electronic circuits, signals, and systems
TRANSCRIPT
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