The circuits and filters handbook = Fundamentals of circuits and filters

Fundamentals of

Circuits and Filters

The Circuits and Filters

Handbook

Third Edition

Fundamentals of Circuits and Filters

Feedback, Nonlinear, and Distributed Circuits

Analog and VLSI Circuits

Computer Aided Design and Design Automation

Passive, Active, and Digital Filters

Edited by

Wai-Kai Chen

Edited by

Wai-Kai Chen

University of Illinois

Chicago, U. S. A.

The Circuits and Filters Handbook

Third Edition

Fundamentals of

Circuits and Filters

CRC Press

Taylor & Francis Group

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Library of Congress Cataloging-in-Publication Data

Fundamentals of circuits and filters / edited by Wai-Kai Chen.

p. cm.

Includes bibliographical references and index.

ISBN-13: 978-1-4200-5887-1

ISBN-10: 1-4200-5887-8

1. Electronic circuits. 2. Electric filters. I. Chen, Wai-Kai, 1936- II. Title.

TK7867.F835 2009

621.3815--dc22 2008048126

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Contents

Preface .................................................................................................................................................. vii

Editor-in-Chief .................................................................................................................................... ix

Contributors ........................................................................................................................................ xi

SECTION I Mathematics

1 Linear Operators and Matrices .......................................................................................... 1-1

Cheryl B. Schrader and Michael K. Sain

2 Bilinear Operators and Matrices........................................................................................ 2-1

Michael K. Sain and Cheryl B. Schrader

3 Laplace Transformation ....................................................................................................... 3-1

John R. Deller, Jr.

4 Fourier Methods for Signal Analysis and Processing ................................................... 4-1

W. Kenneth Jenkins

5 z-Transform ............................................................................................................................ 5-1

Jelena Kovačevi
c

6 Wavelet Transforms ............................................................................................................. 6-1

P. P. Vaidyanathan and Igor Djokovic

7 Graph Theory......................................................................................................................... 7-1

Krishnaiyan Thulasiraman

8 Signal Flow Graphs ............................................................................................................... 8-1

Krishnaiyan Thulasiraman

9 Theory of Two-Dimensional Hurwitz Polynomials ...................................................... 9-1

Hari C. Reddy

10 Application of Symmetry: Two-Dimensional Polynomials,

Fourier Transforms, and Filter Design .......................................................................... 10-1

Hari C. Reddy, I-Hung Khoo, and P. K. Rajan

v

SECTION II Circuit Elements, Devices, and Their Models

11 Passive Circuit Elements.................................................................................................... 11-1

Stanisław Nowak, Tomasz W. Postupolski, Gordon E. Carlson,

and Bogdan M. Wilamowski

12 RF Passive IC Components .............................................................................................. 12-1

Tomas H. Lee, Maria del Mar Hershenson, Sunderarajan S. Mohan,

Hirad Samavati, and C. Patrick Yue

13 Circuit Elements, Modeling, and Equation Formulation ........................................... 13-1

Josef A. Nossek

14 Controlled Circuit Elements ............................................................................................. 14-1

Edwin W. Greeneich and James F. Delansky

15 Bipolar Junction Transistor Amplifiers .......................................................................... 15-1

David J. Comer and Donald T. Comer

16 Operational Amplifiers ...................................................................................................... 16-1

David G. Nairn and Sergio B. Franco

17 High-Frequency Amplifiers .............................................................................................. 17-1

Chris Toumazou and Alison Payne

SECTION III Linear Circuit Analysis

18 Fundamental Circuit Concepts ........................................................................................ 18-1

John Choma, Jr.

19 Network Laws and Theorems .......................................................................................... 19-1

Ray R. Chen, Artice M. Davis, and Marwan A. Simaan

20 Terminal and Port Representations ................................................................................ 20-1

James A. Svoboda

21 Signal Flow Graphs in Filter Analysis and Synthesis ................................................. 21-1

Pen-Min Lin

22 Analysis in the Frequency Domain................................................................................. 22-1

Jiri Vlach and John Choma, Jr.

23 Tableau and Modified Nodal Formulations.................................................................. 23-1

Jiri Vlach

24 Frequency-Domain Methods ............................................................................................ 24-1

Peter B. Aronhime

25 Symbolic Analysis ............................................................................................................... 25-1

Benedykt S. Rodanski and Marwan M. Hassoun

26 Analysis in the Time Domain .......................................................................................... 26-1

Robert W. Newcomb

27 State-Variable Techniques ................................................................................................. 27-1

Kwong S. Chao

Index ................................................................................................................................................IN-1

vi Contents

Preface

The purpose of this book is to provide in a single volume a comprehensive reference work covering the

broad spectrum of mathematics for circuits and filters; circuits elements, devices, and their models; and

linear circuit analysis. This book is written and developed for the practicing electrical engineers in

industry, government, and academia. The goal is to provide the most up-to-date information in the field.

Over the years, the fundamentals of the field have evolved to include a wide range of topics and a broad

range of practice. To encompass such a wide range of knowledge, this book focuses on the key concepts,

models, and equations that enable the design engineer to analyze, design, and predict the behavior of

large-scale circuits. While design formulas and tables are listed, emphasis is placed on the key concepts

and theories underlying the processes.

This book stresses fundamental theories behind professional applications and uses several examples to

reinforce this point. Extensive development of theory and details of proofs have been omitted. The reader

is assumed to have a certain degree of sophistication and experience. However, brief reviews of theories,

principles, and mathematics of some subject areas are given. These reviews have been done concisely with

perception.

The compilation of this book would not have been possible without the dedication and efforts of

Professors Yih-Fang Huang and John Choma, Jr., and most of all the contributing authors. I wish to

thank them all.

Wai-Kai Chen

vii

Editor-in-Chief

Wai-Kai Chen is a professor and head emeritus of the Department

of Electrical Engineering and Computer Science at the University of

Illinois at Chicago. He received his BS and MS in electrical engin￾eering at Ohio University, where he was later recognized as a

distinguished professor. He earned his PhD in electrical engineering

at the University of Illinois at Urbana–Champaign.

Professor Chen has extensive experience in education and indus￾try and is very active professionally in the fields of circuits and

systems. He has served as a visiting professor at Purdue University,

the University of Hawaii at Manoa, and Chuo University in Tokyo,

Japan. He was the editor-in-chief of the IEEE Transactions on

Circuits and Systems, Series I and II, the president of the IEEE

Circuits and Systems Society, and is the founding editor and the

editor-in-chief of the Journal of Circuits, Systems and Computers.

He received the Lester R. Ford Award from the Mathematical

Association of America; the Alexander von Humboldt Award from Germany; the JSPS Fellowship

Award from the Japan Society for the Promotion of Science; the National Taipei University of Science

and Technology Distinguished Alumnus Award; the Ohio University Alumni Medal of Merit for

Distinguished Achievement in Engineering Education; the Senior University Scholar Award and the

2000 Faculty Research Award from the University of Illinois at Chicago; and the Distinguished Alumnus

Award from the University of Illinois at Urbana–Champaign. He is the recipient of the Golden Jubilee

Medal, the Education Award, and the Meritorious Service Award from the IEEE Circuits and Systems

Society, and the Third Millennium Medal from the IEEE. He has also received more than a dozen

honorary professorship awards from major institutions in Taiwan and China.

A fellow of the Institute of Electrical and Electronics Engineers (IEEE) and the American Association

for the Advancement of Science (AAAS), Professor Chen is widely known in the profession for the

following works: Applied Graph Theory (North-Holland), Theory and Design of Broadband Matching

Networks (Pergamon Press), Active Network and Feedback Amplifier Theory (McGraw-Hill), Linear

Networks and Systems (Brooks=Cole), Passive and Active Filters: Theory and Implements (John Wiley),

Theory of Nets: Flows in Networks (Wiley-Interscience), The Electrical Engineering Handbook (Academic

Press), and The VLSI Handbook (CRC Press).

ix

Contributors

Peter B. Aronhime

Electrical and Computer

Engineering Department

University of Louisville

Louisville, Kentucky

Gordon E. Carlson

Department of Electrical and

Computer Engineering

University of Missouri–Rolla

Rolla, Missouri

Kwong S. Chao

Department of Electrical and

Computer Engineering

Texas Tech University

Lubbock, Texas

Ray R. Chen

Department of Electrical

Engineering

San Jose State University

San Jose, California

Wai-Kai Chen

Department of Electrical and

Computer Engineering

University of Illinois at Chicago

Chicago, Illinois

John Choma, Jr.

Ming Hsieh Department of

Electrical Engineering

University of Southern

California

Los Angeles, California

David J. Comer

Department of Electrical and

Computer Engineering

Brigham Young University

Provo, Utah

Donald T. Comer

Department of Electrical and

Computer Engineering

Brigham Young University

Provo, Utah

Artice M. Davis

Department of Electrical

Engineering

San Jose State University

San Jose, California

James F. Delansky

Department of Electrical

Engineering

Pennsylvania State University

University Park, Pennsylvania

John R. Deller, Jr.

Department of Electrical and

Computer Engineering

Michigan State University

East Lansing, Michigan

Igor Djokovic

PairGain Technologies

Tustin, California

Sergio B. Franco

Division of Engineering

San Francisco State University

San Francisco, California

Edwin W. Greeneich

Department of Electrical

Engineering

Arizona State University

Tempe, Arizona

Marwan M. Hassoun

Department of Electrical and

Computer Engineering

Iowa State University

Ames, Iowa

Maria del Mar Hershenson

Center for Integrated Systems

Stanford University

Stanford, California

Yih-Fang Huang

Department of Electrical

Engineering

University of Notre Dame

Notre Dame, Indiana

W. Kenneth Jenkins

Department of Electrical

Engineering

Pennsylvania State University

University Park, Pennsylvania

I-Hung Khoo

Department of Electrical

Engineering

California State University

Long Beach, California

Jelena Kovačevi
c

AT&T Bell Laboratories

Murray Hill, New Jersey

xi

Tomas H. Lee

Center for Integrated Systems

Stanford University

Stanford, California

Pen-Min Lin

School of Electrical Engineering

Purdue University

West Lafayette, Indiana

Sunderarajan S. Mohan

Center for Integrated Systems

Stanford University

Stanford, California

David G. Nairn

Department of Electrical

Engineering

Queen’s University

Kingston, Canada

Robert W. Newcomb

Electrical Engineering

Department

University of Maryland

College Park, Maryland

Josef A. Nossek

Institute for Circuit Theory and

Signal Processing

Technical University of Munich

Munich, Germany

Stanisław Nowak

Institute of Electronics

University of Mining and

Metallurgy

Krakow, Poland

Alison Payne

Institute of Biomedical

Engineering

Imperial College of Science,

Technology and Medicine

London, England

Tomasz W. Postupolski

Institute of Electronic Materials

Technology

Warsaw, Poland

P. K. Rajan

Department of Electrical and

Computer Engineering

Tennessee Tech University

Cookeville, Tennessee

Hari C. Reddy

Department of Electrical

Engineering

California State University

Long Beach, California

and

Department of Computer

Science=Electrical and

Control Engineering

National Chiao-Tung University,

Taiwan

Benedykt S. Rodanski

Faculty of Engineering

University of Technology,

Sydney

Sydney, New South Wales,

Australia

Michael K. Sain

Department of Electrical

Engineering

University of Notre Dame

Notre Dame, Indiana

Hirad Samavati

Center for Integrated Systems

Stanford University

Stanford, California

Cheryl B. Schrader

College of Engineering

Boise State University

Boise, Idaho

Marwan A. Simaan

Department of Electrical and

Computer Engineering

University of Pittsburgh

Pittsburgh, Pennsylvania

James A. Svoboda

Department of Electrical

Engineering

Clarkson University

Potsdam, New York

Krishnaiyan Thulasiraman

School of Computer Science

University of Oklahoma

Norman, Oklahoma

Chris Toumazou

Institute of Biomedical

Engineering

Imperial College of Science,

Technology and Medicine

London, England

P. P. Vaidyanathan

Department of Electrical

Engineering

California Institute of

Technology

Pasadena, California

Jiri Vlach

Department of Electrical and

Computer Engineering

University of Waterloo

Waterloo, Ontario, Canada

Bogdan M. Wilamowski

Alabama Nano=Micro Science

and Technology Center

Department of Electrical and

Computer Engineering

Auburn University

Auburn, Alabama

C. Patrick Yue

Center for Integrated Systems

Stanford University

Stanford, California

xii Contributors

1

Linear Operators and

Matrices

Cheryl B. Schrader

Boise State University

Michael K. Sain

University of Notre Dame

1.1 Introduction ................................................................................ 1-1

1.2 Vector Spaces over Fields ........................................................ 1-2

1.3 Linear Operators and Matrix Representations.................... 1-4

1.4 Matrix Operations ..................................................................... 1-6

1.5 Determinant, Inverse, and Rank ............................................ 1-8

1.6 Basis Transformations ............................................................ 1-12

1.7 Characteristics: Eigenvalues, Eigenvectors,

and Singular Values................................................................. 1-15

1.8 On Linear Systems................................................................... 1-18

References ............................................................................................ 1-20

1.1 Introduction

It is only after the engineer masters’ linear concepts—linear models and circuit and filter theory—that the

possibility of tackling nonlinear ideas becomes achievable. Students frequently encounter linear meth￾odologies, and bits and pieces of mathematics that aid in problem solution are stored away. Unfortu￾nately, in memorizing the process of finding the inverse of a matrix or of solving a system of equations,

the essence of the problem or associated knowledge may be lost. For example, most engineers are fairly

comfortable with the concept of a vector space, but have difficulty in generalizing these ideas to the

module level. Therefore, the intention of this section is to provide a unified view of key concepts in the

theory of linear circuits and filters, to emphasize interrelated concepts, to provide a mathematical

reference to the handbook itself, and to illustrate methodologies through the use of many and varied

examples.

This chapter begins with a basic examination of vector spaces over fields. In relating vector spaces, the

key ideas of linear operators and matrix representations come to the fore. Standard matrix operations

are examined as are the pivotal notions of determinant, inverse, and rank. Next, transformations are

shown to determine similar representations, and matrix characteristics such as singular values and

eigenvalues are defined. Finally, solutions to algebraic equations are presented in the context of matrices

and are related to this introductory chapter on mathematics as a whole.

Standard algebraic notation is introduced first. To denote an element s in a set S, use s 2 S. Consider

two sets S and T. The set of all ordered pairs (s, t) where s 2 S and t 2 T is defined as the Cartesian

product set S 3 T. A function f from S into T, denoted by f : S ! T, is a subset U of ordered pairs (s, t) 2

S 3 T such that for every s 2 S, one and only one t 2 T exists such that (s, t) 2 U. The function evaluated

at the element s gives t as a solution ( f(s) ¼ t), and each s 2 S as a first element in U appears exactly once.

1-1

A binary operation is a function acting on a Cartesian product set S 3 T. When T ¼ S, one speaks of a

binary operation on S.

1.2 Vector Spaces over Fields

A field F is a nonempty set F and two binary operations, sum (þ) and product, such that the following

properties are satisfied for all a, b,c 2 F:

1. Associativity: (a þ b) þ c ¼ a þ (b þ c); (ab)c ¼ a(bc)

2. Commutativity: a þ b ¼ b þ a ; ab ¼ ba

3. Distributivity: a(b þ c) ¼ (ab) þ (ac)

4. Identities: (Additive) 0 2 F exists such that a þ 0 ¼ a

(Multiplicative) 1 2 F exists such that a1 ¼ a

5. Inverses: (Additive) For every a 2 F, b 2 F exists such that a þ b ¼ 0

(Multiplicative) For every nonzero a 2 F, b 2 F exists such that ab ¼ 1

Examples

. Field of real numbers R . Field of complex numbers C . Field of rational functions with real coefficients R(s) . Field of binary numbers

The set of integers Z with the standard notions of addition and multiplication does not form a field

because a multiplicative inverse in Z exists only for 1. The integers form a commutative ring. Likewise,

polynomials in the indeterminate s with coefficients from F form a commutative ring F[s]. If field

property 2 also is not available, then one speaks simply of a ring. An additive group is a nonempty set G

and one binary operation þ satisfying field properties 1, 4, and 5 for addition, that is, associativity and the

existence of additive identity and inverse. Moreover, if the binary operation þ is commutative (field

property 2), then the additive group is said to be abelian. Common notation regarding inverses is that the

additive inverse for a 2 F is b ¼ a 2 F. In the multiplicative case b ¼ a1 2 F.

An F-vector space V is a nonempty set V and a field F together with binary operations þ: V 3 V ! V

and *: F 3 V ! V subject to the following axioms for all elements v, w 2 V and a, b 2 F:

1. V and þ form an additive abelian group

2. a *(vþw) ¼ (a * v)þ(a * w)

3. (aþb)* v ¼ (a * v)þ(b * v)

4. (ab)* v ¼ a *(b * v)

5. 1 * v ¼ v

Examples

. Set of all n-tuples (v1, v2,..., vn) for n > 0 and vi 2 F . Set of polynomials of degree less than n with real coefficients (F ¼ R)

Elements of V are referred to as vectors, whereas elements of F are scalars. Note that the terminology

vector space V over the field F is used often. A module differs from a vector space in only one aspect; the

underlying field in a vector space is replaced by a ring. Thus, a module is a direct generalization of a

vector space.

When considering vector spaces of n-tuples, þ is vector addition defined element by element using the

scalar addition associated with F. Multiplication (*), which is termed scalar multiplication, also is defined

1-2 Fundamentals of Circuits and Filters