Introductory Circuit Theory

1 NETWORK GEOMETRY AND NETWORK VARIABLES 5
Art. 1. The classification of net works 5
2. The graph of a network 5
3. The concept of a \"tree\" 7
4. Network variables .j 8
5. The concept of loop currents; tie sets and tie-set schedules .,., 10
6. The concept of node-pair voltages; cut sets and cut-set schedules 17
7. Alternative methods of choosing current variables 23
8. Alternative methods of choosing voltage variables 33
9. Duality 42
10. Concluding remarks 51
Problems 58
2 THE EQUILIBRIUM EQUATIONS 64
Art. 1. Kirchhoff\'s laws 64
2. Independence among the kirchhoff law equations 68
3. The equilibrium equations on the loop and node bases 71
4. Parameter matrices on the loop and node bases 77
5. Regarding the symmetry of parameter matrices 79
6. Simplified procedures that are adequate in many practical cases 81
7. Sources 86
8. Summary of the procedures for deriving equilibrium equations 96
9. Examples 99
Problems 105
3 L\\IETHODS OF SOLUTION AND RELATED TOPICS 112
Art. 1. Systematic elimination methods 112
2. Use of determinants 116
3. Methods applicable to ladder and other special network configurations
121
4. Network transformations; wye-delta (y-~) equivalents 127
5. Th~venin\'s and norton\'s theorems 138
6. The reciprocity theorem 148
7. Driving-point and transfer functions 153
8. Common net work configurations and their equivalence relations 161
9. Power relations, and transformations under which they remain
Invariant 169
Problems 179
4 CIRCUIT ELEMENTS AND SOURCE FUNCTIONS 188
Art. 1. The volt-ampere relations of the elements 188
2. Voltage and current sources 190
3. The family of singularity functions; some physical interpretations
196
4. Single-element combinations 203
Approximate formulas for parameters of simple geometrical configuration
211
Problems 218
5 IMPULSE AND STEP-FUNCTION RESPONSE OF SIMPLE C1ACMTS 222
Art. 1. The series rl circuit; genera.i properties of the solution 222
2. Correlation between mathematical a.nd physical aspects 230
3. Source transformations; th6venin\'s and norton\'s theorems and
Their uses 235
4. the dual of the series rl circuit 241
5. The series rlc circuit 243
6. The dua.i of the series rlc circuit 251
7. Consideration of arbitrary initial conditions 253
Summary regarding the transient response of one-, two-, and three-element
Combinations 257
Problems 262
6 BEHAVIOR OF SIMPLE CIRCURRS IN THE SINUSOIDAL STEADY STATE 270
Art. 1. Why sinusoids play such a predominant part in the study of electrical
Net works 270
2. Complex representation of sinusoids 273
3. Elaborations upon the impedance concept 282
4. Interpretation of impedance in the complex frequency plane 286
5. Impedance and admittance functions for simple circuits 289
6. The phenomenon of resonance 297
7. Rectangular versus polar forms of impedance and admittance
Functions; an alternative interpretation of resonance 301
8. Reciprocal and complementary impedances and admittances 305
9. Magnitude and frequency sea.ling 309
10. Vector diagrams 311
11. More elaborate impedance functions; their properties and uses 315
Problems 325
7 ENERGY AND POWER IN THE SINUSOIDAL STEADY STATE 340
Art. 1. Energy in the storage elements 340
2. Energy in the storage elements when voltage and current are
Sinusoids 342
3. Energy and power relations in a complete circuit 343
4. Active and reactive power; vector power 348
5. Root-mean-square, or effective va.lues 352
6. Impedance or admittance in terms of energy functions 354
7. Computation of the energy functions for more complex networks 357
8. Some illustrative examples 358
Problems 362
8 MORE GENERAL NETWORKS IN THE SINUSOIDAL STEADY STATE 366
Art. 1. The steady-state equilibrium equations 366
2. Use of parameter matrices 371
3. Duality again 373
4. Mutual inductance and how to deal with it 374
5. Coupling coefficients 380
6. Forming the equilibrium equations when mutual inductances
Are present 382
7. Computation of driving-point and transfer impedances for ladder
Net works 385
8. Net works embodying symmetry in structure and source distribution-
Polyphase circuits 388
Problems 392
9 ADDITIONAL TOPICS DEALING WITH STEADY-STATE AND TRANSIENT BEHAVIOR
OF LUMPED LINEAR CIRCUITS 401
Art. 1. Transient response with alternating excitation 401
2. Further exploitation of the concepts of complex frequency and
Impedance 412
3. Frequency and time domains 414
4. The complete solution for any finite lumped-constant network 419
5. The derivation of equilibrium equations for driving-point and
Transfer situations; reciprocity again 426
6. Properties of the general solution 431
7. Tilustrative examples 440
8. Driving-point and transfer functions 462
9. Arbitrary initial conditions 468
Problems 469
10 GENERALIZATION OF CIRCUIT EQUATIONS AND ENERGY RELATIONS 483
Art. 1. Use of matrix algebra 483
2. Branch-parameter matrices and volt-ampere relations 491
3. Equilibrium equations on the node basis 496
4. Equilibrium equations on the loop basis 499
5. Remarks and examples 502
6. Energy functions 510
7. Equivalence of kirchhoff and lagrange equations 520
8. Relation to impedance functions 522
9. Duality once more 535
Problems 540
INDEX 547