Linear Network Analysis

LINEAR NETWORK ANALYSIS......Page 1
Authors......Page 8
Title......Page 9
Copyright......Page 10
Dedication......Page 11
Preface......Page 13
Contents......Page 17
1.1 Current and Voltage References......Page 21
1.2 Kirchhoff's Laws......Page 23
1.3 Network Elements......Page 30
1.4 Power and Energy......Page 42
2.1 Loop Equations......Page 45
2.2 Node Equations......Page 51
2.3 Solution by Laplace Transforms......Page 55
2.4 Summary......Page 65
Problems......Page 66
3. Matrix Algebra and Elementary Topology......Page 74
3.1 Definitions......Page 75
3.2 Linear Algebraic Equations......Page 81
3.3 Elementary Topology......Page 87
Problems......Page 94
4. General Network Analysis......Page 97
4.1 Loop Currents and General Loop Equations......Page 98
4.2 Node Voltages and General Node Equations......Page 112
4.3 Initial Conditions......Page 121
4.4 The Impulse Function......Page 132
4.5 Impulse Functions and Initial Values......Page 140
4.6 Duality......Page 144
4.7 Network Functions, Driving Point and Transfer......Page 149
Problems......Page 162
5.1 The Principle of Superposition......Page 173
5.2 The Thévenin and Norton Theorems......Page 175
5.3 The Reciprocity Theorem......Page 180
5.4 The Sinusoidal Steady State......Page 182
5.5 Steady-State Response to General Periodic Excitation......Page 188
Problems......Page 206
6.1 The Convolution Theorem......Page 214
6.2 The Impulse Response......Page 217
6.3 The Step Response and the DuHamel Integral......Page 221
6.4 The Principle of Superposition......Page 224
6.5 Representations of Network Response......Page 231
6.6 Relationships Between Frequency and Time Response......Page 235
Problems......Page 243
7. Representations of Network Functions......Page 247
7.1 Representation by Poles and Zeros......Page 248
7.2 Frequency Response Functions......Page 250
7.3 Bode Diagrams......Page 254
7.4 Minimum-phase and Nonminimum-phase Transfer Functions......Page 260
7.5 Complex Loci......Page 264
7.6 Calculation of Network Function from a Given Magnitude......Page 268
7.7 Calculation of Network Function from a Given Angle......Page 273
7.8 Calculation of Network Function from a Given Real Part......Page 277
7.9 Integral Relationships Between Real and Imaginary Parts......Page 281
7.10 The Potential Analog......Page 296
Problems......Page 307
8. Two-Port Networks......Page 311
8.1 Two-Port Parameters and Their Interrelations......Page 313
8.2 The Scattering Parameters......Page 323
8.3 Equivalence of Two-Ports......Page 332
8.4 Transformer Equivalents......Page 337
8.5 Interconnection of Two-Port Networks......Page 339
8.6 Certain Simple Reciprocal Two-Ports......Page 344
Problems......Page 358
9. Analytic Properties of Network Functions......Page 363
9.1 Preliminary......Page 364
9.2 Quadratic Forms......Page 366
9.3 Energy Functions......Page 372
9.4 Positive Real Functions......Page 377
9.5 Reactance Functions......Page 385
9.6 RC and RL Impedances......Page 391
9.7 Open- and Short-Circuit Functions......Page 397
9.8 Topological Formulas for Network Functions......Page 401
Problems......Page 415
10. Feedback and Related Topics......Page 421
10.1 Block Diagrams and Elementary Concepts of Feedback......Page 422
10.2 Signal-Flow Graphs......Page 427
10.3 Feedback and Stability—The Nyquist Criterion......Page 445
10.4 Root Locus......Page 459
Problems......Page 467
11. Image Parameters and Filter Theory......Page 473
11.1 Image Parameters......Page 474
11.2 Image Parameters of Lossless Networks......Page 480
11.3 Image Parameter Filter Theory......Page 484
11.4 Component Filter Sections......Page 495
11.5 Determination of the Image Parameters......Page 512
11.6 Frequency Transformations......Page 520
Problems......Page 524
A.1 Analytic Functions......Page 525
A.2 Mapping......Page 529
A.3 Integration......Page 533
A.4 Infinite Series......Page 540
A.5 Multi-Valued Functions......Page 547
A.6 The Residue Theorem......Page 553
A.7 Partial-Fraction Expansions......Page 562
A.8 Analytic Continuation......Page 563
A.9 Laplace Transforms: Definition and Convergence Properties......Page 565
A.10 Analytic Properties of the Laplace Transform......Page 570
A.11 Operations on the Determining and Generating Functions......Page 573
A.12 The Complex Inversion Integral......Page 578
2. Topology of Networks......Page 581
6. Potential Analog......Page 582
10. Image Parameter Theory......Page 583
11. General......Page 584
Index 585......Page 0
A,B,C......Page 585
D,E,F......Page 586
G,H,I......Page 587
J,K,L,M,N......Page 588
O,P,Q,R......Page 589
S,T,......Page 590
U,V,W,Z......Page 591