Network Analysis And Synthesis

Description

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. 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