Network Analysis And Synthesis

✍ Scribed by Franklin F. Kuo

• Publisher: John Wiley & Sons, Inc., New York
• Year: 1966
• Tongue: English
• Leaves: 531
• Series: FANTOMASPING
• Edition: 2
• Category: Library

✦ Synopsis

In the second edition, I have tried to keep the organization of the first
edition. Most of the new material are additions aimed at strengthening
the weaknesses of the original edition. Some specific changes deserve
mention. The most important of these is a new chapter on computer
applications (Chapter 15). In the past five years, digital computers have
brought about many significant changes in the content of engineering
subject matter concerned with both analysis and design. In analysis,
computation has become an important adjunct to theory. Theory establishes
the foundation of the subject matter; computation provides clarity,
depth, and insight. In design, the computer has not only contributed
precision and speed to existing procedures but has made practicable
design methods that employ iteration and simulation. The importance of
computer-aided design cannot be overemphasized. In Chapter 15 I have
attempted to survey some digital computer applications in the areas of
network analysis and design. I strongly encourage all students to read
this chapter for cultural interest, if not for survival.
Another new section contains a rigorous treatment of the unit impulse.
It was difficult to decide whether to incorporate this m3~rial in Chapter 2
in the discussion of signals or in a separate appendix. By putting generalized
functions in an appendix, I have left the decision of whether to teach
the rigorous treatment up to the individual instructor.
Other changes worth mentioning are: (1) two new sections on the
Fourier integral in Chapter 3; (2) a section on initial and final conditions
in Chapter 5; (3) a section on Bode plots in Chapter 8; (4) revised
material on two-port parameters in Chapter 9; and (5) new sections on
frequency and transient responses of filters in Chapter 13. Major or
minor changes may be found in every chapter, with the exception of
Chapters 11 and 12. In addition, many new problems are included at the
end of each chapter.

✦ Table of Contents

Cho,cer I: Sipals and Systems I
1.1 Signal Analysis 1
1.2 Complex Frequency 4
1.3 Network Analysis 7
1.4 Network Synthesis u
Chof)ter 2: Si1nals and Waveforms 20
2.1 General Characteristics of Signals 20
2.2 General Descriptions of Signals 24
2.3 The Step Function and Associated Waveforms 28
2.4 The Unit Impulse 33
Cho,cer l: The Frequency Domain: Fourier Analysis 46
3.1 Introduction 46
3.2 Orthogonal Functions 47
3.3 Approximation Using Orthogonal Functions 48
3.4 Fourier Series 50
3.5 Evaluation of Fourier Coefficients 52
3.6 Evaluation of Fourier Coefficients Using Unit
Impulses 58
3.7 The Fourier Integral 63
3.8 Properties of Fourier Transforms 67
xiii
xiv Contents
Chapter 4: Differential Equations 75
4.1 Introduction 75
4.2 Homogeneous Linear Differential Equations 76
4.3 Nonhomogeneous Equations 82
4.4 Step and Impulse Response 85
4.5 lntegrodifferential Equations 91
4.6 Simultaneous Differential Equations 93
Chapter 5: Network Analysis: 100
5.1 Introduction 100
5.2 Network Elements 103
5.3 Initial and Final Conditions 106
5.4 Step and Impulse Response 111
5.5 Solution of Network Equations 114
5.6 Analysis of Transformers 122
Chapter 6: The Laplace Transform l:U
6.1 The Philosophy of Transform Methods 134
6.2 The Laplace Transform 135
6.3 Properties of Laplace Transforms 137
6.4 Uses of Laplace Transforms 144
6.5 Partial-Fraction Expansions 148
6.6 Poles and .zeros 155
6.7 Evaluation of Residues 162
6.8 The Initial and Final Value Theorems 165
Chapter 7: Transform Methods In Network Analysis 175
7.1 The Transformed Circuit 175
7.2 Thevenin's and Norton's Theorems 180
7.3 The System Function 187
7.4 The Step and Impulse Responses 194
7.5 The Convolution Integral 197
7.6 The Duhamel Superposition Integral 201
Contents xv
Chapter I: Amplitude, Phase, and Delay 212
8.1 Amplitude and Phase Response 212
8.2 Bode Plots 221
8.3 Single-Tuned Circuits 229
8.4 Double-Tuned Circuits 238
8.5 On Poles and Zeros and Time Delay 245
Chapter 9: Network Analysls: II 153
9.1 Network Functions 253
9.2 Relationships Between Two-Port Parameters 264
9.3 Transfer Functions Using Two-Port Parameters 266
9.4 Interconnection of Two-Ports 271
9.5 Incidental Dissipation 276
9.6 Analysis of Ladder Networks 279
Chapter 10: Elements of Realizability Theory 290
10.1 Causality and Stability 29(J
10.2 Hurwitz Polynomials 294
10.3 Positive Real Functions 299
10.4 Elementary Synthesis Procedures 308
Cho,.,. II: Synthesis of One-Port Networks with Two Kinds
of Elements 315
11.l Properties of L-C Immittance Functions 315
11.2 Synthesis of L-C Driving-Point lmmittances 319
11.3 Properties of R-C Driving-Point Impedances 325
11.4 Synthesis of R-C Impedances or R-L. Admittances 329
11.S Properties of R-L Impedances and R-C Admittances 331
11.6 Synthesis of Certain R-L-C Functions 333
xvi Contents
Chaj,te, 12: Elements of Transfer Function Synthesis :UI
12.1 Properties of Tran.sfer Functions 341
12.2 2.eros of Transmission 345
12.3 Synthesis of Y11 and Z11 with a 1-0 Termination 347
12.4 Synthesis of Constant-Resistance Networks 352
Chapter 13: Topics in FIiter 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
Contents xvii
Appendix A: Introduction to Matrix Algebra 461
A. I Fundamental Operations
A.2 Elementary Concepts
A.3 Operations on Matrices
A.4 Solutions of Linear Equations
A.5 References on Matrix Algebra
461
462
464
468
469
Appendix 8: Generalized Functions and the Unit Impulse 470
B.1 Generalized Functions 470
B.2 Properties of the Unit Impulse 476
Appendix C: Elements of Complex Variables 481
C. l Elementary Definitions and Operations
C.2 Analysis
C.3 Singularities and Residues
C.4 Contour Integration
Appendix D: Proofs of Some Theorems on Positive Real
Functions 490
Appendix E: An Aid to the Improvement of Filter Approximation
493
E.1 Introduction
E.2 Constant Logarithmic Gain Contours
E.3 Constant Phase Contours
E.4 Contour Drawings
E.5 Correction Procedure
E.6 Correction Network Design
E. 7 Conclusion
Bibliography
Name Index
Subject Index