ELECTRONIC

CIRCUITS,

SIGNALS,

AND SYSTEMS

SAMUEL J. MASON Professor of Electrical Engineering

HENRY J. ZIMMERMANN Professor of Electrical Engineering

Department of Electrical Engineering and Research Laboratory of Electronics

Massachusetts Institute of Technology

JOHN WILEY & SONS, INC.

New York • London

C O N T E N T S

Chapter 1 Introduction 1

1.1 Circuits, Signals, and Systems, 1 1.2 Signal Transmission and Processing, 2 1.3 System Models, 2 1.4 Methods of Analysis, 3

2 Matr ix Circuit Analysis 6

2.1 Introduction, 6 2.2 Matrix Operations, 8 2.3 Matrix Representation of Linear Simultaneous

Equations, 13 2.4 Some Properties of Determinants, 14 2.5 Inversion of a Matrix, 17 2.6 Formulation of the Nodal Admittance Matrix of

a Branch Network, 20 2.7 The Nodal Impedance Matrix, 24 2.8 Voltage Ratios and Current Ratios, 26 2.9 The Floating Nodal Admittance Matrix, 27 2.10 Floating Admittance Matrices for Circuit Models

of Electronic Devices, 31 2.11 An Illustrative Example—the Cathode Fol­

lower, 37 2.12 Another Illustrative Example-—the Miller In­

tegrator, 38 2.13 Other Matrices for Three-Terminal-Device

Models, 39 2.14 Complex Power, 41

xiii

xiv CONTENTS

3 Topological Circuit Analysis 54

3.1 Introduction, 54 3.2 The Network Determinant, 55 3.3 Partial Factoring of Determinants, 56 3.4 The Topological Transmission Law for a Branch

Network, 59 3.5 A Branchlike Model for the General Linear Net­

work, 62 3.6 The Topological Transmission Law for a General

Linear Network, 66 3.7 Analysis of a Simple Triode Circuit, 68 3.8 Analysis of a Triode Amplifier, 69 3.9 Analysis of a Transistor Amplifier, 69 3.10 The Gyristor and the Gyrator, 71 3.11 Outline of a Proof of the Topological Transmission

Laws, 76 3.12 Absorption of a Node, 81

4 Linear Signal-Flow Graphs 92

4.1 Introduction, 92 4.2 The Linear Signal-Flow Graph, 93 4.3 Elementary Equivalences, 95 4.4 The Effect of a Self-Loop, 96 4.5 Absorption of a Node, 98 4.6 The Transmission of a Flow Graph, 99 4.7 The General Flow Graph, 100 4.8 Evaluation of a Graph Transmission by Identi­

fication of Paths and Loops, 100 4.9 Node Splitting, 105 4.10 The Loop Transmission of a Node or a Branch, 105 4.11 The Determinant of a Flow Graph, 107 4.12 Expansion of the Determinant in Loops, 110 4.13 Factorable Determinants, 111 4.14 Expansion on a Node or on a Branch, 112 4.15 Outline of a Proof of the General Transmission

Expression, 114 4.16 Inversion of a Path or Loop, 115 4.17 Normalization of Branch Transmissions, 120 4.18 Reversal of a Flow Graph, 122

CONTENTS XV

5 Flow-Graph Circuit Analysis 127

5.1 Introduction, 127 5.2 Two-Terminal-Pair Networks, 129 5.3 Cascaded Two-Terminal-Pair Networks, 137 5.4 The Primitive Flow Graph for a Branch Net­

work, 140 5.5 Node-Voltage and Loop-Current Analysis, 145 5.6 Unilateral Constraints, 153 5.7 The Node-Voltage Flow Graph for a Unistor Net­

work, 155 5.8 Basic Transistor and Vacuum-Triode Models, 157 5.9 The Cathode-Coupled Amplifier, 169 5.10 The Cascode Amplifier, 170 5.11 The Pentode Amplifier, 172

6 Signal Analysis 178

6.1 Introduction, 178 6.2 Pulse Signals, 180 6.3 Periodic Signals, 182 6.4 Almost-Periodic Signals, 184 6.5 Random Signals, 185 6.6 Stationary Random Processes, 188 6.7 Direct and Alternating Components, 190 6.8 Even and Odd Components, 193 6.9 Real and Imaginary Components, 194 6.10 Comparison of Vectors, 195 6.11 Comparison of Signals, 197 6.12 The Correlation Function, 206 6.13 The Trigonometric Fourier Series for a Periodic

Signal, 222 6.14 The Exponential Fourier Series, 227 6.15 Some Fundamental Properties of the Fourier

Series, 231 6.16 Transition to the Fourier Integral of a Pulse

Signal, 232 6.17 Some Fundamental Properties of Fourier Trans­

forms, 235 6.18 Bounds on the Spectrum, 237 6.19 The Fourier Series as a Limiting Form of the

Fourier Integral, 242

CONTENTS

6.20 Comparison of Spectra, 247 6.21 Completeness of the Fourier Representation, 249 6.22 Some Pulse Signals and Their Spectra, 251 6.23 Some Periodic Signals and Their Spectra, 261 6.24 Some Random Power Signals and Their Spectra,

269 6.25 A Word About Random Pulse Signals, 278 6.26 Crosscorrelation of Spectra, 279 6.27 The Sampling Theorem, 281 6.28 More About Combinations of Signals, 282

Transmission of Signals Through Linear Systems 3

7.1 Introduction, 310 7.2 The Singularity Signals, 310 7.3 The Impulse Response of a Linear Transmission

System, 318 7.4 The Superposition Integral, 320 7.5 Interpretation of the Superposition Integral as a

Correlation Operation, 324 7.6 Convolution Algebra, 326 7.7 The Solution of Certain Convolution Equa­

tions, 330 7.8 Complex Exponential Signals, 335 7.9 The System Function H(s), 340 7.10 Correlation of Input and Output Signals, 343 7.11 Signal Matching, 345 7.12 Real and Imaginary Parts of a Realizable Stable

Frequency-Response Function, 350 7.13 The Real Part Integral, 354 7.14 Gain and Phase, 357 7.15 Carrier Delay and Envelope Delay, 366 7.16 Exponential Transforms, 369 7.17 Some Fundamental Properties of Exponential

Transforms, 373 7.18 Contour Integration, 376 7.19 The One-Pole Transmission, 385 7.20 Circle Diagrams, 392 7.21 An Illustrative Example—a Feedback Inte­

grator, 395 7.22 The Two-Pole Transmission, 399 7.23 The Resonant Two-Pole Transmission, 406

CONTENTS xvii

7.24 Resonance in an ДС-Coupled Feedback Cir­cuit, 418

7.25 The Basic Definition of Q in Terms of Energy, 420 7.26 The Flat Low-Pass Transmission, 422 7.27 The Flat Band-Pass Transmission, 428 7.28 Rational Transmissions, 432 7.29 The One-Pole All-Pass Transmission, 436 7.30 The Exponential Transmission—Ideal Delay, 440 7.31 Reflection of Waves, 444 7.32 Wave Launching, 449 7.33 A Lumped Attenuator, 450 7.34 Discontinuities in Characteristic Resistance, 451 7.35 Scattering Coefficients, 455 7.36 A System Containing Random-Phase Transmis­

sions, 458 7.37 A "Pulse-Forming" Transmission-Line Sys­

tem, 460 7.38 A Potentially Unstable Transmission-Line Sys­

tem, 461 7.39 Some General Remarks About Systems Contain­

ing Ideal-Delay Elements, 464 7.40 The "Binomial" Delay System, 466

8 Nonlinear and Time-Varying Linear Systems 503

8.1 Introduction, 503 8.2 Multiplication of Signals in a Nonlinear Sys­

tem, 505 8.3 The Pentode as a Modulator, 508 8.4 Elementary Systems Containing Multipliers, 509 8.5 Power Amplification in a Time-Varying Sys­

tem, 511 8.6 General Representation of a Time-Varying Linear

System, 514 8.7 Amplitude Modulation, 515 8.8 Suppressed-Carrier Modulation, 520 8.9 A Two-Channel Modulation System, 524 8.10 Illustrations of Different Types of Modulation in

Terms of the Two-Channel System, 527 8.11 Phase and Frequency Modulation, 531 8.12 Frequency Multiplexing, 534 8.13 Pulse-Amplitude Modulation, 535

xviii CONTENTS

8.14 Time Multiplexing, 538 8.15 Pulse-Code Modulation, 543 8.16 Some General Remarks About Nonlinear Sys­

tems, 549

9 The Negative-Feedback Concept 565

9.1 Introduction, 565 9.2 Automatic Control by Means of Negative Feed­

back, 566 9.3 Control of a Nonlinear Transmission, 569 9.4 Control of a Linear Frequency-Dependent Trans­

mission, 572 9.5 Control of a Nonlinear Frequency-Dependent

Transmission, 575 9.6 Reduction of Noise and Distortion, 577 9.7 Sensitivity, 579 9.8 Control of Impedance, 583 9.9 Stability Considerations, 584 9.10 The Stability of an Arbitrary Linear Flow

Graph, 592 9.11 Illustrative Examples of Feedback in Electronic

Circuits, 595

Appendix A Bessel Functions of the First Kind 612

Index 613