Electronic Circuits, Signals, and Systems

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. Matrix 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 Follower 37
....2.12 Another Illustrative Example—the Miller Integrator 38
....2.13 Other Matrices for Three-Terminal-Device Models 39
....2.14 Complex Power 41

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 Network 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-L00p 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 Identification 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

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 Network 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 Network 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 Transforms 235
....6.18 Bounds on the Spectrum 237
....6.19 The Fourier Series as a Limiting Form of the Fourier Integral 242
....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

7. Transmission of Signals Through Linear Systems 310
....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 Equations 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 Integrator 395
....7.22 The Two-Pole Transmission 399
....7.23 The Resonant Two-Pole Transmission 406
....7.24 Resonance in an RC-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 Transmissions 458
....7.37 A “Pulse-Forming” Transmission-Line System 460
....7.38 A Potentially Unstable Transmission-Line System 461
....7.39 Some General Remarks About Systems Containing 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 3 Nonlinear System 505
....8.3 The Pentode as a Modulator 508
....8.4 Elementary Systems Containing Multipliers 509
....8.5 Power Amplification in a Time-Varying System 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
....8.14 Time Multiplexing 538
....8.15 Pulse-Code Modulation 543
....8.16 Some General Remarks About Nonlinear Systems 549

9. The Negative-Feedback Concept 565
....9.1 Introduction 565
....9.2 Automatic Control by Means of Negative Feedback 566
....9.3 Control of a Nonlinear Transmission 569
....9.4 Control of a Linear Frequency-Dependent Transmission 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