Role of Op-Amps

1Analog and Mixed-Signal VLSI Design Center

IOWA STATE UNIVERSITY

Role of Op-Amps

• widely used building blocks for analog circuits

• widely used in communication circuits• Widely used in analog signal processing

– critical block for data-converters• Widely Used in High Volume ICs

– memory read out– Disk-driver reading-writing



New challenges in Analog Design

• Decreased Supply Voltage• Increased Digital/Analog Interference• Reduced Testability• Increased Parametric Variations



Critical Specifications for Op-Amps

• High DC Gain• High Speed/Large Gain-Bandwidth • Sufficient Output Swing• High power efficiency

Desirable: digital built-in-self-test and self-calibration



Existing structures & Limitations

Cascode AmplifierDC Gain: Modest

Speed: Excellent

Output Swing: Small

Power Efficiency: Good

Vi2

M4

Mb

M1 M1

M3 M3

Vi1

M2 M2

M4

bias1

bias2

bias3

cmfb

Frequency Response: Good




Cascaded AmplifierDC Gain: High

Output Swings: Large

Speed: Poor

CP1

CP2

in outA1 A2 A3

Frequency Response: Poor




Positive Feedback AmplifierDC Gain: Large

Output Swing: Good

Speed: High

Low Yield

Frequency Response: Good

Vi1 Vi2

Vbn

Vbp Vbp

Vo1 Vo2



Our Objective

• Low Voltage Compatible• High DC Gain• High Speed• Good Output Swing• High Yield• Standard Digital Process Compatible• Good Power Efficiency



Our Approach

• Find new amplifier architectures• Rely on digital logic to enhance

performance• Use simple digital circuit sensing amplifier

performance• Integrate controllability• Use adaptive feedback control



Positive Feedback Gain-Boosting

• Can operate at very low voltages• Can achieve very high DC gain• No compromise in bandwidth• No appreciable power increase• Conventional wisdom has two concerns

– positive feedback leads to RHP poles– gain boosting is limited if requiring robustness w.r.t.

process variations



Our response to the concerns

• positive feedback causes RHP open-loop poles, but do not necessarily cause RHP closed-loop poles!

• RHP open-loop poles can actually improve performance of closed-loop amplifiers!

• F16/F18 fighter jets have open-loop RHP poles, they play critical role in achieving their superior closed-loop performance

• no need for robustness across process variations• use positive feedback pole control after fabrication



Positive Feedback Operational Amplifiers

A(s)

-

+Vin

-

+Vd VoutA(s)

-

+Vin

-

+Vd Vout

Open loop transfer function ps

GBps

pAA(s)

0

Closed-loop transfer function βGBps

GBβA(s)A(s)(s)Af

1

Open-loop pole: Closed-loop pole: βGBppf p



Positive Feedback Amplifier Architecture Exploration

• Some positive feedback amplifier architectures have a dc gain that is much more sensitive to the feedback control variable than others

• Although architecture optimality may be difficult to determine, synthesis techniques may yield better structures than those already considered

• Comparative study of several structures with existing positive feedback structures



A)(1gggsCg(s)A

dsnds2ds1L

m1v

Vdd

Vi

Vbias1 Vo

M1

M2

AVxx

CL

Mn

AVo

ADC = gm1

gds1+gds2- (A-1)gdsn

As (A-1)gdsn → gds1+gds2,

ADC → ∞ !

Negative Output Conductance Op Amp



Implementation Block Diagram

Bias Generator

CMFB

Vip

Vin Von

VopBasic Amp

2nd stage

Negative Conductance GeneratorVi-

Vi+

2nd stage

First Stage



Basic Amplifier and the Second Stage

Basic amplifier Second stage

VBP

Vin

VCMVBN

Vip

Von Vop

M1

M5

M4M3

M2

M6Vin

M8M9

M7

Vout



Negative Conductance Generator

Vdd

M1

VopVon

Vctrl

AM5

Mg1Mn1

M4

M3 M2

Mn2

M8

M7M6

Mg2

Vi+ Vi-

Vctrl

VXX VXX



Low Gain Stage A

Vin

VBN

Vip

VopMa1

Ma3

Ma2Von

Ma4

Ma8

Ma5

Ma6

Ma7

Ma9



Positive Feedback Amplifier Architecture Exploration

VOUT

VIN

M1

M2

M3

M4

VA

VB

f1(-θ1VA-θ2VB-θ3VOUT)



Overhead for realizing this structure can be very small


IOWA STATE UNIVERSITY 43212122

433343

2221 )(

omoooombm

oombmoo

ombmm

gkggggggggggggg

ggggA

Mb

M1 M1

M3 M3

k

Vi1 Vi2

M2 M2

M4 M4

bias1

bias2

Example positive feedback amp1:

43

212122

433343

om

oooombm

oombmoo

gg

gggggggggggg

k

Gain = infinity


IOWA STATE UNIVERSITY 2122

12

2122

21

4333

43

2122

2221

oombm

om

oombm

oo

oombm

oo

oombm

ombmm

i

o

gggggkg

gggggg

gggggg

gggggggg

vv


Mb

M1 M1

M3 M3

k

Vi1 Vi2

M2 M2

M4 M4

bias1

bias2

Vo1 Vo2

2122

12

2122

21

4333

43

oombm

om

oombm

oo

oombm

oo

gggggg

gggggg

gggggg

k

Gain = infinity



M4

Mb

M1 M1

M3 M3

k

Vi1 Vi2

M2 M2

M4

bias1

bias2

422122

321

2122

433343

2221 )(

oooombm

moo

oombm

oombmoo

ombmm

gggggg

gkgggggggggggg

ggggA


2122

423

212122

433343

oombm

oom

oooombm

oombmoo

ggggggg

gggggggggggg

k

Gain = infinity



M2

M1

M4

Mb

M1

M3 M3

k

Vi1 Vi2

M2

M4

bias1

bias2

314333

243

4333

212221

2221 )(

oooombm

moo

oombm

oombmoo

ombmm

gggggg

gkgggggggggggg

ggggA


314333

2

434333

212221

oooombm

m

oooombm

oombmoo

gggggg

g

gggggggggg

ggk

Gain = infinity



DC Sweep of amp1 in 0.1um process

-6 -4 -2 0 2 4 6x 10-3

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

differential input(V)

diffe

rent

ial o

utpu

t(V)

A High Gain Positive Feedback Amplifier in 0.1um Process



Preliminary Results: DBISTSC PFAmp

A Digital Programmable Amplifier

Bifurcation in Positive Feedback Amplifier

Simulation and Measurement Results



A digital controllable Amplifier•Low-Voltage Compatible

3 transistors from VDD to VSS

•High GainAttenuator provides positive feedbacknegative-conductance compensation

•High SpeedSingle Stage

M2 M2

Vi1

Vi2

Vbn

Vo1 Vo2 CL CL

VDD

VSS



Small Signal Linear Equivalence

21 ii VVx

21 oo VVy gopgongmnx

y

xsCL-gmpy

0A=0

opon

mp

ggg

0mpoponL

mn

gggsCgA



Nonlinear Dynamic

04})](1[)(4{ 232 xgyxVVgggy mnSOCMnnnmponoppp

xCgy

CxVVy

Cy

Cggg

yL

mn

L

SOCMnnn

L

pp

L

mponop

4

)](1[4

23

2

Dynamic equation

Equilibrium manifold (DC Transfer)



Amplifier’s DC Characteristics

x

y

0

0.020.021

0.03



y

-0.1 -0.05 0 0.05 0.1-1.5

-1

-0.5

0

0.5

1

1.5

x

y

0=0.02=0

=0.021

=0.03

L

Amplifier’s DC Characteristics



0

>0 Hysteresis

No Hysteresis

Decrease L Gain

Hysteresis

Observations



Phase Diagram in Y- Plane

0.017 0.018 0.019 0.02 0.021 0.022 0.023-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0

unstable

stable

stable

stable

yx=0




0.018 0.019 0.02 0.021 0.022 0.023 0.024-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

y

y

*x=-0.001




0.018 0.019 0.02 0.021 0.022 0.023 0.024-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

yy

*x=0.001



Observations

>0 Bifurcation

For some given x, 3 solutions for y2 stable and 1 unstableFor some given x, one unique solution for y

0 No Bifurcation

For a given x, one unique solution for y



Pull up/Pull down Circuit

-0.5 0 0.5-1.5

-1

-0.5

0

0.5

1

1.5

x

yDiscontinouity

Stable

Unstable

Stable

pullup pulldown



-0.5 0 0.5-1.5

-1

-0.5

0

0.5

1

1.5

x

yDiscontinouity

Stable

Unstable

Stable

x

Pull down, stay low

OHOL=10

y

Pull up/Pull Down

Pull up, stay high



-0.5 0 0.5-1.5

-1

-0.5

0

0.5

1

1.5

x

yDiscontinouity

Stable

Unstable

Stable

x

Pull down, return high

OHOL=11

y

Pull up/Pull Down

Pull up, stay high



-0.5 0 0.5-1.5

-1

-0.5

0

0.5

1

1.5

x

yDiscontinouity

Stable

Unstable

Stable

x

Pull down, stay low

OHOL=00

y

Pull up/Pull Down

Pull up, return low



Sensing Processpull up

release

record OH

pull down

release

record OL

OHOL=?

no bifurcation bifurcation detected

11/00 10



Linear MOS Attenuator

111 k1.

3. controlled by Aspect Ratio Vo

M2

M1

Vi

W2/L2

W1/L1

2211

221 //

/LWLW

LW

2.

4. k controlled by Aspect Ratio

5. Infinite input impedance at DC



Adaptively Controllable Attenuator

M2

M1

M4

M3

M6

M5

d6 d0

1.Quiescent-voltage shifting

)11( 132 kk2.

3.Decreased Sensitivity to transistor size change

m4.

: input code <d6…d0>



Programmable Attenuation

0 20 40 60 80 100 120 1400.016

0.017

0.018

0.019

0.02

0.021

0.022

input

atte

nuat

ion



Gain Enhancement Requirement

mpm

mng

gA)]([ 0

||1

A

Gain is related to controllable Attenuator

Required Attenuator Control Code

Achievable Gain Lower Bound

mm or 02

01 ,



Design Specification for Attenuator DAC

1. Sufficient Coverage)2()0( 1

max0min0N

2. Fine Resolution

specAN

1)}()1({max120 1

3. DAC Size

min0max012 N



Effect of Offset on Sensing

-0.1 -0.05 0 0.05 0.1-1.5

-1

-0.5

0

0.5

1

1.5

x

y

offset

O



Offset Compensated Sensing Circuit

pull up pull down

VICM

DACcomparator O



Design Specifications for input DAC

1. Sufficient Coverage)2()0( 2

maxminNOffsetOffset

2. Fine Resolution

specLN

)}()1({max120 2

3. DAC Size

spec

NL

OffsetOffset minmax22



Design Specifications

y

-0.1 -0.05 0 0.05 0.1-1.5

-1

-0.5

0

0.5

1

1.5

x

y

=0.021

Lspec

Aspec:80dB

Lspec:20V

N2 12

:0.0001

offset variation:50mV

0variation:0.006N16



Combined Sensing and Control Logic

• Implement with inexpensive digital logic• Time-efficient processing• Accomplish offset compensation• Realize optimal control code searching• Adaptive feedback control



Functional Block Diagram

pull up pull down

VICM

ComparatorO

branching parameter controland offset cancellation

DAC

cal/un



Nested attenuation/bifurcation control

initialize

=(L+H)/2

bifurcation detection

Bifurcation?

L=H=

no

: Attenuator DAC input

yes no

step=N1?yes

finish searching

inner loop



Bifurcation Detection Algorithm

initialize

=(L+H)/2

Pull-up/Down

OHOL=? bifurcationdetected

H=

: Input of offset compensation DAC

00 10

break L= 11

no2N2+1input codes

step=N2?yes

break withoutbifurcation



Convergence Proof

Conditions on offset-DAC range guarantee initial conditions:

H

()

x

offset

L

at step 01.When =L=0, OHOL=112.When =H=2N2,

OHOL=003. (L)< offset (H)4. H-L=2N2



Convergence Proof (Continue)• at step k+1,

=(L+ H)/2, pull up/down

– if OHOL=10, bifurcation is detected, break

– if OHOL=11, ()<offset, let L=

– if OHOL=00, ()offset, let H= – if bifurcation is not detected, continue.

• then (L)< offset (H) H - L=2N2-(k+1)

– At L, OHOL=11; at H ,OHOL=00• This iteration ends either with ‘bifurcation detected’ or ‘step=N2’

without bifurcation.



Convergence Proof (Continue)• If step=N2, H-L=1 (L)< offset (H)

• when =L, OHOL=11, (L)< lower bound of hysteresis

• when =H, OHOL=00, (H)> up bound of hysteresis

• Lhys>(H)- (L)offset

(L) (H)

potential

hysteresis width

x

lower bound up boundLhys



Convergence Proof (Attenuator)

L

H

0 128

control code

Converge tobifurcation

nobifurcation

0

L L+1

Conditions on -DAC range guarantee initial conditions:at step 01.When = L=0, no bifurcation

2.When = H=2N1, bifurcation

3. (L)0< (H)4. H- L=2N1



Convergence Proof (Attenuator)•step k+1: (L)0< (H), H- L=2N2-k •let =(L+ H)/2, do ‘bifurcation detection’•if bifurcation is detected, ()> 0 ,let H= •else let L= •at both situations, (L)0< (H), H- L=2N1-k-1



Convergence Proof (Attenuator)

• This iteration ends with no bifurcation and finds an optimal control code L

spec

Lachieved

AN

1)}()1({max

)(

120

0

1

• Aachieved Aspec

(L) (H)

0



Simulation Environment• Ami 0.5um CMOS (most)• Cadence

– Spectre (simulator)– Hspice (simulator)– SpectreVerilog (simulator)– Analog Artist– Schematic– Virtuoso (layout tool)– SEDSM (Floor-plan /Route )

• Synopsys



Simulation Results

0 50 100 150 200 2500

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

DAC input (MSB)

Volta

ge

Offset Compensation DAC Characteristics

16-b R-1.8R DAC=5V<Lspe

c



M2

M1

M4

M3

M6

M5

d6 d0



Digitally controlled PF Amplifier

+ -

cmfb

- +

VDD

VSS

+

-

-

+

A1

+ -

cmfb

- +

VDD

VSS

Vbp

+

-

-

+A2



Two Stage Amplifier

PU PDA1 A2

vi1

vi2

vop

von

vo1

vo2

vi1

vi2

PU

PD

vo1

vo2

vop

von

Amp



R-2R DAC

DAC

R-2R

ground

reference

2R 2R 2R 2R 2R 1.9R

R R 0.94R

Matched 2R-R

For K LSBDesigned 2R-xR

For N-K MSB

X<1LSB MSB

0 1 N-2 N-1

ground

reference

2R 2R 2R 2R 2R 1.9R

R R 0.94R

Matched 2R-R


For N-K MSB

X<1

ground

reference

2R 2R 2R 2R 2R 1.9R

R R 0.94R

ground

reference

2R 2R 2R 2R 2R 1.9R

R R 0.94R

Matched 2R-R


For N-K MSB

X<1

output

LSBLSB MSBMSB

0 1 N-2 N-1



Two way switch

00

VHVL

VoVo

VH

VL



Comparator

Vin+ Vin-

latch

M1 M2Vin+ Vin-

latch

Vin+ Vin-

latch

M1 M2

Vout Comparator



Self-Calibrated High Gain Amplifier

vi1

vi2

PU

PD

vo1

vo2

vop

von

DACcode

calibr

PU

PD

vcm

DS

CLK

RN

controller Amp Comparator

16-bit R-2R



Algorithm for Controller

• Step 1: Initialize • Step 2: Sweep input• Step 3: Use pull-up/down method to detect hysteresis• Step 4: if hysteresis exists, decrease ; else increase • Step 5: if is very close to 0, finish; else goto step 2



Offset Compensation DAC

Attenuator Control DAC

32768 16384 24576 16384 28672 25578 24577

No Bifurcation

64 32 48 52 50 49 48

yesbifurcation: no no yes yes yesMax searching time: 7x16 cycles

Searching Process



Bifurcation Simulation

pull up

OH=1

pull down

OL=0

x=0



Pull-up/Pull Down

pull up

OH=1

pull down

OL=1

x=-0.1mV



AC Response

50dB gain enhancement



Step Response

1.8 2 2.2 2.4 2.6 2.8x 10-7

-0.1

-0.05

0

0.05

0.1

time

outp

ut(V

)

before calibrationafter calibration



Step Response

2.28 2.3 2.32 2.34 2.36 2.38x 10-7

0.0988

0.099

0.0992

0.0994

0.0996

0.0998

0.1

time

outp

ut(V

)

before calibrationafter calibration

Significant Settling

accuracy Improvement



Robustness Over Temperature

-40 -20 0 20 40 60 80 10050

60

70

80

90

100

110

temperature(C)

DC

Gai

ns (d

B)

No temperature compesation

With Temperature Compensation



Simulated Performance in 90nm CMOS

Easy Migration



One Fabricated Amplifier’s Performance

Tab. 1 Simulated DC gain over wide temperature range

Gain (dB)

SS SF FS FF NN

0°C 84 85 72 92 103

27°C 82.2

89 84 85 110

80°C 70.4

84.5

83.7

89 88

AMI 0.5um CMOS

Tab. 2 Measured DC gain of fabricated chipsChip #

1#2 #3 #4 #5

Gain (dB)

90 87.6

89.3

84.5

86.5

manual tuning



Two-Stage to enhance linearity

Mb

M1 M1

M3 M3

k

Vi1 Vi2

M2 M2

M4 M4

bias1

bias2

CMFB1

CMFB2



Two stage amp DC Sweep

-2 -1 0 1 2x 10-4

-1

-0.5

0

0.5

1

differential inputs(V)

diffe

rent

ial o

utpu

ts(V

)



Two stage Gain vs Vout

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1110

120

130

140

150

160

170

180

differential outputs(V)

Gai

n(dB

)

Equivalent Gain Plot

>130dBover +- 0.75V



Amplifier performance summary

• Berkeley projected 90nm process• power supply voltage Vdd=1.1 • two stage total current Itot=18ma• Total power consumption Ptot=20mw• Capacitive load CL=4p • Unity gain frequency UGF = 1.35GHz• Phase margin at UGF = 39 deg• Frequency at gain 2: G2F = 804MHz • Phase margin at G2F = 65 deg



Switched-Capacitor Amplifier

Vout

S1C1

C2

S2

S3

S4

S1

C1

S2

S5Vin

S4

S3

pos

neg

Vicm

Vicm

C3

Precision Multiply-by-Two Circuit



100 MS/s

60% swing:0.3Vdiff

Settlingaccuracy:8.9e-4=10.1 bits

Transient Simulation Results



100 MS/s

full swing0.5Vdiff

Settlingaccuracy:0.0013=9.6 bits




80 MS/s

60% swing0.3Vdiff

Settlingaccuracy:2.1e-4=12.24 bits





input=0.25V

output=0.499969V

40 MS/s

Settling accuracy:3.1e-5/0.5=6.2e-5=14.0 bits




input=0.25V

output=0.499994V

10 MS/s

Settling accuracy:6e-6/0.5=1.2e-5=16.3 bits

Documents

Role of Op-Amps