 اسم المؤلف
K. C. a Smith, R. E. Alley
التاريخ
24 أغسطس 2016
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Electrical Circuits an Introduction – K. C. a Smith R. E. Alley
Contents
Preface xv
1 Basic concepts, units, and laws of circuit theory
1.1 Properties of the elcotrical circuit 1
1.2 The lumped circuit model 3
1.3 Charge and current S
1.4 Potential difference, energy and power 7
1.3 Ideal voltage and current sources 11
1.6 KirchhofTs laws 13
1.6.1 The current law 13
1.6.2 Worked example on the current law 15
1.6.3 The voltage law 16
1.6.4 Worked example on the voltage law 17
1.7 Resistance 18
1.7.1 Ohm’s law 18
1.7.2. Power dissipation in resistance 20
1.7.3 Resistances in combination 21
1.8 Capacitance 23
1.8.1 The voltage-current relationship for capacitance 23
1.8.2 Energy storage in capacitance 24
1.8.3 Capacitances in combination 24
1.9 Inductance 26
1.9.1 The voltage-current relationship for inductance 26
1.9.2 Energy storage in inductance 28
1.9.3 Inductances in combination 29
1.10 Inductively coupled circuits 30
1.10.1 Mutual inductance 31
1.10.2 The coefficient of coupling 33
viii Contents
1.10.3 The effective inductance of two series-connected
coupled coils 35
1.11 Passive circuit components 36
1.12 Summary of basic circuit relations 37
1.13 Problems 37
2 Theorems and techniques of linear circuit analysis
2.1 Introduction
2.2 Voltage and current dividers
2.3 Mesh analysis
2.4 Worked example
2.5 The general mesh equations
2.6 The superposition and reciprocity theorems
2.6.1 Superposition
2.6.2 Reciprocity
2.7 Thevenin’s theorem
2.8 Worked example 61
2.9 Network transformations 64
2.9.1 The Thcvenin-Norton transformation 64
2.9.2 The star-delta transformation 66
2.10 Nodal analysis 67
2.11 Comparison of mesh and nodal analysis 71
2.12 Worked example 73
2.13 Analysis of networks containing dependent sources 75
214 Worked example 78
215 Miscellaneous theorems and techniques 81
t2.15.1 The substitution and compensation theorems 81
2.15.2 Circuit reduction 84
t215.4 Ring mains 88
t215.5 Worked example 90
2.16 Summary 92
2.17 Problems 93
3 Alternating current circuits
3.1 Introduction 98
3.2 A.C. voltage-current relationships for the linear circuit
elements 101
3.3 Representation of a.c. voltage and current by the complex
exponential: Phasors
I O O O W l W l N O
»
J i N
Contents ix
3.4 Vollage-current relationships for the general network branch:
Impedance 109
3.5 Phasor and impedance diagrams 113
3.6 Linear circuit theorems and techniques in a.c. circuit analysis 115
3.7 Worked example 119
3.9 Frequency response: transfer function 126
3.10 A.C. bridges 132
3.10.1 The Schering bridge 133
3.10.2 The Wien bridge 135
3.11 Worked example 136
3.12 Inductively coupled circuits 141
3.13 Resonant circuits 146
3.13.) Losses in inductors and capacitors 146
3.13.2 The series resonant circuit 151
3.13.3 The parallel resonant circuit 164
3.13.4 Worked example 166
t3.13.5 Definition of 2-factor in terms of stored energy 169
t3.13.6 Multiple resonance 169
+3.13.7 Inductively coupled resonant circuits 173
3.14 Summary 178
3.15 Problems 179
4 Power and transformers in single-phase circuits
4.1 Introduction 187
4.2 Average power 187
4.3 Reactive power and apparent power 190
4.4 Power factor 194
4.5 Worked example 196
4.6 Complex power 198
4.7 The ideal transformer 199
4.8 Worked example 201
4.9 Single-phase power transformers 201
4.10 Worked example 208
4.11 Transformer tests 209
4.12 Voltage regulation 211
4.13 Conditions for maximum efficiency 213
4.14 The autotransformer 214
4.15 Maximum power transfer 217
t4.16 The transformer bridge 221
X Contents
4.17 Summary 224
4.18 Problems 225
5 Three- phase alternating current circuits
5.1 Introduction 231
5.2 Advantages of three-phase systems 233
5.3 Three-phase circuits 233
5.3.1 Phase and line voltages 233
5.3.3 Worked example 237
5.3.4 Star and delta connections 239
5.3.5 Worked example 241
5.3.6 Use of Y-A transformation 244
5.3.8 Worked example 245
5.4 Power, reactive power and apparent power in balanced loads 248
5.5 Worked example: power factor correction 249
5.6 Three-phase power measurement 251
5.6.1 Alternating current meters 251
5.6.2 Methods of power measurement 253
5.6.3 Worked example 257
5.7 Transformers for three-phase systems 258
5.7.1 Applications 258
5.7.2 Equivalent circuit parameters 261
5.7.3 Worked example 261
t5.7.4 Harmonic currents 269
t5.8 Phase transformation 270
tS.9 Instantaneous power to balanced load 273
5.10 Summary 275
5.11 Problems 276
6.1 Introduction 280
6.2 Qualitative analysis of the RL circuit 281
6.3 Mathematical analysis of the RL circuit 283
6.4 Time constant 286
6.5 Natural response of some basic series circuits 288
6.5.1 RL circuit 288
6.5.2 RC circuit 290
6.5.3 RLC circuit 291
6.5.4 Q-factor and logarithmic decrement 294
Contents xi
6.6 Total response 295
6.6.1 RL circuit with sinusoidal driving voltage 296
6.6.2 RC circuit with constant voltage source 297
6.6.3 Worked example 297
6.6.4 RLC circuit with constant voltage source 299
6.6.5 RLC circuit with sinusoidal driving voltage 300
6.6.6 RLC circuit with sinusoidal driving voltage and <Uo
— u>. 301
6.7 The D-operator 303
6.7.1 The operators D and D” 1 304
6.7.2 Solution of differential equations by D-operalor 305
6.7.3 D-impedance 309
6.7.4 Worked example 309
6.7.5 Thevenin’s theorem in transient analysis 313
6.7.6 Differentiating and integrating circuits 316
6.8 The unit step and related driving functions 317
6.8.1 Step function 318
6.8.2 Impulse function 319
6.8.3 Worked example 323
6.8.4 Ramp and other singularity functions 325
6.8.5 Delayed functions 326
6.9 The Laplace transform 327
6.9.1 Definition of the Laplace transform 328
6.9.2 Laplace transforms of some functions of time 328
6.9.3 Partial fractions 334
6.9.4 Network analysis by Laplace transform 340
6.9.5 Worked example 345
6.9.6 Generalized impedance, network function and impulse
response 347
6.9.7 Third and higher order networks 352
6.9.8 Worked example 355
6.9.9 Further Laplace transform theorems 357
6.10 Pole-zero methods 359
6.11 Worked example 372
6.12 Pulse and repeated driving functions 375
6.12.1 Pulse response of first order circuits 375
6.12.2 Delayed singularity functions: transforms of
recurrent waveforms 380
6.12.3 Response by the Laplace transform 385
6.13 Worked example 389
t6.!4 Convolution 392
6.14.1 Representation of a function by an impulse train 392
xii Contents
6.14.2 The convolution integral 394
6.14.3 The convolution theorem 401
6.14.4 Worked example 403
6.15 Summary 405
6.16 Problems 408
7 Non-linear circuit analysis
7.1 Introduction: linear and non
-linear elements 418
7.2 Graphical analysis 419
7.3 Small-signal models 425
7.3.1 Non
-linear resistor model 425
7.3.2 Transistor model 426
7.4 Piecewise-linear circuits 428
7.4.1 Piecewise-linear approximation 428
7.4.2 The ideal diode 429
7.4.3 Combinations of resistances and ideal diodes 430
7.4.4 The real diode 437
7.4.5 The Zener diode 437
7.4.6 Analysis of piecewise-linear circuits 440
7.4.7 Worked example 440
7.4.8 Synthesis of piecewise-linear circuits 441
7.4.9 Worked example 443
7.5 Analytical methods 443
7.6 Rectifier circuits 448
7.6.1 Half
-wave rectifier 448
7.6.2 Worked example 451
7.6.3 Full-wave rectifier 453
7.7 Thyristor circuits 455
7.8 Fourier analysis of periodic waves 460
7.8.1 Fourier expansion 460
7.8.2 Worked example 463
7.8.3 Odd and even functions 466
7.8.4 Worked example 466
7.8.5 Fourier expansion for rectifier output 469
7.8.6 Expansion of functions of time 471
7.8.7 Complex exponential form of Fourier series 471
t7.8.8 Expansions for r.m.s. values and power 474
7.8.9 Summary of formulae 479
t7.9 Filter circuits for rectifiers 481
7.9.1 Inductor 482
7.9.2 L
-scction 484
Contents xiii
7.9.3 Capacitor 484
7.9.4 a-section 486
7.10 Summary 487
7.11 Problems 488
8 Two- port networks
8.1 Introduction 501
8.2 Admittance, impedance and hybrid parameters 503
8.2.2 Impedance parameters 505
8.2.3 Hybrid and inverse hybrid parameters 506
8.3 Equivalent circuits and circuit models 507
8.4 Transmission, inverse transmission and ABCD parameters 511
8.5 Matrix notation 513
8.6 Worked example 514
8.7 Relationships between direct and inverse ABCD parameters 515
8.8 Parameter relationships for it- and T-networks 516
8.9 Worked example 517
8.10 Cascaded two-ports and chain matrices 518
8.11 Worked example 526
t8.12 Series and parallel connections of two-ports 527
t8.13 Worked example 528
t8.14 Iterative and image impedances 530
8.14.1 Iterative impedances 530
8.14.2 Image impedances 531
t8.15 Attenuators 533
+8.16 Worked example 534
t8.l7 Insertion loss 536
+8.18 Worked example 536
8.19 Summary 537
8.20 Problems 538
Appendices
A Units, symbols and abbreviations 542
B The general mesh equations and proofs of the network 545
theorems
C Computer programs 549
D Laplace transform pairs 563
Bibliography