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Network Analysis and Synthesis

Engineering Electronics and Design

Network Analysis and Synthesis
Franklin G. Kuo
531 pages

Open: Network Analysis and Synthesis
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Preface

This book is an introduction to the study of electric networks based upon a system theoretic approach. In contrast to many present textbooks, the emphasis is not on the form and structure of a network but rather on its excitation-response properties. In other words, the major theme is concerned with how a linear network behaves as a signal processor. Special emphasis is given to the descriptions of a linear network by its system function in the frequency domain and its impulse response in the time domain. With the use of the system function as a unifying link, the transition from network analysis to synthesis can be accomplished with relative ease.

The book was originally conceived as a set of notes for a second course in network analysis at the Polytechnic Institute of Brooklyn. It assumes that the student has already had a course in steady-state circuit analysis. He should be familiar with Kirchhoff's laws, mesh and node equations, standard network theorems, and, preferably, he should have an elementary understanding of network topology.

A brief description of the subject matter follows. Chapters 1 and 2 deal with signal representation and certain characteristics of linear networks. Chapters 3, 4, 5, and 6 discuss transient analysis from both a time domain viewpoint, i.e., in terms of differential equations and the impulse response, and a frequency domain viewpoint using Fourier and Laplace transforms. Chapter 7 is concerned with the use of poles and zeros in both transient and steady-state analysis. Chapter 8 contains a classical treatment of network functions.

The final five chapters deal with network synthesis. In Chapter 9, the elements of realizability theory are presented. Chapters 10 and 1 1 are concerned with elementary driving-point and transfer function synthesis procedures. In Chapter 12, some fundamental concepts in modern filter design are introduced. Chapter 13 deals with the use of scattering matrices in network analysis and synthesis. In addition, there are three appendices covering the rudiments of matrix algebra, complex variables, and proofs of Brune's realizability theorems.

TOC

Chapter I: Signals and Systems I
1.1 Signal Analysis
1.2 Complex Frequency
1.3 Network Analysis
1.4 Network Synthesis

Chapter 2: Signals and Waveforms 20
2.1 General Characteristics of Signals
2.2 General Descriptions of Signals
2.3 The Step Function and Associated Waveforms
2.4 The Unit Impulse

Chapter 3: The Frequency Domain: Fourier Analysis 46
3.1 Introduction
3.2 Orthogonal Functions
3.3 Approximation Using Orthogonal Functions
3.4 Fourier Series
3.5 Evaluation of Fourier Coefficients
3.6 Evaluation of Fourier Coefficients Using Unit Impulses
3.7 The Fourier Integral
3.8 Properties of Fourier Transforms

Chapter 4: Differential Equations
4.1 Introduction
4.2 Homogeneous Linear Differential Equations
4.3 Nonhomogeneous Equations
4.4 Step and Impulse Response
4.5 Integrodifferential Equations
4.6 Simultaneous Differential Equations

Chapter 5: Network Analysis: I
5.1 Introduction
5.2 Network Elements
5.3 Initial and Final Conditions
5.4 Step and Impulse Response
5.5 Solution of Network Equations
5.6 Analysis of Transformers

Chapter 6: The Laplace Transform
6.1 The Philosophy of Transform Methods
6.2 The Laplace Transform
6.3 Properties of Laplace Transforms
6.4 Uses of Laplace Transforms
6.5 Partial-Fraction Expansions
6.6 Poles and Zeros
6.7 Evaluation of Residues
6.8 The Initial and Final Value Theorems

Chapter 7: Transform Methods in Network Analysis 175
7.1 The Transformed Circuit
7.2 Thevenin's and Norton's Theorems
7.3 The System Function
7.4 The Step and Impulse Responses
7.5 The Convolution Integral
7.6 The Duhamel Superposition Integral

Chapter 8: Amplitude, Phase, and Delay 212
8.1 Amplitude and Phase Response
8.2 Bode Plots
8.3 Single-Tuned Circuits
8.4 Double-Tuned Circuits
8.5 On Poles and Zeros and Time Delay

Chapter 9: Network Analysis: II 253
9.1 Network Functions
9.2 Relationships Between Two-Port Parameters
9.3 Transfer Functions Using Two-Port Parameters
9.4 Interconnection of Two-Ports
9.5 Incidental Dissipation
9.6 Analysis of Ladder Networks

Chapter 10: Elements of Readability Theory 290
10.1 Causality and Stability
10.2 Hurwitz Polynomials
10.3 Positive Real Functions
10.4 Elementary Synthesis Procedures

Chapter 1 1 : Synthesis of One-Port Networks with Two Kinds of Elements 315
Properties of L-C Immittance Functions
Synthesis of L-C Driving-Point Immittances
Properties of R-C Driving-Point Impedances
Synthesis of R-C Impedances or R-L. Admittances
Properties of R-L Impedances and R-C Admittances
Synthesis of Certain R-L-C Functions

Chapter 12: Elements of Transfer Function Synthesis 341
12.1 Properties of Transfer Functions 341
12.2 Zeros of Transmission 345
12.3 Synthesis of Yn and ZS1 with a 1-Q Termination 347
12.4 Synthesis of Constant-Resistance Networks 352

Chapter 13: Topics in Filter Design 365
13.1 The Filter Design Problem 365
13.2 The Approximation Problem in Network Theory 365
13.3 The Maximally Flat Low-Pass Filter Approximation 368
13.4 Other Low-Pass Filter Approximations 373
13.5 Transient Response of Low-Pass Filters 388
13.6 A Method to Reduce Overshoot in Filters 392
13.7 A Maximally Flat Delay and Controllable Magnitude Approximation 395
13.8 Synthesis of Low-Pass Filters 397
13.9 Magnitude and Frequency Normalization 402
13.10 Frequency Transformations 404

Chapter 14: The Scattering Matrix 413
14.1 Incident and Reflected Power Flow 413
14.2 The Scattering Parameters for a One-Port Network 415
14.3 The Scattering Matrix for a Two-Port Network 419
14.4 Properties of the Scattering Matrix 426
14.5 Insertion Loss 429
14.6 Darlington's Insertion Loss Filter Synthesis 431

Chapter 15: Computer Techniques in Circuit Analysis 438
15.1 The Uses of Digital Computers in Circuit Analysis 438
15.2 Amplitude and Phase Subroutine 450
15.3 A Fortran Program for the Analysis of Ladder Networks 453
15.4 Programs that Aid in Darlington Filter Synthesis 457

Appendix A: Introduction to Matrix Algebra 461
A.1 Fundamental Operations 461
A.2 Elementary Concepts 462
A.3 Operations on Matrices 464
A.4 Solutions of Linear Equations 468
A. 5 References on Matrix Algebra 469

Appendix B: Generalized Functions and the Unit Impulse 470
B.l Generalized Functions 470
B.2 Properties of the Unit Impulse 476

Appendix C: Elements of Complex Variables 481
C.l Elementary Definitions and Operations 481
C.2 Analysis 483
C.3 Singularities and Residues 486
C.4 Contour Integration 487

Appendix D: Proofs of Some Theorems on Positive Real
Functions 490

Appendix E: An Aid to the Improvement of Filter Approximation
493
E.l Introduction 493
E.2 Constant Logarithmic Gain Contours 494
E.3 Constant Phase Contours 495
E.4 Contour Drawings 496
E.5 Correction Procedure 498
E.6 Correction Network Design 502
E.7 Conclusion 504