Steady-State Methods for Simulating Analog and Microwave Circuits

258 Pages·1990·5.02 MB·English

by  Kenneth S. Kundert

STEADY-STATE METHODS FOR SIMULATING
ANALOG AND MICROWAVE CIRCUITS
THE KLUWER INTERNATIONAL SERIES
IN ENGINEERING AND COMPUTER SCIENCE
VLSI, COMPUTER ARCHITECTURE AND
DIGITAL SIGNAL PROCESSING
Consulting Editor
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STEADY-STATE METHODS FOR
SIMULATING ANALOG AND
MICROWAVE CIRCUITS
by
Kenneth S. Kundert
Cadence Design Systems
Jacob K. White
Massachusetts Institute of Technology
and
Alberto Sangiovanni-Vincentelli
University of California, Berkeley
l1li...
"
Springer-Science+Business Media, B.V.
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Library of Congress Cataloging.in·Publication Data
Kundert, Kenneth S.
Steady-state methods for simulating analog and microwave circuits
/ by Kenneth S. Kundert, Jacob K. White, Alberto Sangiovanni
-Vincentelli.
p. cm. - (The Kluwer international series in engineering and
computer science)
I. Microwave circuits-Mathematical models. 2. Linear integrated
circuits-Mathematical models. I. White, Jacob K. II. Sangiovanni
-Vincentelli, Alberto. III. Title. IV. Series.
TK7876.K845 1990 89-78195
621.39 '5-dc20 CIP
ISBN 978-1-4419-5121-2 ISBN 978-1-4757-2081-5 (eBook)
DOI 10.1007/978-1-4757-2081-5
Copyright © 1990 by Springer Science+Business Media Dordrecht
Originally published by Kluwer Academic Publishers in 1990.
Softcover reprint of the hardcover I st edition 1990
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system
or transmitted in any form or by any means, mechanical, photocopying, recording, or other
wise, without the prior written permission of the publisher, Springer-Science+Business Media, B.Y.
Table of Contents
Preface .................................................................................... xi
Acknowledgements ..................................................................... xv
Chapter 1.
Introduction ................ ................ .... .... ............ ................ ..... 1
1. The Standard Circuit Simulation Method .... .......................... 2
2. Steady State ........ .................... ............ ........................ ........... 4
3. Distributed Devices ................ ............ ........................ ........... 7
4. Computing the Steady-State ........................ ................ .......... 11
4.1. Time-Domain Methods ................................................ 12
4.2. Frequency Domain Methods ........................................ 14
Chapter 2.
Motivation .................... ................ .................... ............ ......... 17
1. Self-Biasing Amplifiers ......................................................... 17
2. Mixers ................................................................................... 19
3. Narrow-Band Amplifiers and Filters ..................................... 20
4. Low-Distortion Amplifiers .................................................... 21
5. Switched-Capacitor Filters .................................................... 22
6. Traveling-Wave Amplifiers .................... ................ ............... 23
7. Measured Devices ................................................................. 24
8. Crystal and Cavity Oscillators ............................................... 25
Chapter 3.
Background ............ ............ ........ ............ ............ ........ .......... 27
1. Fourier Representation of Signals .................... ..................... 27
v
vi
1.1. Truncation and Discretization 29
2. Almost-Periodic Fourier Transform .................................... .. 31
3. Systems ................................................................................ . 33
3.1. State ............................................................................ . 34
4. Problem Formulation ............................................................ . 35
4.1. Lumped Test Problem ................................................ .. 36
4.2. Distributed Test Problem ............................................ . 36
5. Differential Equations .......................................................... .. 37
5.1. Initial-Value Problems ................................................ . 38
5.2. Boundary-Value Problems .......................................... . 39
5.2.1. Existence and Uniqueness of Solutions ............ .. 39
5.3. Applications in Circuit Simulation .............................. . 41
5.3.1. Periodic Boundary Constraint ............................ . 42
5.3.2. Oscillators .......................................................... . 43
5.4. Numerical Solution of Initial-Value Problems ............ . 44
5.4.1. Discretization .................................................... .. 44
6. Numerical Solution of Nonlinear Equations ........................ .. 45
6.1. Convergence Criteria .................................................. .. 48
6.2. Simplified Newton-Raphson Methods ........................ .. 48
6.3. Continuation Methods ................................................ .. 50
Chapter 4.
Time-Domain Methods 55
1. Finite-Difference Methods .................................................... . 55
2. Shooting Methods ................................................................ . 60
2.1. Shooting by Extrapolation ........................................... . 61
2.2. Shooting with Newton-Raphson ................................ .. 65
2.3. Oscillators .................................................................. .. 70
2.4. Distributed Devices .................................................... .. 76
2.5. Parallel Shooting ......................................................... . 77
vii
Chapter 5.
Harmonic Balance Theory 81
1. Introduction ........................................................................... 81
2. Historical Development ................. ....... .............. .......... .... ..... 83
2.1. Harmonic Balance for Quasiperiodic Signals .... .... ...... 86
2.2. An Example .... ..... ....... .... .... ..... ... .... .... .... ............ .... ..... 88
3. Error Mechanisms ................................................................. 90
4. Derivation .............................................................................. 91
5. Harmonic Programming .... ............ .... .... .... .... .... ................ .... 94
5.1. Root Finding with Nonlinear Least Squares ........ ........ 96
5.2. Performance Optimization ............................................ 99
6. Harmonic Relaxation ............................................................. 101
6.1. Splitting ........................................................................ 101
6.2. Gauss-Jacobi-Newton Harmonic Relaxation ................ 104
7. Harmonic Newton ................................................................. 110
8. Error Estimation .................................................................... 112
9. Oscillators.............................................................................. 115
Chapter 6.
Implementing Harmonic Balance .... ............ .... ......... 117
1. Accelerating Harmonic Balance ............................................ 118
2. Quasiperiodic Harmonic Balance Transforms ............. ....... ... 119
2.1. Harmonic Balance and the DFT .................................. 120
2.1.1. Choosing the Artificial Frequencies .................... 121
3. Harmonic Newton .... .... ........ ............ .... .................... .... ......... 124
3.1. Harmonic Relaxation-Newton .... .... .... ........ .... .... .......... 133
3.1.1. Adaptively Pruning the Jacobian .... .... ........ .... .... 134
3.1.2. Harmonic Jacobian Data Structure ..................... 138
4. Spectre ................................................................................... 138
4.1. Comparisons to Transient Analysis ................ .... .......... 138
viii
4.2. Profiles ......................................................................... 145
4.3. Harmonic Relaxation vs. Harmonic Newton ............... 150
4.4. APFT versus FFT .......................................................... 155
Chapter 7.
Mixed Frequency-Time Method ................................ 157
1. Previous Quasiperiodic Boundary Constraints ...................... 158
1.1. The Periodic Boundary Constraint ........ ........ .... ........... 158
1.2. The N-Point Boundary Constraint ............................... 159
2. The Mixed Frequency-Time Method ..................................... 161
2.1. The Delay Operator ........ .... ........ ............................. .... 165
2.2. The Differential Equation Relation .............................. 168
2.3. An Example ........ ................ .... ........ ........ ........ .... .... ..... 170
2.4. MFT as a Two-Point Boundary Constraint .................. 172
3. Practical Issues ...................................................................... 173
3.1. The Quasiperiodic Sampled Waveform ....................... 173
3.2. Selecting the Clock ...................................................... 174
4. Nitswit ................................................................................... 177
4.1. Equation Formulation .... ................. ....... .... ......... ....... ... 177
4.2. Implementation ........................ ........ .... .... ........ ........ ..... 178
4.2.1. Application Examples ......................................... 178
4.2.2. Comparison to Direct Methods ........................... 184
Chapter 8.
Comparisons ........................................................................ 187
1. Finite-Difference Methods .................... ................................. 187
2. Shooting Methods ........... ..... .... ..... ... .... ........ .... ............ .... ..... 189
3. Harmonic Balance ................................................................. 190
4. Examples .... .... .... ........ ............... ..... ........ ........ ........ ....... ........ 192
4.1. Self-Biasing Amplifier ........ ............ ................ ........ ..... 193
ix
4.2. Mixers .......................................................................... 193
4.3. Narrow-Band Amplifiers and Filters ............................ 193
4.4. Low-Distortion Amplifiers ........................................... 194
4.5. Switched-Capacitor Filters ........................................... 194
4.6. Traveling-Wave Amplifiers .......................................... 195
4.7. Measured Devices ........................................................ 195
4.8. Crystal and Cavity Oscillators ..................................... 195
Chapter 9.
Summary ............................................................................... 197
Appendix A.
Nomenclature ...................................................................... 201
Appendix B.
APFT Time-Point Selection ......................................... 205
1. Matrix Formulation ............................................................... 205
1.1. Previous Work ............................................................. 207
1.2. Condition Number and Orthonormality ............ ........... 208
1.3. Condition Number and Time-Point Selection .............. 209
1.4. Condition Number and Aliasing .................................. 210
2. Near-Orthogonal Selection Algorithm .... ........ ........ ............... 213
2.1. Time-Point Selection .................................................... 213
2.2. Constructing the Transform Matrix .............................. 216
2.3. APFT Algorithm Results ............................................. 217
Appendix C.
Arc-Length Continuation 221
Bibliography.... ................ ............ ........ .... ............ ................ 227
x
Index ........................................................................................
241