FREQUENCY COMPENSATION TECHNIQUES FOR LOW-POWER

OPERATIONAL AMPLIFIERS

THE KLUWER INTERNATIONAL SERIES IN ENGINEERING AND COMPUTER SCIENCE

ANALOG CIRCUITS AND SIGNAL PROCESSING Consulting Editor

Mohammed Ismail Ohio State University

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FREQUENCY COMPENSATION TECHNIQUES FOR LOW-POWER

OPERATIONAL AMPLIFIERS

by

Rudy G. H. Eschauzier Philips Semiconductors, Sunnyvale, CA, U.S.A.

and

J ohan H. Huijsing Deljt University ofTechnology, Deljt, The Netherlands

Springer-Science+Business Media, B.Y.

A C.I.P. Catalogue record for this book is available from the Library of Congress

ISBN 978-1-4419-5154-0 ISBN 978-1-4757-2375-5 (eBook) DOI 10.1007/978-1-4757-2375-5

Printed on acid-free paper

All Rights Reserved © Springer Science+ Business Media Dordrecht 1995 Originally published by K1uwer Academic Publishers in 1995.

Softcover reprint ofthe hardcover 1st edition 1995

No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical,

incIuding photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner.

Preface

"Frequency Compensation Techniques for Low-Power OperationaJ Amplifiers" is intended for professional designers of integrated amplifiers and graduate students in this field. It serves as a guide to the frequency compensation of integrated amplifiers, emphasizing low-voltage and low­power solutions.

The basis of this text was written as a dissertation at the Delft Uni­versity ofTechnology. The aim ofthe Ph.D. project was to investigate ne\\­frequency compensation techniques that were suited for the new genera­tion low-voltage, low-power integrated amplifiers. During the four years of research it soon became apparent that, although frequency compensa­ti on is a subject that every integrated-circuit designer is likely to come across, surprisingly few attempts have been made to systematically address this subject.

The book aims at bridging the gap between the professional designer's needs and available techniques for frequency compensation. It does so in the first place by explaining existing techniques. Furthermore, the text covers several new techniques which are the direct results of the Ph.D. study. Examples of the latter are Hybrid Nested Miller compensa­tion (Sect. 5.4), Multipath Miller Zero cancellation (Sect. 6.4) and Multi­path Conditionally Stable compensation (Sect. 6.5). All compensation techniques are treated in a stage-number based order, progressing from a single transistor to circuits with six stages and more. Apart from discuss-

vii

Preface

ing the mathematical basis of the compensation methods, the book pro­vides the reader with the factual information that is required for practicing the design of integrated feedback amplifiers and many worked out exam­pIes. What is more, many bipolar and CMOS operational amplifier realiza­tions, along with their measurement results, prove the effectiveness of the compensation techniques in real-life circuits.

In li ne with the current trends in analog circuit design, the text focuses on low-voltage, low-power integrated amplifiers. Many of the pre­sented bipolar circuits operate at supply voltages down to 1 V, while sev­eral CMOS amplifiers that function correctly just slightly above this voltage are demonstrated. The lowest measured power consumption amounts to 17flW for a dass AB CMOS opamp with 120dB gain. Despite this attention to low-voltage and low-power, the frequency compensation strategies provided are universally applicable. The fundamental approach followed leads to efficient compensation strategies that are wen guarded against the parameter variations inherent to the mass-fabrication of inte­grated circuits.

The book is divided into three main parts. The first part (chapters 1,2 and 3) is optional. The interested reader will find the basic theory of negative feedback amplifiers here. The second and the third parts, span­ning chapters 4 through 7, establish the core of the work. Of these, the sec­ond part (chapters 4 through 6) introduces the various compensation techniques, induding the theory and several simple examples, while the third (chapter 7) discusses the worked-out silicon realizations and the mea­surement results. Although the last two parts build upon the theory of part one, they are intended to be usable without prior reading of the first.

Ruud G.H. Eschauzier Johan H. Huijsing

Delft, January 4,1995.

viii Frequency Compensation Techniques for Low-Power Operational Amplifiers

Contents

Preface vii

List of Symbols xiii

1. Introduction 1

1.1. Low voltage and low power 2

1.2. Low-power frequency compensation 3

1.3. Organization of the work 4

2. Properties of Feedback Circuits 7

2.1. Feedback in linear networks 11 2.1.1. The solution of a linear network 12 2.1.2. Return differenee and sensitivity 14

2.1.3. The impedanee of feedback cireuits 17

2.2. Non-linear distortion and noise 18 2.2.1. Harmonie distortion 18 2.2.2. Harmonie distortion and non-linearity 19

2.2.3. 1ntermodulation distortion 21 2.2.4. An example of distortion in a non-linear network 24 2.2.5. Modeling ofnon-linear distortion in linear networks 26 2.2.6. Noise infeedbaek cireuits 27

2.3. Conc1usions 28

3. Stability of Feedback Circuits 29

3.1. Stability analysis 31 3.1.1. Open-loop requirementsfor stability 32

3.1.2. Cauehy's theorem 32 3.1.3. The Nyquist criterion 34

ix

Contents

3.1.4. Conditional stability 37

3.1.5. Gain and phase margin 38

3.2. Maximum obtainable feedback 39 3.2.1. MaximumJeedback absolutely stable amplijiers 40

3.2.2. Optimal Jrequency response Jor integrated amplijiers 49

3.2.3. Conditional stability 53

3.3. Conclusions 55

4. Basic Frequency Compensation of Integrated Circuits 57

4.1. The single-stage case 58

4.2. Two-stage parallel compensation 60

4.3. Miller compensation 67 4.3.1. Optimal dimensioning oJthe output stage and Miller capacitor 73 4.3.2. Current-mode Miller compensation 75

4.4. Parallel VS. Miller compensation 76 4.4.1. Bandwidth-to-power ratio 76 4.4.2. Noise 83 4.4.3. Distortion 88

4.5. Conclusions 93

5. Multistage Compensation Techniques 95

5.1. Multi-stage parallel compensation 99 5.1.1. Bandwidth reduction oJ parallel compensation 103

5.2. Nested Miller compensation 105 5.2.1. Dimensioning oJNMC with more than three stages 115 5.2.2. Current-mode Nested Miller compensation 117

5.3. Reversed Nested Miller compensation 118 5.3.1. Eliminating the loading caused by the Miller capacitors 123

5.3.2. Cascode based Reversed Nested Miller compensation 126

5.4. Hybrid Nested Miller compensation 131 5.4.1. Hybrid Nested Miller compensation Jor more than Jour stages 137

5.5. Merging of compensation techniques 138

5.6. Conclusions 140

x Frequency Compensation Techniques tor Low-Power Operational Amplitiers

6. Multipath Compensation Techniques 143

6.1. Multipath Nested Miller compensation 144 6.1.1. MultipathDarlington 150

6.2. Pole-zero doublets and settling time 153

6.3. Multipath Hybrid Nested Miller compensation 157

6.4. Multipath Miller Zero Cancellation 160 6.4.1. Multipath Miller Zero Cancellationjor more than two stages 165

6.5. Multipath Conditionally Stable compensation 166 6.5.1. Conditionally stable compensationjor more thanjour stages 169

6.6. Conclusions 171

7. Realizations 175

7.1. Precision operational amplifiers with NMC and MNMC 176 7.1.1. Introduction 176 7.1.2. Circuit description 177 7.1.3. Realizations and experimental results 182 7.1.4. Conclusions 192

7.2. Opamp with Multipath Miller Zero Cancellation 193 7.2. J. 1ntroduction 193 7.2.2. Multipath Miller Zero Cancellation 195 7.2.3. Realizations 196

7.3. Low-voltage opamps with HNMC and MHNMC 201 7.3.1. Introduction 201 7.3.2. Principle oj operation 207 7.3.3. The ultimate low-voltage opamps 210 7.3.4. The bipolar MHNMC opamp 213 7.3.5. Realizations and measurement results 217 7.3.6. Conclusions 222

7.4. Multipath Conditionally Stable amplifier 224

7.5. Conclusions 227

Bibliography 231

xi

List 01 Symbols

symbol quantity unit

ß backward gain

ßf current gain of a bipolar transistor

Ll system' s determinant

Llij cofactor of the system's determinant

r contour in complex plane

f..L charge carrier mobility cm2Ns (0 frequency rad

(00 useful bandwidth rad

(Oa transit frequency of the gain asymptote rad

(Ob intercept frequency rad

(Oe secondary pole frequency rad

(Od doublet frequency rad

(Ot transit frequency rad

a- real part of complex frequency rad 't time constant s

a settling accuracy

a1 first Taylor expansion component V,A

A forward gain

Ao forward gain at D.C.

A2 second order harmonie distortion component V,A

Am ultimate gain limit

C capacitance F

Cl load capacitance F cm Miller capacitance F

cp interstage capacitance F

xiii

List of Symbols

C symbol for capacitor

Cox specific capacitance MOS device F D2 second order relative harmonic dist. comp.

D1 total intermodulation distortion

DI2 second order relative intermod. dist. comp.

DT total harmonic distortion

E signal V,A

E amplitude of sinusoidal signal V,A

F return difference

gm transconductance 0-1

G closed loop gain

GB gain-bandwidth product

H(s) arbitrary complex function

small-signal current A

small-signal current vector A :y squared equivalent input noise current A2IHz leq :y squared equivalent base noise current A2IHz I nb :y I ne squared equivalent collector noise current A2/Hz :y Illd squared equivalent drain noise current A2IHz Ib base current A

I current A

le collector current A

Ie emitter current A

Id drain current A

Is source current A

jro imaginary part of complex frequency rad

J current density Alm

k Boltzmann's constant, 1.3805.10-23 J/K k bandwidth reduction factor

k normalized unity gain factor

K gain constant

Kj first unity gain factor s-1

mll (1,1) entry of the nodal-equations matrix 0-1

xiv Frequency Compensation Techniques tor Low-Power Operational Amplifiers

M nodal equations matrix 0-1

M symbol for MOS transistor

n slope of gain asymptote 20dB/dec

N number of stages

P pole s-1

Pt' bandwidth limiting pole s-I

P power W

Ps supply power W

P(s) arbitrary complex function

q electron charge, 1.6·\0-19 C

Q symbol for bipolar transistor

R symbol for resistor

s complex frequency rad

Sd doublet spacing

S/N signal-to-noise ratio

Si{; plus or minus sign

SA sensitivity of G to A

T return ratio

T absolute temperature K

T symbol for generic transistor

Ts settling time s

u transformed real part of frequency

v small-signal voltage V v transformed imaginary part of frequency

v small-signal voltage vector V V2 eq squared equivalent input noise voltage V2/Hz

V voltage V

Vdsat saturation voltage of a MOS device V

VAl]) MOS voltage V

Vth threshold voItage of a MOS device V

VT thermal voltage V

w constituent of an immittance

w specific MOS channel width mlA

xv

List of Symbols

W width of MOS channeI m

x gain margin dB

y smalI-signaI admittance 0-1

y phase margin 1800

y admittance 0-1

z smaIl-signaI impedance 0

z zero s-I

Z impedance 0

xvi Frequency Compensation Techniques tor Low-Power Operational Amplitiers