Electric circuits

Cover......Page 1
Dedication......Page 6
Brief Contents......Page 8
Contents......Page 10
List of Examples......Page 14
Preface......Page 18
Chapter 1 : Circuit Variables......Page 25
 Practical Perspective: Balancing Power......Page 26
 1.1 Electrical Engineering: An Overview......Page 27
  Circuit Theory......Page 29
  Problem Solving......Page 30
 1.2 The International System of Units......Page 31
 1.3 Circuit Analysis: An Overview......Page 33
 1.4 Voltage and Current......Page 34
 1.5 The Ideal Basic Circuit Element......Page 35
 1.6 Power and Energy......Page 37
 Practical Perspective: Balancing Power......Page 40
 Summary......Page 41
 Problems......Page 42
Chapter 2 : Circuit Elements......Page 47
 Practical Perspective: Heating with Electric Radiators......Page 48
 2.1 Voltage and Current Sources......Page 49
 2.2 Electrical Resistance (Ohm’s Law)......Page 53
 2.3 Construction of a Circuit Model......Page 57
 2.4 Kirchhoff’s Laws......Page 60
 2.5 Analysis of a Circuit Containing Dependent Sources......Page 65
 Practical Perspective: Heating with Electric Radiators......Page 69
 Problems......Page 71
Chapter 3 : Simple Resistive Circuits......Page 79
 Practical Perspective: Resistive Touch Screens......Page 80
 3.1 Resistors in Series......Page 81
 3.2 Resistors in Parallel......Page 82
 3.3 The Voltage-Divider and Current-Divider Circuits......Page 84
  The Current-Divider Circuit......Page 86
 3.4 Voltage Division and Current Division......Page 87
 3.5 Measuring Voltage and Current......Page 89
 3.6 Measuring Resistance— The Wheatstone Bridge......Page 92
 3.7 Delta-to-Wye (Pi-to-Tee) Equivalent Circuits......Page 94
 Practical Perspective: Resistive Touch Screens......Page 96
 Summary......Page 98
 Problems......Page 99
Chapter 4 : Techniques of Circuit Analysis......Page 111
 Practical Perspective: Circuits with Realistic Resistors......Page 112
  Describing a Circuit—The Vocabulary......Page 113
  Simultaneous Equations—How Many?......Page 114
  The Systematic Approach—An Illustration......Page 115
 4.2 Introduction to the Node-Voltage Method......Page 116
 4.3 The Node-Voltage Method and Dependent Sources......Page 118
 4.4 The Node-Voltage Method: Some Special Cases......Page 119
  The Concept of a Supernode......Page 120
  Node-Voltage Analysis of the Amplifier Circuit......Page 121
 4.5 Introduction to the Mesh-Current Method......Page 122
 4.6 The Mesh-Current Method and Dependent Sources......Page 125
 4.7 The Mesh-Current Method: Some Special Cases......Page 126
  The Concept of a Supermesh......Page 127
  Mesh-Current Analysis of the Amplifier Circuit......Page 128
 4.8 The Node-Voltage Method Versus the Mesh-Current Method......Page 129
 4.9 Source Transformations......Page 132
 4.10 Thévenin and Norton Equivalents......Page 136
  Finding a Thévenin Equivalent......Page 137
  Using Source Transformations......Page 138
 4.11 More on Deriving a Thévenin Equivalent......Page 140
  Using the Thévenin Equivalent in the Amplifier Circuit......Page 141
 4.12 Maximum Power Transfer......Page 143
 4.13 Superposition......Page 145
 Practical Perspective: Circuits with Realistic Resistors......Page 148
 Summary......Page 152
 Problems......Page 153
Chapter 5 : The Operational Amplifier......Page 167
 Practical Perspective : Strain Gages......Page 168
 5.2 Terminal Voltages and Currents......Page 169
 5.3 The Inverting-Amplifier Circuit......Page 173
 5.4 The Summing-Amplifier Circuit......Page 175
 5.5 The Noninverting-Amplifier Circuit......Page 176
 5.6 The Difference-Amplifier Circuit......Page 178
  The Difference Amplifier—Another Perspective......Page 179
  Measuring Difference-Amplifier Performance— The Common Mode Rejection Ratio......Page 180
 5.7 A More Realistic Model for the Operational Amplifier......Page 182
  Analysis of a Noninverting-Amplifier Circuit Using the More Realistic Op Amp Model......Page 183
 Practical Perspective: Strain Gages......Page 185
 Summary......Page 187
 Problems......Page 188
Chapter 6 : Inductance, Capacitance,and Mutual Inductance......Page 197
 Practical Perspective: Capacitive Touch Screens......Page 198
 6.1 The Inductor......Page 199
  Current in an Inductor in Terms of the Voltage Across the Inductor......Page 200
  Power and Energy in the Inductor......Page 202
 6.2 The Capacitor......Page 205
 6.3 Series-Parallel Combinations of Inductance and Capacitance......Page 210
 6.4 Mutual Inductance......Page 212
  The Procedure for Determining Dot Markings......Page 214
  A Review of Self-Inductance......Page 216
  The Concept of Mutual Inductance......Page 217
  Mutual Inductance in Terms of Self-Inductance......Page 219
  Energy Calculations......Page 220
 Practical Perspective: Capacitive Touch Screens......Page 223
 Summary......Page 225
 Problems......Page 227
Chapter 7 : Response of First-Order RL and RC Circuits......Page 235
 Practical Perspective: Artificial Pacemaker......Page 236
  Deriving the Expression for the Current......Page 237
  The Significance of the Time Constant......Page 239
 7.2 The Natural Response of an RC Circuit......Page 243
  Deriving the Expression for the Voltage......Page 244
  The Step Response of an RL Circuit......Page 247
  The Step Response of an RC Circuit......Page 252
 7.4 A General Solution for Step and Natural Responses......Page 254
 7.5 Sequential Switching......Page 259
 7.6 Unbounded Response......Page 263
 7.7 The Integrating Amplifier......Page 264
 Practical Perspective: Artificial Pacemaker......Page 268
 Summary......Page 269
 Problems......Page 270
Chapter 8 : Natural and Step Responses of RLC Circuits......Page 287
 Practical Perspective: Clock for Computer Timing......Page 288
  The General Solution of the Second-Order Differential Equation......Page 289
 8.2 The Forms of the Natural Response of a Parallel RLC Circuit......Page 293
  The Overdamped Voltage Response......Page 294
  The Underdamped Voltage Response......Page 297
  Characteristics of the Underdamped Response......Page 299
  The Critically Damped Voltage Response......Page 300
  A Summary of the Results......Page 302
 8.3 The Step Response of a Parallel RLC Circuit......Page 303
  The Direct Approach......Page 304
 8.4 The Natural and Step Response of a Series RLC Circuit......Page 308
 8.5 A Circuit with Two Integrating Amplifiers......Page 312
  Two Integrating Amplifiers with Feedback Resistors......Page 314
 Practical Perspective: Clock for Computer Timing......Page 316
 Summary......Page 318
 Problems......Page 319
Chapter 9 : Sinusoidal Steady-State Analysis......Page 327
 Practical Perspective: A Household Distribution Circuit......Page 328
 9.1 The Sinusoidal Source......Page 329
 9.2 The Sinusoidal Response......Page 332
 9.3 The Phasor......Page 333
  Inverse Phasor Transform......Page 335
  The V-I Relationship for a Resistor......Page 338
  The V-I Relationship for an Inductor......Page 339
  The V-I Relationship for a Capacitor......Page 340
  Impedance and Reactance......Page 341
  Kirchhoff’s Current Law in the Frequency Domain......Page 342
  Combining Impedances in Series and Parallel......Page 343
  Delta-to-Wye Transformations......Page 347
 9.7 Source Transformations and Thévenin-Norton Equivalent Circuits......Page 350
 9.8 The Node-Voltage Method......Page 353
 9.9 The Mesh-Current Method......Page 354
 9.10 The Transformer......Page 355
  The Analysis of a Linear Transformer Circuit......Page 356
  Reflected Impedance......Page 357
  Exploring Limiting Values......Page 359
  Determining the Voltage and Current Ratios......Page 361
  Determining the Polarity of the Voltage and Current Ratios......Page 362
  The Use of an Ideal Transformer for Impedance Matching......Page 364
 9.12 Phasor Diagrams......Page 365
 Practical Perspective: A Household Distribution Circuit......Page 367
 Summary......Page 368
 Problems......Page 369
Chapter 10 : Sinusoidal Steady-State Power Calculations......Page 381
 Practical Perspective: Vampire Power......Page 382
 10.1 Instantaneous Power......Page 383
 10.2 Average and Reactive Power......Page 384
  Power for Purely Inductive Circuits......Page 385
  The Power Factor......Page 386
  Appliance Ratings......Page 388
 10.3 The rms Value and Power Calculations......Page 389
 10.4 Complex Power......Page 391
 10.5 Power Calculations......Page 392
  Alternate Forms for Complex Power......Page 394
 10.6 Maximum Power Transfer......Page 399
  Maximum Power Transfer When Z is Restricted......Page 401
 Practical Perspective: Vampire Power......Page 405
 Summary......Page 407
 Problems......Page 408
Chapter 11 : Balanced Three-Phase Circuits......Page 419
 Practical Perspective: Transmission and Distribution of Electric Power......Page 420
 11.1 Balanced Three-Phase Voltages......Page 421
 11.2 Three-Phase Voltage Sources......Page 422
 11.3 Analysis of the Wye-Wye Circuit......Page 423
 11.4 Analysis of the Wye-Delta Circuit......Page 428
  Average Power in a Balanced Wye Load......Page 431
  Power Calculations in a Balanced Delta Load......Page 432
  Instantaneous Power in Three-Phase Circuits......Page 433
  The Two-Wattmeter Method......Page 436
 Practical Perspective: Transmission and Distribution of Electric Power......Page 439
 Summary......Page 440
 Problems......Page 441
Chapter 12 : Introduction to the Laplace Transform......Page 449
 Practical Perspective: Transient Effects......Page 450
 12.1 Definition of the Laplace Transform......Page 451
 12.2 The Step Function......Page 452
 12.3 The Impulse Function......Page 454
 12.4 Functional Transforms......Page 457
  Multiplication by a Constant......Page 458
  Differentiation......Page 459
  Integration......Page 460
  Translation in the Time Domain......Page 461
  Scale Changing......Page 462
 12.6 Applying the Laplace Transform......Page 463
  Partial Fraction Expansion: Proper Rational Functions......Page 465
  Partial Fraction Expansion: Distinct Real Roots of D(s)......Page 466
  Partial Fraction Expansion: Distinct Complex Roots of D(s)......Page 468
  Partial Fraction Expansion: Repeated Real Roots of D(s)......Page 470
  Partial Fraction Expansion: Repeated Complex Roots of D(s)......Page 472
  Partial Fraction Expansion: Improper Rational Functions......Page 474
 12.8 Poles and Zeros of F(s)......Page 475
 12.9 Initial- and Final-Value Theorems......Page 476
  The Application of Initial- and Final-Value Theorems......Page 478
 Practical Perspective: Transient Effects......Page 479
 Summary......Page 480
 Problems......Page 481
Chapter 13 : The Laplace Transformin Circuit Analysis......Page 487
 Practical Perspective: Surge Suppressors......Page 488
  An Inductor in the s Domain......Page 489
  A Capacitor in the s Domain......Page 490
 13.2 Circuit Analysis in the s Domain......Page 491
  The Natural Response of an RC Circuit......Page 493
  The Step Response of a Parallel Circuit......Page 494
  The Transient Response of a Parallel RLC Circuit......Page 496
  The Step Response of a Multiple Mesh Circuit......Page 497
  The Use of Thévenin’s Equivalent......Page 500
  A Circuit with Mutual Inductance......Page 501
  The Use of Superposition......Page 503
 13.4 The Transfer Function......Page 505
 13.5 The Transfer Function in Partial Fraction Expansions......Page 507
  Observations on the Use of H(s) in Circuit Analysis......Page 509
 13.6 The Transfer Function and the Convolution Integral......Page 510
  The Concepts of Memory and the Weighting Function......Page 515
 13.7 The Transfer Function and the Steady-State Sinusoidal Response......Page 516
  Switching Operations......Page 519
  Impulsive Sources......Page 522
 Practical Perspective: Surge Suppressors......Page 526
 Summary......Page 527
 Problems......Page 528
Chapter 14 : Introduction to Frequency Selective Circuits......Page 543
 Practical Perspective: Pushbutton Telephone Circuits......Page 544
 14.1 Some Preliminaries......Page 545
  The Series RL Circuit—Qualitative Analysis......Page 547
  Defining the Cutoff Frequency......Page 548
  The Series RL Circuit—Quantitative Analysis......Page 549
  A Series RC Circuit......Page 551
  Relating the Frequency Domain to the Time Domain......Page 552
  The Series RC Circuit—Qualitative Analysis......Page 553
  The Series RC Circuit—Quantitative Analysis......Page 554
  Center Frequency, Bandwidth, and Quality Factor......Page 557
  The Series RLC Circuit—Qualitative Analysis......Page 558
  The Series RLC Circuit—Quantitative Analysis......Page 559
 14.5 Bandreject Filters......Page 566
  The Series RLC Circuit—Quantitative Analysis......Page 567
 Summary......Page 571
 Problems......Page 572
Chapter 15 : Active Filter Circuits......Page 579
 Practical Perspective: Bass Volume Control......Page 580
  A Note About Frequency Response Plots......Page 581
 15.2 Scaling......Page 585
  The Use of Scaling in the Design of Op Amp Filters......Page 586
 15.3 Op Amp Bandpass and Bandreject Filters......Page 587
 15.4 Higher Order Op Amp Filters......Page 594
  Cascading Identical Filters......Page 595
  Butterworth Filters......Page 599
  Butterworth Filter Circuits......Page 600
  The Order of a Butterworth Filter......Page 603
  Butterworth High-Pass, Bandpass, and Bandreject Filters......Page 606
 15.5 Narrowband Bandpass and Bandreject Filters......Page 607
 Practical Perspective: Bass Volume Control......Page 612
 Summary......Page 615
 Problems......Page 616
Chapter 16 : Fourier Series......Page 625
 Practical Perspective: Active High-Q Filters......Page 626
 16.1 Fourier Series Analysis: An Overview......Page 628
 16.2 The Fourier Coefficients......Page 629
  Even-Function Symmetry......Page 632
  Odd-Function Symmetry......Page 633
  Half-Wave Symmetry......Page 634
  Quarter-Wave Symmetry......Page 635
 16.4 An Alternative Trigonometric Form of the Fourier Series......Page 638
 16.5 An Application......Page 640
  An Application of the Direct Approach to the Steady-State Response......Page 642
 16.6 Average-Power Calculations with Periodic Functions......Page 644
 16.7 The rms Value of a Periodic Function......Page 647
 16.8 The Exponential Form of the Fourier Series......Page 648
  An Illustration of Amplitude and Phase Spectra......Page 651
 Practical Perspective: Active High-Q Filters......Page 653
 Summary......Page 655
 Problems......Page 656
Chapter 17 : The Fourier Transform......Page 665
 Practical Perspective: Filtering Digital Signals......Page 666
 17.1 The Derivation of the Fourier Transform......Page 667
 17.2 The Convergence of the Fourier Integral......Page 669
 17.3 Using Laplace Transforms to Find Fourier Transforms......Page 671
  The Fourier Transform of a Signum Function......Page 674
  The Fourier Transform of a Cosine Function......Page 675
 17.5 Some Mathematical Properties......Page 676
  Multiplication by a Constant......Page 678
  Integration......Page 679
  Convolution in the Time Domain......Page 680
  Convolution in the Frequency Domain......Page 681
 17.7 Circuit Applications......Page 682
 17.8 Parseval’s Theorem......Page 685
  The Interpretation of Parseval’s Theorem......Page 686
  The Energy Contained in a Rectangular Voltage Pulse......Page 689
 Practical Perspective: Filtering Digital Signals......Page 692
 Problems......Page 693
Chapter 18 : Two-Port Circuits......Page 699
 Practical Perspective: Characterizing an Unknown Circuit......Page 700
 18.1 The Terminal Equations......Page 701
  Relationships Among the Two-Port Parameters......Page 705
  Reciprocal Two-Port Circuits......Page 708
 18.2 The Two-Port Parameters......Page 702
  The Six Characteristics in Terms of the z Parameters......Page 710
 18.4 Interconnected Two-Port Circuits......Page 715
 Practical Perspective: Characterizing an Unknown Circuit......Page 718
 Problems......Page 719
 A.1 Preliminary Steps......Page 726
 A.4 The Numerator Determinant......Page 727
 A.5 The Evaluation of a Determinant......Page 728
 A.6 Matrices......Page 730
 A.7 Matrix Algebra......Page 731
 A.8 Identity, Adjoint, and Inverse Matrices......Page 735
 A.9 Partitioned Matrices......Page 738
 A.10 Applications......Page 741
 B.1 Notation......Page 746
 B.2 The Graphical Representation of a Complex Number......Page 747
  Addition (Subtraction)......Page 748
 B.4 Useful Identities......Page 749
 B.6 The Roots of a Complex Number......Page 750
  The T-Equivalent Circuit......Page 752
  The π-Equivalent Circuit......Page 753
 C.2 The Need for Ideal Transformers in the Equivalent Circuits......Page 756
Appendix D : The Decibel......Page 760
 E.1 Real, First-Order Poles and Zeros......Page 762
 E.2 Straight-Line Amplitude Plots......Page 763
 E.3 More Accurate Amplitude Plots......Page 767
 E.4 Straight-Line Phase Angle Plots......Page 768
 E.5 Bode Diagrams: Complex Poles and Zeros......Page 770
 E.6 Amplitude Plots......Page 772
 E.7 Correcting Straight-Line Amplitude Plots......Page 773
 E.8 Phase Angle Plots......Page 776
Appendix F : An Abbreviated Table of Trigonometric Identities......Page 780
Appendix G : An Abbreviated Table of Integrals......Page 782
Appendix H : Common Standard Component Values......Page 784
Answers to Selected Problems......Page 786
Index......Page 798