Electric Circuits – James W. Nilsson – 9th Edition

List of Examples xiii

Preface xvii

Chapter 1 Circuit Variables 2

Practical Perspective: Balancing Power 3

1.1 Electrical Engineering: An Overview 4

1.2 The International System of Units 8

1.3 Circuit Analysis: An Overview 10

1.4 Voltage and Current 11

1.5 The Ideal Basic Circuit Element 12

1.6 Power and Energy 14

Practical Perspective: Balancing Power 17

Summary 18

Problems 19

Chapter 2 Circuit Elements 24

Practical Perspective: Electrical Safety 25

2.1 Voltage and Current Sources 26

2.2 Electrical Resistance (Ohm’s Law) 30

2.3 Construction of a Circuit Model 34

2.4 Kirchhoff’s Laws 37

2.5 Analysis of a Circuit Containing Dependent Sources 42

Practical Perspective: Electrical Safety 46

Summary 47

Problems 48

Chapter 3 Simple Resistive Circuits 56

Practical Perspective: A Rear Window Defroster 57

3.1 Resistors in Series 58

3.2 Resistors in Parallel 59

3.3 The Voltage-Divider and Current-DividerCircuits 61

3.4 Voltage Division and Current Division 64

3.5 Measuring Voltage and Current 66

3.6 Measuring Resistance—The Wheatstone Bridge 69

3.7 Delta-to-Wye (Pi-to-Tee) Equivalent Circuits 71

Practical Perspective: A Rear Window Defroster 73

Summary 76

Problems 77



Chapter 4 Techniques of Circuit Analysis 88

Practical Perspective: Circuits with Realistic Resistors 89

4.1 Terminology 90

4.2 Introduction to the Node-Voltage Method 93

4.3 The Node-Voltage Method and Dependent Sources 95

4.4 The Node-Voltage Method: Some Special Cases 96

4.5 Introduction to the Mesh-Current Method 99

4.6 The Mesh-Current Method and Dependent Sources 102

4.7 The Mesh-Current Method: Some Special Cases 103

4.8 The Node-Voltage Method Versus the Mesh-Current Method 106

4.9 Source Transformations 109

4.10 Thévenin and Norton Equivalents 113

4.11 More on Deriving a Thévenin Equivalent 117

4.12 Maximum Power Transfer 120

4.13 Superposition 122

Practical Perspective: Circuits with Realistic Resistors 125

Summary 129

Problems 130

Chapter 5 The Operational Amplifier 144

Practical Perspective: Strain Gages 145

5.1 Operational Amplifier Terminals 146

5.2 Terminal Voltages and Currents 146

5.3 The Inverting-Amplifier Circuit 150

5.4 The Summing-Amplifier Circuit 152

5.5 The Noninverting-Amplifier Circuit 153

5.6 The Difference-Amplifier Circuit 155

5.7 A More Realistic Model for the Operational Amplifier 159

Practical Perspective: Strain Gages 162

Summary 164

Problems 165



Chapter 6 Inductance, Capacitance, and Mutual Inductance 174

Practical Perspective: Proximity Switches 175

6.1 The Inductor 176

6.2 The Capacitor 182

6.3 Series-Parallel Combinations of Inductance and Capacitance 187

6.4 Mutual Inductance 189

6.5 A Closer Look at Mutual Inductance 193

Practical Perspective: Proximity Switches 200

Summary 203

Problems 204

Chapter 7 Response of First-Order RL and RC Circuits 212

Practical Perspective: A Flashing Light Circuit 213

7.1 The Natural Response of an RL Circuit 214

7.2 The Natural Response of an RC Circuit 220

7.3 The Step Response of RL and RC Circuits 224

7.4 A General Solution for Step and Natural Responses 231

7.5 Sequential Switching 236

7.6 Unbounded Response 240

7.7 The Integrating Amplifier 241

Practical Perspective: A Flashing Light Circuit 245

Summary 246

Problems 247

Chapter 8 Natural and Step Responses of RLC Circuits 264

Practical Perspective: An Ignition Circuit 265

8.1 Introduction to the Natural Response of a Parallel RLC Circuit 266

8.2 The Forms of the Natural Response of a Parallel RLC Circuit 270

8.3 The Step Response of a Parallel RLC Circuit 280

8.4 The Natural and Step Response of a Series RLC Circuit 285

8.5 A Circuit with Two Integrating Amplifiers 289

Practical Perspective: An Ignition Circuit 294

Summary 297

Problems 298

Chapter 9 Sinusoidal Steady-State Analysis 306

Practical Perspective: A Household Distribution Circuit 307

9.1 The Sinusoidal Source 308

9.2 The Sinusoidal Response 311

9.3 The Phasor 312

9.4 The Passive Circuit Elements in the Frequency Domain 317

9.5 Kirchhoff’s Laws in the Frequency Domain 321

9.6 Series, Parallel, and Delta-to-Wye Simplifications 322

9.7 Source Transformations and Thévenin-Norton Equivalent Circuits 329

9.8 The Node-Voltage Method 332

9.9 The Mesh-Current Method 333

9.10 The Transformer 334

9.11 The Ideal Transformer 338

9.12 Phasor Diagrams 344

Practical Perspective: A Household Distribution Circuit 346

Summary 347

Problems 348

Chapter 10 Sinusoidal Steady-State Power Calculations 360

Practical Perspective: Heating Appliances 361

10.1 Instantaneous Power 362

10.2 Average and Reactive Power 363

10.3 The rms Value and Power Calculations 368

10.4 Complex Power 370

10.5 Power Calculations 371

10.6 Maximum Power Transfer 378

Practical Perspective: Heating Appliances 384

Summary 386

Problems 387

Chapter 11 Balanced Three-Phase Circuits 398

Practical Perspective: Transmission and Distribution of Electric Power 399

11.1 Balanced Three-Phase Voltages 400

11.2 Three-Phase Voltage Sources 401

11.3 Analysis of the Wye-Wye Circuit 402

11.4 Analysis of the Wye-Delta Circuit 407

11.5 Power Calculations in Balanced Three-Phase Circuits 410

11.6 Measuring Average Power in Three-Phase Circuits 415

Practical Perspective: Transmission and Distribution of Electric Power 418

Summary 419

Problems 420



Chapter 12 Introduction to the Laplace Transform 428

Practical Perspective: Transient Effects 429

12.1 Definition of the Laplace Transform 430

12.2 The Step Function 431

12.3 The Impulse Function 433

12.4 Functional Transforms 436

12.5 Operational Transforms 437

12.6 Applying the Laplace Transform 442

12.7 Inverse Transforms 444

12.8 Poles and Zeros of F(s) 454

12.9 Initial- and Final-Value Theorems 455

Practical Perspective: Transient Effects 458

Summary 459

Problems 460



Chapter 13 The Laplace Transform in Circuit Analysis 466

Practical Perspective: Surge Suppressors 467

13.1 Circuit Elements in the s Domain 468

13.2 Circuit Analysis in the s Domain 470

13.3 Applications 472

13.4 The Transfer Function 484

13.5 The Transfer Function in Partial Fraction Expansions 486

13.6 The Transfer Function and the Convolution Integral 489

13.7 The Transfer Function and the Steady-State Sinusoidal Response 495

13.8 The Impulse Function in Circuit Analysis 498

Practical Perspective: Surge Suppressors 505

Summary 506

Problems 507

Chapter 14 Introduction to Frequency Selective Circuits 522

Practical Perspective: Pushbutton Telephone Circuits 523

14.1 Some Preliminaries 524

14.2 Low-Pass Filters 526

14.3 High-Pass Filters 532

14.4 Bandpass Filters 536

14.5 Bandreject Filters 545

Practical Perspective: Pushbutton Telephone Circuits 550

Summary 550

Problems 551



Chapter 15 Active Filter Circuits 558

Practical Perspective: Bass Volume Control 559

15.1 First-Order Low-Pass and High-Pass Filters 560

15.2 Scaling 564

15.3 Op Amp Bandpass and Bandreject Filters 566

15.4 Higher Order Op Amp Filters 573

15.5 Narrowband Bandpass and Bandreject Filters 586

Practical Perspective: Bass Volume Control 591

Summary 594

Problems 595

Chapter 16 Fourier Series 604

Practical Perspective: Active High-Q Filters 605

16.1 Fourier Series Analysis: An Overview 607

16.2 The Fourier Coefficients 608

16.3 The Effect of Symmetry on the Fourier Coefficients 611

16.4 An Alternative Trigonometric Form of the Fourier Series 617

16.5 An Application 619

16.6 Average-Power Calculations with Periodic Functions 623

16.7 The rms Value of a Periodic Function 626

16.8 The Exponential Form of the Fourier Series 627

16.9 Amplitude and Phase Spectra 630

Practical Perspective: Active High-Q Filters 632

Summary 634

Problems 635

Chapter 17 The Fourier Transform 644

Practical Perspective: Filtering Digital Signals 645

17.1 The Derivation of the Fourier Transform 646

17.2 The Convergence of the Fourier Integral 648

17.3 Using Laplace Transforms to Find Fourier Transforms 650

17.4 Fourier Transforms in the Limit 653

17.5 Some Mathematical Properties 655

17.6 Operational Transforms 657

17.7 Circuit Applications 661

17.8 Parseval’s Theorem 664

Practical Perspective: Filtering Digital Signals 671

Summary 672

Problems 672



Chapter 18 Two-Port Circuits 678

Practical Perspective: Characterizing an Unknown Circuit 679

18.1 The Terminal Equations 680

18.2 The Two-Port Parameters 681

18.3 Analysis of the Terminated Two-Port Circuit 689

18.4 Interconnected Two-Port Circuits 694

Practical Perspective: Characterizing an Unknown Circuit 697

Summary 698

Problems 698

Appendix A The Solution of Linear Simultaneous Equations 705

A.1 Preliminary Steps 705

A.2 Cramer’s Method 706

A.3 The Characteristic Determinant 706

A.4 The Numerator Determinant 706

A.5 The Evaluation of a Determinant 707

A.6 Matrices 709

A.7 Matrix Algebra 710

A.8 Identity, Adjoint, and Inverse Matrices 714

A.9 Partitioned Matrices 717

A.10 Applications 720

Appendix B Complex Numbers 725

B.1 Notation 725

B.2 The Graphical Representation of a Complex Number 726

B.3 Arithmetic Operations 727

B.4 Useful Identities 728

B.5 The Integer Power of a Complex Number 729

B.6 The Roots of a Complex Number 729

Appendix C More on Magnetically Coupled Coils and Ideal Transformers 731

C.1 Equivalent Circuits for Magnetically Coupled Coils 731

C.2 The Need for Ideal Transformers in the Equivalent Circuits 735

Appendix D The Decibel 739

Appendix E Bode Diagrams 741

E.1 Real, First-Order Poles and Zeros 741

E.2 Straight-Line Amplitude Plots 742

E.3 More Accurate Amplitude Plots 746

E.4 Straight-Line Phase Angle Plots 747

E.5 Bode Diagrams: Complex Poles and Zeros 749

E.6 Amplitude Plots 751

E.7 Correcting Straight-Line Amplitude Plots 752

E.8 Phase Angle Plots 755

Appendix F An Abbreviated Table of Trigonometric Identities 759

Appendix G An Abbreviated Table of Integrals 761

Appendix H Common Standard Component Values 763

Answers to Selected Problems 765

Index 781