Table Of ContentTOLERANCE
ANALYSIS
ELECTRONIC
OF
CIRCUITS
"USI:NG
IVIATLAB®
Robert R. Boyd
0 CRC Press
Taylor & Francis Group
Boca Raton London New York
CRC Press is an imprint of the
Taylor & Francis Group, an informa business
Library or Coqrest Cataloging·ln-PubUcadon Data
Boyd, Robert {Robert R.)
Tolerance analysis of electronic circuits using MATI.AB I by
Robert Boyd.
p. em.
ISBN 0-8493-2276-6
I. Electronic circuits--Data processing. 2. Tolerance
(Engineering)--Data processing. 3. Electric circuit analysis-Data
processing. 4. MATI.AB. I. Title.
TK7867.B65 1999
621.3815-dc21 99-26898
CIP
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Preface
This book is written for the practicing electronics professional.
Knowledge of the capabilities and limitations of tolerance analysis
is a valuable asset to both the engineer and senior technician.
Tolerance analysis is necessary in several phases of the design
task, primarily to show that a circuit card, and a system of circuit
cards, will meet requirements over production life. Methods are
shown which can be used in the design process to perform worst-
case analysis, determine manufacturing yields, calculate limits for
production testing, determine if a design meets specification limits,
and for component stress analysis.
Topics include rxtreme value analysis and root-sum-square anal-
ysis using symmetric and asymmetric tolerances, Monte Carlo anal-
ysis using normal and uniform component distributions, Spice com-
parisons, sensitivity formulas, and ratiometric tolerances. Also
included are tolerance analyses of opamp offsets and anomalies of
high-Q and high-gain circuits.
Much ofthis material is not found in textbooks. 1be information
will benefit those involved in the following areas of engineering:
analog design/analysis, RF design/analysis, test, system, reliability,
and quality assurance. The book will also be of value to specification
writers, programmers, and senior technicians.
It is the author's hope that this work will fulfill the maxim of
Richard. W. Hamming:
"The purpose of computing is insight, not numbers."
iii
About the Author
Robert R. Boyd was a technical instructor in the United States
Air Force for 19 years. Upon his retirement from the Air Force in
1971, he enrolled at the University of New Mexico and obtained a
BSEE degree with honors in 1974. Mr. Boyd was employed in the
aerospace industry in anlog circuit design until 1996. He is presently
a consultant in analog circuit design and analysis and teaches a course
in the tolerance analysis of electronic circuits at the University of
California Extension (Irvine, CA).
v
Contents
PART I
Root-Sum-Square and Extreme Valuue Analysis
Derivatives and Sensitivities .....•......•.••...................••.••....•.••••...•••••..• I
Approximate Derivatives and Sensitivities ...................................... 2
Tolerance Analysis of a DC Differential Amplifier •••••••••.••••••••.•••..• 3
MATLAB M-file diffamp.m ........................................................... ll
Nominal Output = Zero .................................................................. 14
Combined Gain and Offset Analysis ..••..••••..••••..•••.••••.••••..••••••••••••• 17
More Complicated Circuits ............................................................ 19
Tolerance Analysis of AC Circuits ................................................. 26
Tolerance Analysis of Bandpass Filter ........................................... 29
Bandpass Filter with Asymmetric Tolerances •.•.............••.•••.....•.•.. 39
Lowpass Filter ................................................................................ 41
Spice Results Compared •••••••••••••••••••••••.••.•••••••••••••••••••••••••••••••••••••• 4S
Tolerance Analysis of Stability ••••.•.••.•..••..••••••••.•••.•••••.•••.••.•.••..•.•.• 46
PART2
Monte Carlo Analysis
General Comments Concening RSS .............................................. 65
66
Uniform vs. Gaussian Distribution. .•..••............•.•.....•.•••.••.•.•..•.....••
····-············································6··6· ········-····
Ratiometric Tolerances
MCA of Opamp de Offsets ............................................................ 70
MCA of RTD Circuit ....•...•••••...••••••••.•.•.•.•.••...•.••.•..•••••••.•••••••...••••. 75
MCA of Bandpass Filter (BPF) Circuit •••.•.••••••.•.••••••••.••••••••••.•••••• 78
Fast Monte Carlo Analysis ......•...•.•.•..•..•.•...••..••••••••..•.•.•.•...••••.••.... 85
Sallen and Key BPF ....................................................................... 92
vii
viii Tolerance Analysis of Electronic Circuits
More MCAIFMCA Examples ........................................................ 99
Delyiannis BPF• .....•.••.•..•.•.•••..•.....•...•.••••....•..•.•••.•..•..•.•..•••.....•. 100
Twin-T Passive Notch Filter. .•...•..•..........••.........•••.••..•..•.••.•••... l02
LTC 1562 BPF. ............................................................................. 103
MFB All-Pass Filter. ..................................................................... I 05
NS MF10 Switched Capacitor Filters .......................................... 106
Buffered 60-Hz Notch Filter ........................................................ 109
APPENDIX
Derivation of the RSS Equation ................................................... 113
BPF Sensitivity Expressions ......................................................... 115
Confidence Intervals ..................................................................... 119
Percent Yield ................................................................................. l20
Mathematical Curios ..................................................................... l22
An "Accurate" Cancer Test ...................................................... 122
Easter Dates .............................................................................. 123
Number of Weekdays Between Two Datcs .............................. l24
M-file Listings .............................................................................. 125
REFERENCES ............................................................................ 147
Introduction
There are three well-known tolerance analysis methods. The first two
are covered in Part 1:
1. Root-Sum-Square analysis (RSS)
2. Extreme Value Analysis (EVA) (sometimes called worst-case
analysis)
The third is covered in Part 2:
3. Monte Carlo Analysis (MCA)
The author has added a fourth method that is an application of an
old idea:
4. Fast Monte Carlo Analysis (FMCA).
As will be shown, this method exposes several weaknesses in methods
I and 2 above.
The treatment of asymmetric tolerances is neglected in what few
existing publications there are on the subject. (See References.)
Asymmetric tolerances can occur when performing design verifica-
tion analyses where the specification temperature extremes, and
hence the temperature variation of the components are most always
asymmetric. For example: -55°C to +85°C. The worst-case methods
used in circuit analysis packages derived from Spice cannot acco-
modate asymmetric tolerances. In addition, for ac circuits the sensi-
tivity portion and the resulting output of the present-day
Spice .WCASE analyses is incorrect as will be shown.
In ac analyses, especially in high-Q, high-gain filter circuits,
there are some pitfalls that the analyst must be aware of. These
anomalies will be illustrated by several examples.
ix
