vi1

Vout

Vi2M1 M2

Vb1

M5 M6

M7 M8

M3 M4

Vb2

• Increased output signal swing

• Requires an additional bias

5

Unity-Gain Feedback Connection• Another major drawback to the telescopic opamp is the very limited

range for unity-feedback connections

• Therefore, this opamp is rarely used as a unity-gain buffer

• Often used in switched-capacitor circuits, where the output is fed back to the input only for short durations of time

MbVb

Vi1

Vout

M1 M2

Vb1

M5 M6

M7 M8

M3 M4

Vx

For M2 and M4 to stay in saturation

24141

441

22412

for

for

TgsboutTb

Tbout

TgsbTxout

VVVVVV

MVVV

MVVVVVV

+−≤≤−

−≥

+−=+≤

Voltage range for Vout

42

244minmax

ovT

TgsT

VV

VVVVV

−=

+−=−

Always less than a threshold voltage

6

Folded Cascode Structure

Used in opamps to increase input/output voltage ranges

VoutVin

Vb

Iref1

Iref2MbVb

Vi1 Vi2M1 M2

M3 M4

Iref1

Vb

Vo2Vo1

Iref2

Iref3 Iref4

132

refb

ref II

I +=

• Iref1 is typically greater than Ib to improve response after slewing

• Burns more power than the telescopic version

7

Folded Cascode Opamp

MbVb

Vi1 Vi2M1 M2 Vb2

M7 M8

M9 M10

M5 M6

M3 M4

Vb3

Vb1

Vb4

Vo2Vo1

Vout

M5 M6

M3 M4

Vout

M5 M6

M3 M4

Vb1

8

Differential Gain of the Folded Cascode Opamp

MbVb

Vi1 Vi2M1 M2

M7 M8

M9 M10

Vb3

Vb4

Vout

M5 M6

M3 M4

Vb1

• Resistance looking into the source of M7 is much less than ro1||r09

• Virtually all current flowing out of M1

will flow into the source of M7

( )( )[ ]466210881

|||| oxoooxomv rgrrrgrgA =

[Slightly] reduced gain from telescopic amplifier

ICMR

19,

11,9,,1

Tovdd

gssatsatddbsatgs

VVV

VVVVVV

+−=

+−−+

to

Output range

satddsat VVV 22 − to

Can use pFET inputs for operation to ground

9

Folded Cascode Summary

Comparison to Telescopic Opamp• Larger input/output swings• Can be used in unity-gain configuration• One less voltage is required to be set

• Do not need to worry about the CM voltage

• Decreased voltage gain• Increased power consumption (plus, I9 should

be ~1.2-1.5 times Ib)• Lower frequency of operation• More noise

Overall, the folded cascode opamp is a good, widely used opamp

10

Two-Stage Opamp

• Cascade of two amplifier stages– First stage – Differential amplifier

– Second stage – High-gain amplifier

V1 V2M1 M2

M3 M4

MbVb1

M5 M6

M7M8

Vb2

Vb3

Vo2Vo1

11

Two-Stage Opamp (Single-Ended Output)

• Cascade of two amplifier stages– First stage – Differential amplifier

– Second stage – High-gain amplifier (CS Amp)

VoutV1 V2M1 M2

M3 M4

Mb

Vb

M5

M6

4211|| oomv rrgA −=

6552|| oomv rrgA −=

( )( )655421

|||| oomoomv rrgrrgA =

• Large output swing (Vsat,6 to Vdd – Vsat,5)• ICMR same as 5T opamp

• Unity-gain configuration sets a

minimum voltage to Vgs1-Vsat,b

• Can include cascodes, as well

• Adding an amplifier stage adds a pole

• Typically requires compensation to remain stable

12

Feedback Systems

H(s)

F(s)

+-

Vin(s) Vout(s)

If F(s)=1, then unity gain feedback

VinVout

13

Opamp Poles

• Several poles in an opamp

• Typically, one pole dominates– Dominant pole is closest to the origin (Re-Im Plot)– Dominant pole has the largest time constant

• Dominant pole is often associated with the output node in an unbuffered opamp

– Large Rout and load capacitance

|H(jω)|dB

log(ω)

Av,dc

ω-3dB GB

Gain Bandwidth, GB

( )

out

m

outout

outm

dBdcv

C

G

CRRG

AGB

=

−−=

=−

1

3,ω

14

Multiple Poles

• For multi-pole systems, other poles may be close enough to the dominant pole to affect stability

• Typically two poles are of primary concern

• Typically, for a two-stage, unbuffered opamp

– Pole at output of stage 1

– Pole at output of stage 2

– Dominant pole is usually associated with a large load capacitance (i.e. output node)

15

Multiple Poles

Gm1Vin Rout1 Cout1

Vin

Vx

Gm2Vx Rout2 Cout2

Vout

22

2

11

1

1

1

CRp

CRp

−=

−=

p2 typically dominates because of the load capacitance

16

Multiple Poles

Unity Gain

Phase of -180°

|H(jω)|dB

log(ω)

Av,dc

ω2 ω1

log(ω)

arg(H(jω))

-90o

-180o

17

Negative Feedback

In negative feedback configuration, if

Then, combined with subtraction (-180°) at the input

• Results in -360°phase shift

• This is addition (positive feedback)

• Since the gain is > 1 at this frequency, the output will grow without bound

• Therefore, this system is unstable at this frequency

• For stability, must ensure that

( ) ( ) o1801 −=∠≥ ωω jHjH and

( ) ( ) o1801 −=∠< ωωω jHjH where for

18

Phase Margin

• Typically, we like to design to provide a margin of error– These conditions (magnitude and phase) can deviate

from their designed values due to processes like noise and temperature drift

• Phase margin– A measure of how far away from a complete 360°

phase shift– Phase margin = 180°- arg(H(jω))– Measure at ω where |H(jω)| = 1

• Typical designs call for Phase margins of greater than 45°– Often higher, e.g. 60°- 90°

19

Miller Compensation

• Need to spread the poles apart

• Add a capacitor from input to output of

stage 2

VoutV1 V2M1 M2

M3 M4

Mb

Vb

M5

M6

Cc

20

Miller Compensation

Gm1Vin Rout1 Cout1

Vin

Vx

Gm2Vx Rout2 Cout2

Vout

Cc

( )

( )

( )

( ) ( ) ( )[ ] 1

1

2122211212121

2

222121

++++++++

−=

cmcccc

mmm

in

out

CRRGCCRCCRsCCCCCCRRs

GsCRRGG

sV

sV

2

2

1221

2

2

212

1

1

C

G

CCCCCC

CGp

CRRGp

m

cc

cm

cm

−≈

++

−≈

−≈

If C2 >> C1 and Cc > C1

21

Miller Compensation|H(jω)|dB

log(ω)

Av,dc

ω2ω1

log(ω)

arg(H(jω))

-90o

-180o

Phase Margin

c

m

C

GGB 1≈

ω2 should be ≥ GB

22

Opamp Comparison

GainOutput

SwingSpeed

Power

DissipationNoise

Telescopic Medium Medium Highest Low Low

Folded-

CascodeMedium Medium High Medium Medium

Two-Stage High Highest Low Medium Low