MOS Switched-Capacitor and Continuous-Time Integrated Circuits and Systems: Analysis and Design

631 Pages·1989·6.23 MB·English

by  Prof. Dr.-Ing. Rolf Unbehauen

Communications and Control Engineering Series
Editors: A. Fettweis . 1. L. Massey· 1. W Modestino . M. Thoma
Rolf Unbehauen, Andrzej Cichocki
MOS Switched-Capacitor
and
Continuous-Time Integrated
Circuits and Systems
Analysis and Design
With 284 Figures
Springer-Verlag
Berlin Heidelberg New York
London Paris Tokyo
Prof. Dr.-Ing. ROLF UNBEHAUEN
Lehrstuhl flir Allgemeine und Theoretische Elektrotechnik
Universitat Erlangen-Niirnberg
CauerstraBe 7
D-8520 Erlangen
Dr.-Ing.ANDRZEJ CICHOCKI
Technical University
Koszykowa 75
PL-OO-661 Warsaw
Poland
ISBN- 13: 978-3-642-83679-4 e-ISBN -13: 978-3-642-83677-0
DOl: 10.1007/978-3-642-83677-0
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is
concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broad
casting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this
publication or parts thereof is only permitted under the provision of the German Copyright Law of
September9, 1965, in its version ofJ une 24, 1985,and a copyright fee must always be paid. Violations fall
under the prosecution act of the German Copyright Law.
© Springer-Verlag Berlin Heidelberg 1989
Softcover reprint of the hardcover 1st edition 1989
The use ofr egistered names,trademarks,etc. in this publication does not implY,even in the absence ofa
specific statement, that such names are exempt from the relevant protective laws and regulations and
therefore free for general use.
Camera-ready copy prepared by the authors using Troff.
216113020 543210 -Printed on acid-free paper
Preface
The purpose of this book is to present analysis and design principles, procedures
and techniques of analog integrated circuits which are to be implemented in MOS
(metal oxide semiconductor) technology. MOS technology is becoming dominant
in the realization of digital systems, and its use for analog circuits opens new pos
sibilities for the design of complex mixed analog/digital VLSI (very large scale in
tegration) chips. Although we are focusing attention in this book principally on
circuits and systems which can be implemented in CMOS technology, many con
siderations and structures are of a general nature and can be adapted to other
promising and emerging technologies, namely GaAs (Gallium Arsenide) and BI
MOS (bipolar MOS, i.e. circuits which combine both bipolar and CMOS devices)
technology. Moreover, some of the structures and circuits described in this book
can also be useful without integration.
In this book we describe two large classes of analog integrated circuits:
• switched capacitor (SC) networks,
• continuous-time CMOS (unswitched) circuits.
SC networks are sampled-data systems in which electric charges are transferred
from one point to another at regular discrete intervals of time and thus the signal
samples are stored and processed. Other circuits belonging to this class of
sampled-data systems are charge transfer devices (CTD) and charge coupled dev
ices (CCD).
In contrast to SC circuits, continuous-time CMOS circuits operate continuously
in time. They can be considered as subcircuits or building blocks (e.g. operational
amplifiers) of SC networks. However, they can also be used independently of SC
circuits to construct whole filtering and non-filtering nonlinear signal processing
systems. In fact continuous-time CMOS circuits represent potential contenders to
SC circuits for the realization of monolithic analog microsystems.
This book is especially intended for advanced and graduate electrical engineer
ing students and engineers in industry working in the area of analog circuit design.
We hope that the book may serve as a text for graduate level courses on analog
integrated circuits for signal processing. Certain parts of the book can also be used
to supplement existing courses in electrical engineering curricula of universities on
related topics, for instance courses on filter design, nonlinear circuits, analysis and
design of sampled-data systems. The book may also be useful as training and
VI Preface
quick-reference material for practising engineers.
This book is virtually self-contained although some mathematical background
(matrix algebra, simple ordinary differential equations, Laplace transform etc.) is
very helpful. A knowledge of elementary courses on electronics and circuit theory
is a desirable prerequisite for studying the book. Some background in sampled
data systems and the physics of semiconductors will also be helpful but not neces
sary.
Although we do not expect that readers will be totally satisfied, we hope that all
who seek some ideas, hints, guidance or enlightenment on the subject of linear
and/or nonlinear analog circuits will find something of value in this book. One can
read through this book sequentially, but it is not necessary since each chapter is
essentially self-contained with as few cross-references as possible. The authors
believe that the following aspects are important features of the book:
• Many new ideas and concepts as expressed in recent publications and symposia
on circuit and system theory and design (from 1977 to 1988) have been
brought together, described in detail,compared and illustrated with many prac
tical examples. Some results are also new and have not been published till now.
• The book presents a unified approach to the design of complex analog func
tions using a library of standard building blocks (macrocells). In this approach
the circuit designer has the possibility of using predesigned and proved macro
cells, often without getting involved in the design of these blocks themselves.
The designer should rather choose appropriate building blocks and intercon
nect them to realize a desired system.
• Many illustrative examples with detailed step-by-step solutions have been
presented to explain the topics and to enable students to obtain a thorough
grasp of the principles involved.
• A detailed state-of-the-art list of references and sources for further reading
which have theoretical and/or practical significance can be found at the end of
each chapter.
The book consists of seven chapters.
Chapter I provides an introduction and overview of the basic properties of
sampled-data signals and systems. Where it seems useful similarities to or differ
ences from continuous-time signals and systems are emphasized. Various useful
interrelationships between continuous-time and discrete-time signals in the time
and frequency domains are also discussed.
In Chapter II we focus our attention principally on MOS devices and their
modeling. Properties and characteristics of MOS transistors, switches and capaci
tors are discussed. In this chapter basic CMOS subcircuits are also presented, e.g.
biasing circuits, current mirrors, gain stages and transconductor elements which
are building blocks of more complex devices such as operational amplifiers and
transconductance operational amplifiers. Moreover, properties, parameters and
limitations of CMOS operational amplifiers are discussed in detail.
Chapter III provides insight into the principles of operation of linear SC net
works. The main purpose of this chapter is to give a straightforward analysis
method of SC networks in the time-, frequency- and z -domains. In particular it is
Preface VII
shown how to construct z -domain equivalent circuits. Techniques for evaluation
of arbitrary network functions in closed (symbolic) form are described. Next,
starting from the equivalent z -domain and continuous-time circuits it is shown
how SC circuits can be analyzed and/or optimized using general purpose simula
tion programs such as SPICE or NAP.
Chapter IV covers the description of linear SC building blocks such as sample
and-hold circuits, summing amplifiers, instrumentation amplifiers, integrators, dif
ferentiators, equalizers, analog delay lines, decimators and interpolators. For most
of the macrocells realizable transfer functions as well as the best way to imple
ment them are determined. Some parasitic effects such as clock-feedthrough,
offset voltage and finite gain of the operational amplifiers, which influence the
performance of such building blocks, are also discussed.
Chapter V is entirely devoted to the design of SC filters which represent the
largest application area of the SC technique up to now. The discussion is limited
to three very important and actual approaches:
• design of SC biquad filters,
• ladder type simulation,
• SC wave filter design.
Chapter VI describes CMOS nonlinear and adaptive building blocks such as
modulators, demodulators, comparators, Schmitt triggers, multipliers, oscillators,
function generators, etc. The first purpose of this chapter is to describe basic non
linear building blocks, i.e. their practical realizations, performance and limitations.
The second purpose is to illustrate their applications in the' design of more com
plex systems consisting of many basic building blocks (both linear and nonlinear).
Lastly we discuss the applicability of CMOS circuits in the design of nonlinear and
adaptive systems.
Digital-to-analog and analog-to-digital converters are the subject of Chapter
VII. Such converters build up the interface between sampled-data or digital sys
tems and analog systems. Different conversion techniques between continuous
time and digital signals, which are compatible with CMOS technology, are
described in this chapter. The performance and the main characteristics of such
converters are discussed.
The authors would like to express their appreciation and gratitude to a number
of people who have contributed in a variety of ways to the development of this
work. Special thanks must go to Professor G.O. Martens of the University of
Manitoba in Canada for reading an early version of the text and his very helpful
comments and suggestions. We are grateful to our colleagues Dr.-Ing. U. Forster,
Dr.-Ing. KP. Frohmader, Dipl.-Ing. J. Kintscher, Dipl.-Ing. H. Rossmanith, Dr.
lng. W. G6ttlicher, Dipl.-Ing. F. Heinrichmeyer, Dr.-Ing. D. Lehner, Dr.-Ing. M.
Doss for review, discussion, criticism and help with the computer simulation of
circuits.
All the artwork was designed on a computer by Dipl.-Ing. H. Weglehner. The
authors would also like to acknowledge the artwork assistance of our students:
Mr. Heinzelmann, Mr. Gramann, Mr. Heinkel and Miss Schmidt.
VIII Preface
Most of the original manuscript and its revisions were processed on a computer
with remarkable efficiency and accuracy by Mrs. H. Geisenfelder-G6hl, Miss H.
G6rzig, Mrs. H. Schadel and Miss M. V6lkner. We are grateful for their help and
patience through endless revisions.
The second author would like to express his gratitude to the Alexander von
Humboldt Foundation, Federal Republic of Germany, for making possible a fruit
ful scientific cooperation with the first author.
Rolf Unbehauen
Andrzej Cichocki
Contents
Chapter 1. Fundamentals of Sampled-Data Systems ...................... . 1
1.1. Introduction ............................................................ . 1
1.2. Sampled-Data Signals and Systems and Their Representa-
tions ...................................................................... . 2
1.2.1. Classification of Signals ............................................. . 2
1.2.2. Systems .................................................................. . 7
1.3. Review of Laplace Transforms .................................... . 10
1.4. Review of the Theory of z-Transforms and Their use in the
Analysis of Sampled-Data Systems ............................... . 16
1.4.1. Definition and Properties ........................................... . 16
1.4.2. Evaluation of the Inverse z-Transform .......................... . 22
1.4.3. Z-Transforms and Difference Equations ........................ . 25
1.4.4. Systems with Non-Synchronous Sampling: the Modified
(Non-Standard) z-Transform ...................................... . 27
1.5. Representation of Sampled-Data Systems by Block-Dia-
grams and Signal-Flow Graphs .................................... . 29
1.6. Review of Fourier Transforms and Frequency Responses .. . 34
1.6.1. Frequency Response of Sampled-Data Systems, Discrete-
Time Fourier Transform ............................................ . 34
1.6.2. Properties of D1Ff .................................................. . 39
1.6.3. Discrete Fourier Transform ........................................ . 41
1.6.4. The Relationship Between Time-Continuous Sampled and
Discrete-Time Signals in the Frequency- and Time-Domain 42
1.6.5. The Sampling Theorem ............................................. . 48
1.7. Reconstruction of Signals ........................................... . 50
1.7.1. Zero-Order Sample-and-Hold Element. ........................ . 51
1.7.2. First-Order Sample-and-Hold Element with Correction. ... . 56
1.7.3. The Piecewise Linear Interpolator ............................... . 58
1.8. Mapping Between the s-Plane and the z-Plane ................ . 59
x Contents
1.8.1. Poles and Zeros; Relations Between Signals and Location
of Poles and Zeros..................................................... 59
1.8.2. Sampled-Data Simulation of Analog Systems: s- z-Trans-
formation... .. . ... ..... .. ...... ....... . . .. .. .. .. ... . ...... .... .. . ... . .. . . 64
References and Sources for Further Reading. ... .. .... . .. . .. . . . 81
Chapter 2. MOS Devices for Linear Analog Integrated Circuits........ 83
2.1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
2.2. The MOS Transistor Operation and Modeling................. 84
2.2.1. Physical Structure and Operation Principles. . . . . . . . . . . . . . . . . . . . 84
2.2.2. DC Characteristics of MOS Transistors - Large Signal
Modeling.. . .. . ... . .. .. ... .. .. .... . ... . . .. .. . . .. .. . . . . . . . . . .. .. . . . .. . . . . . . 88
2.2.3. Body Effect. . .. . .. . .. .. .. .. .. .. .. .. . ... . .. .. .. .. .. . .. .. ... . . . . . .. . . . . . . . 93
2.2.4. Channel Length Modulation.. . ... . .. .. .. .. .. . . . . . . . . . . . . . .. . .. . . .. . 96
2.2.5. Effective Mobility Reduction and Series Resistance Effect. 97
2.2.6. MOSF!3T Model in the Subthreshold (Weak Inversion)
Region.................................................................... 99
2.2.7. A Compact Model of MOS Transistors with Small Geo-
metry ..................................................................... 103
2.2.8. A Small Signal Equivalent Model of MOS Transistors....... 106
2.3. Noise in MOS Transistors.................................. ......... 111
2.4. MOS Switches.......................................................... 112
2.5. MOS Capacitors....................................................... 117
2.6. Basic MOS Analog Subcircuits..................................... 120
2.6.1. MOS Bias Voltage Circuits ......................................... 120
2.6.2. MOS Current Sources................................................ 122
2.6.3. Inverter and Cascode Amplifying Stages......................... 127
2.6.4. Composite MOS Transistor Operating in Saturation......... 131
2.7. CMOS Voltage-to-Current Transducers......................... 132
2.8. MOS Operational Amplifiers: Basic Parameters and Pro-
perties .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
2.9. CMOS Operational Amplifier Architecture..................... 158
2.9.1. Differential Gain Stages...................... ... ..... ... ........ ..... 158
2.9.2. CMOS Two-Stage Operational Amplifiers...................... 162
2.9.3. Single-Stage Operational Amplifiers.... ............... ........... 165
Reference and Sources for Further Reading.................... 169
Chapter 3. Basic Properties and Systematic Analysis of S\\itcbed-
Capacitor Networks.. .. . . .. . .. .. ... . ...... . .. ... .. ... .. . .. . . ... . . . . . . 172
3.1. Introduction............................................................. 172