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List of Examples11

Preface15

Chapter 1 Circuit Variables22

1.1 Electrical Engineering:An Overview23

1.2 The International System of Units28

1.3 Circuit Analysis:An Overview30

1.4 Voltage and Current31

1.5 The Ideal Basic Circuit Element32

1.6 Power and Energy34

Summary36

Problems37

Chapter 2 Circuit Elements42

Practical Perspective:Electrical Safety43

2.1 Voltage and Current Sources44

2.2 Electrical Resistance(Ohm's Law)48

2.3 Construction of a Circuit Model52

2.4 Kirchhoff's Laws56

2.5 Analysis of a Circuit Containing Dependent Sources62

Practical Perspective:Electrical Safety66

Summary67

Problems68

Chapter 3 Simple Resistive Circuits76

Practical Perspective:A Rear Window Defroster77

3.1 Resistors in Series78

3.2 Resistors in Parallel79

3.3 The Voltage-Divider and Current-Divider Circuits82

3.4 Voltage Division and Current Division85

3.5 Measuring Voltage and Current88

3.6 Measuring Resistance—The Wheatstone Bridge91

3.7 Delta-to-Wye(Pi-to-Tee)Equivalent Circuits93

Practical Perspective:A Rear Window Defroster96

Summary99

Problems100

Chapter 4 Techniques of Circuit Analysis112

Practical Perspective:Circuits with Realistic Resistors113

4.1 Terminology114

4.2 Introduction to the Node-Voltage Method117

4.3 The Node-Voltage Method and Dependent Sources120

4.4 The Node-Voltage Method:Some Special Cases121

4.5 Introduction to the Mesh-Current Method125

4.6 The Mesh-Current Method and Dependent Sources127

4.7 The Mesh-Current Method:Some Special Cases129

4.8 The Node-Voltage Method Versus the Mesh-Current Method132

4.9 Source Transformations136

4.10 Thévenin and Norton Equivalents139

4.11 More on Deriving a Thévenin Equivalent143

4.12 Maximum Power Transfer146

4.13 Superposition149

Practical Perspective:Circuits with Realistic Resistors153

Summary157

Problems158

Chapter 5 The Operational Amplifier174

Practical Perspective:Strain Gages175

5.1 Operational Amplifier Terminals176

5.2 Terminal Voltages and Currents176

5.3 The Inverting-Amplifier Circuit181

5.4 The Summing-Amplifier Circuit183

5.5 The Noninverting-Amplifier Circuit184

5.6 The Difference-Amplifier Circuit185

5.7 A More Realistic Model for the Operational Amplifier190

Practical Perspective:Strain Gages193

Summary195

Problems196

Chapter 6 Inductance,Capacitance,and Mutual Inductance206

Practical Perspective:Proximity Switches207

6.1 The Inductor208

6.2 The Capacitor215

6.3 Series-Parallel Combinations of Inductance and Capacitance220

6.4 Mutual Inductance223

6.5 A Closer Look at Mutual Inductance227

Practical Perspective:Proximity Switches234

Summary237

Problems238

Chapter 7 Response of First-Order RL and RC Circuits248

Practical Perspective:A Flashing Light Circuit249

7.1 The Natural Response of an RL Circuit250

7.2 The Natural Response of an RC Circuit256

7.3 The Step Response of RL and RC Circuits260

7.4 A General Solution for Step and Natural Responses268

7.5 Sequential Switching274

7.6 Unbounded Response278

7.7 The Integrating Amplifier280

Practical Perspective：A Flashing Light Circuit283

Summary285

Problems285

Chapter 8 Natural and Step Responses of RLC Circuits304

Practical Perspective:An Ignition Circuit305

8.1 Introduction to the Natural Response of a Parallel RLC Circuit306

8.2 The Forms of the Natural Response of a Parallel RLC Circuit311

8.3 The Step Response of a Parallel RLC Circuit321

8.4 The Natural and Step Response of a Series RLC Circuit328

8.5 A Circuit with Two Integrating Amplifiers332

Practical Perspective:An Ignition Circuit337

Summary340

Problems341

Chapter 9 Sinusoidal Steady-State Analysis350

Practical Perspective:A Household Distribution Circuit351

9.1 The Sinusoidal Source352

9.2 The Sinusoidal Response355

9.3 The Phasor357

9.4 The Passive Circuit Elements in the Frequency Domain362

9.5 Kirchhoff's Laws in the Frequency Domain366

9.6 Series,Parallel,and Delta-to-Wye Simplifications368

9.7 Source Transformations and Thévenin-Norton Equivalent Circuits375

9.8 The Node-Voltage Method379

9.9 The Mesh-Current Method380

9.10 The Transformer381

9.11 The Ideal Transformer385

9.12 Phasor Diagrams392

Practical Perspective:A Household Distribution Circuit395

Summary395

Problems396

Chapter 10 Sinusoidal Steady-State Power Calculations410

Practical Perspective:Heating Appliances411

10.1 Instantaneous Power412

10.2 Average and Reactive Power414

10.3 The rms Value and Power Calculations419

10.4 Complex Power421

10.5 Power Calculations423

10.6 Maximum Power Transfer430

Practical Perspective:Heating Appliances437

Summary439

Problems440

Chapter 11 Balanced Three-Phase Circuits452

Practical Perspective:Transmission and Distribution of Electric Power453

11.1 Balanced Three-Phase Voltages454

11.2 Three-Phase Voltage Sources455

11.3 Analysis of the Wye-Wye Circuit456

11.4 Analysis of the Wye-Delta Circuit462

11.5 Power Calculations in Balanced Three-Phase Circuits465

11.6 Measuring Average Power in Three-Phase Circuits472

Practical Perspective:Transmission and Distribution of Electric Power475

Summary476

Problems477

Chapter 12 Introduction to the Laplace Transform486

12.1 Definition of the Laplace Transform487

12.2 The Step Function488

12.3 The Impulse Function490

12.4 Functional Transforms494

12.5 Operational Transforms495

12.6 Applying the Laplace Transform501

12.7 Inverse Transforms502

12.8 Poles and Zeros of F(s)514

12.9 Initial-and Final-Value Theorems515

Summary518

Problems519

Chapter 13 The Laplace Transform in Circuit Analysis526

Practical Perspective:Surge Suppressors527

13.1 Circuit Elements in the s Domain528

13.2 Circuit Analysis in the s Domain531

13.3 Applications532

13.4 The Transfer Function546

13.5 The Transfer Function in Partial Fraction Expansions548

13.6 The Transfer Function and the Convolution Integral551

13.7 The Transfer Function and the Steady-State Sinusoidal Response557

13.8 The Impulse Function Circuit Analysis560

Practical Perspective:Surge Suppressors568

Summary569

Problems570

Chapter 14 Introduction to Frequency Selective Circuits586

Practical Perspective:Pushbutton Telephone Circuits587

14.1 Some Preliminaries588

14.2 Low-Pass Filters590

14.3 High-Pass Filters597

14.4 Bandpass Filters602

14.5 Bandreject Filters613

Practical Perspective:Pushbutton Telephone Circuits618

Summary619

Problems619

Chapter 15 Active Filter Circuits626

Practical Perspective:Bass Volume Control627

15.1 First-Order Low-Pass and High-Pass Filters628

15.2 Scaling632

15.3 Op Amp Bandpass and Bandreject Filters635

15.4 Higher Order Op Amp Filters642

15.5 Narrowband Bandpass and Bandreject Filters656

Practical Perspective:Bass Volume Control662

Summary664

Problems666

Chapter 16 Fourier Series676

16.1 Fourier Series Analysis:An Overview678

16.2 The Fourier Coefficients679

16.3 The Effect of Symmetry on the Fourier Coefficients682

16.4 An Alternative Trigonometric Form of the Fourier Series688

16.5 An Application690

16.6 Average-Power Calculations with Periodic Functions695

16.7 The rms Value of a Periodic Function698

16.8 The Exponential Form of the Fourier Series699

16.9 Amplitude and Phase Spectra702

Summary705

Problems706

Chapter 17 The Fourier Transform718

17.1 The Derivation of the Fourier Transform719

17.2 The Convergence of the Fourier Integral721

17.3 Using Laplace Transforms to Find Fourier Transforms723

17.4 Fourier Transforms in the Limit726

17.5 Some Mathematical Properties728

17.6 Operational Transforms730

17.7 Circuit Applications734

17.8 Parseval's Theorem737

Summary744

Problems745

Chapter 18 Two-Port Circuits750

18.1 The Terminal Equations751

18.2 The Two-Port Parameters752

18.3 Analysis of the Terminated Two-Port Circuit761

18.4 Interconnected Two-Port Circuits767

Summary771

Problems772

Appendix A The Solution of Linear Simultaneous Equations779

A.1 Preliminary Steps779

A.2 Cramer's Method780

A.3 The Characteristic Determinant780

A.4 The Numerator Determinant780

A.5 The Evaluation of a Determinant781

A.6 Matrices784

A.7 Matrix Algebra785

A.8 Identity,Adjoint,and Inverse Matrices790

A.9 Partitioned Matrices792

A.10 Applications796

Appendix B Complex Numbers801

B.1 Notation801

B.2 The Graphical Representation of a Complex Number802

B.3 Arithmetic Operations803

B.4 Useful Identities805

B.5 The Integer Power of a Complex Number805

B.6 The Roots of a Complex Number806

Appendix C More on Magnetically Coupled Coils and Ideal Transformers807

C.1 Equivalent Circuits for Magnetically Coupled Coils807

C.2 The Need for Ideal Transformers in the Equivalent Circuits812

Appendix D The Decibel817

Appendix E Bode Diagrams819

E.1 Real,First-Order Poles and Zeros819

E.2 Straight-Line Amplitude Plots820

E.3 More Accurate Amplitude Plots824

E.4 Straight-Line Phase Angle Plots825

E.5 Bode Diagrams:Complex Poles and Zeros827

E.6 Amplitude Plots829

E.7 Correcting Straight-Line Amplitude Plots830

E.8 Phase Angle Plots833

Appendix F An Abbreviated Table of Trigonometric Identities837

Appendix G An Abbreviated Table of Integrals839

Appendix H Answers to Selected Problems841

Index859

Chapter2

2.1 Testing Interconnections of Ideal Sources46

2.2 Testing Interconnections of Ideal Independent and Dependent Sources47

2.3 Calculating Voltage,Current,and Power for a Simple Resistive Circuit51

2.4 Constructing a Circuit Model of a Flashlight53

2.5 Constructing a Circuit Model Based on Terminal Measurements55

2.6 Using Kirchhoff's Current Law59

2.7 Using Kirchhoff's Voltage Law59

2.8 Applying Ohm's Law and Kirchhoff's Laws to Find an Unknown Current60

2.9 Constructing a Circuit Model Based on Terminal Measurements61

2.10 Applying Ohm's Law and Kirchhoff's Laws to Find an Unknown Voltage64

2.11 Applying Ohm's Law and Kirchhoff's Law in an Amplifier Circuit65

Chapter3

3.1 Applying Series-Parallel Simplification81

3.2 Analyzing the Voltage-Divider Circuit83

3.3 Analyzing a Current-Divider Circuit84

3.4 Using Voltage Division and Current Division to Solve a Circuit87

3.5 Using a d'Arsonval Ammeter89

3.6 Using a d'Arsonval Voltmeter90

3.7 Applying a Delta-to-Wye Transform95

Chapter4

4.1 Identifying Node,Branch,Mesh,and Loop in a Circuit115

4.2 Using the Node-Voltage Method119

4.3 Using the Node-Voltage Method with Dependent Sources120

4.4 Using the Mesh-Current Method126

4.5 Using the Mesh-Current Method with Dependent Sources128

4.6 Understanding the Node-Voltage Method Versus Mesh-Current Method133

4.7 Comparing the Node-Voltage and Mesh-Current Methods135

4.8 Using Source Transformations to Solve a Circuit137

4.9 Using Special Source Transformation Techniques138

4.10 Finding the Thévenin Equivalent of a Circuit with a Dependent Source142

4.11 Finding the Thévenin Equivalent Using a Test Source144

4.12 Calculating the Condition for Maximum Power Transfer148

4.13 Using Superposition to Solve a Circuit152

Chapter5

5.1 Analyzing an Op Amp Circuit180

Chapter6

6.1 Determining the Voltage,Given the Current,at the Terminals of an Inductor209

6.2 Determining the Current,Given the Voltage,at the Terminals of an Inductor211

6.3 Determining the Current,Voltage,Power,and Energy for an Inductor213

6.4 Determining Current,Voltage,Power,and Energy for a Capacitor217

6.5 Finding v,p,and w Induced by a Triangular Current Pulse for a Capacitor218

6.6 Finding Mesh-Current Equations for a Circuit with Magnetically Coupled Coils226

Chapter7

7.1 Determining the Natural Response of an RL Circuit254

7.2 Determining the Natural Response of an RL Circuit with Parallel Inductors255

7.3 Determining the Natural Response of an RC Circuit258

7.4 Determining the Natural Response of an RC Circuit with Series Capacitors259

7.5 Determining the Step Response of an RL Circuit264

7.6 Determining the Step Response of an RC Circuit267

7.7 Using the General Solution Method to Find an RC Circuit's Step Response270

7.8 Using the General Solution Method with Zero Initial Conditions271

7.9 Using the General Solution Method to Find an RL Circuit's Step Response272

7.10 Determining the Step Response of a Circuit with Magnetically Coupled Coils273

7.11 Analyzing an RL Circuit that has Sequential Switching275

7.12 Analyzing an RC Circuit that has Sequential Switching277

7.13 Finding the Unbounded Response in an RC Circuit279

7.14 Analyzing an Integrating Amplifier281

7.15 Analyzing an Integrating Amplifier that has Sequential Switching282

Chapter8

8.1 Finding the Roots of the Characteristic Equation of a Parallel RLC Circuit310

8.2 Finding the Overdamped Natural Response of a Parallel RLC Circuit313

8.3 Calculating Branch Currents in the Natural Response of a Parallel RLC Circuit314

8.4 Finding the Underdamped Natural Response of a Parallel RLC Circuit317

8.5 Finding the Critically Damped Natural Response of a Parallel RLC Circuit320

8.6 Finding the Overdamped Step Response of a Parallel RLC Circuit324

8.7 Finding the Underdamped Step Response of a Parallel RLC Circuit325

8.8 Finding the Critically Damped Step Response of a Parallel RLC Circuit325

8.9 Comparing the Three-Step Response Forms326

8.10 Finding Step Response of a Parallel RLC Circuit with Initial Stored Energy326

8.11 Finding the Underdamped Natural Response of a Series RLC Circuit330

8.12 Finding the Underdamped Step Response of a Series RLC Circuit331

8.13 Analyzing Two Cascaded Integrating Amplifiers333

8.14 Analyzing Two Cascaded Integrating Amplifiers with Feedback Resistors336

Chapter9

9.1 Finding the Characteristics of a Sinusoidal Current354

9.2 Finding the Characteristics of a Sinusoidal Voltage354

9.3 Translating a Sine Expression to a Cosine Expression354

9.4 Calculating the rms Value of a Triangular Waveform355

9.5 Adding Cosines Using Phasors361

9.6 Combining Impedances in Series369

9.7 Combining Impedances in Series and in Parallel371

9.8 Using a Delta-to-Wye Transform in the Frequency Domain373

9.9 Performing Source Transformations in the Frequency Domain376

9.10 Finding a Thévenin Equivalent in the Frequency Domain377

9.11 Using the Node-Voltage Method in the Frequency Domain379

9.12 Using the Mesh-Current Method in the Frequency Domain380

9.13 Analyzing a Linear Transformer in the Frequency Domain384

9.14 Analyzing an Ideal Transformer Circuit in the Frequency Domain390

9.15 Using Phasor Diagrams to Analyze a Circuit392

9.16 Using Phasor Diagrams to Analyze Capacitive Loading Effects393

Chapter10

10.1 Calculating Average and Reactive Power416

10.2 Making Power Calculations Involving Household Appliances418

10.3 Determining Average Power Delivered to a Resistor by a Sinusoidal Voltage420

10.4 Calculating Complex Power422

10.5 Calculating Average and Reactive Power426

10.6 Calculating Power in Parallel Loads427

10.7 Balancing Power Delivered with Power Absorbed in an ac Circuit428

10.8 Determining Maximum Power Transfer without Load Restrictions433

10.9 Determining Maximum Power Transfer with Load Impedance Restriction434

10.10 Finding Maximum Power Transfer with Impedance Angle Restrictions434

10.11 Finding Maximum Power Transfer in a Circuit with an Ideal Transformer435

Chapter11

11.1 Analyzing a Wye-Wye Circuit460

11.2 Analyzing a Wye-Delta Circuit464

11.3 Calculating Power in a Three-Phase Wye-Wye Circuit469

11.4 Calculating Power in a Three-Phase Wye-Delta Circuit470

11.5 Calculating Three-Phase Power with an Unspecified Load470

11.6 Computing Wattmeter Readings in Three-Phase Circuits474

Chapter12

12.1 Using Step Functions to Represent a Function of Finite Duration490

Chapter13

13.1 Deriving the Transfer Function of a Circuit547

13.2 Analyzing the Transfer Function of a Circuit549

13.3 Using the Convolution Integral to Find an Output Signal555

13.4 Using the Transfer Function to Find the Steady-State Sinusoidal Response559

Chapter14

14.1 Designing a Low-Pass Filter594

14.2 Designing a Series RC Low-Pass Filter595

14.3 Designing a Series RL High-Pass Filter599

14.4 Loading the Series RL High-Pass Filter600

14.5 Designing a Bandpass Filter607

14.6 Designing a Parallel RLC Bandpass Filter608

14.7 Determining Effect of a Nonideal Voltage Source on a RLC Bandpass Filter609

14.8 Designing a Series RLC Bandreject Filter616

Chapter15

15.1 Designing a Low-Pass Op Amp Filter629

15.2 Designing a High-Pass Op Amp Filter631

15.3 Scaling a Series RLC Circuit633

15.4 Scaling a Prototype Low-Pass Op Amp Filter634

15.5 Designing a Broadband Bandpass Op Amp Filter638

15.6 Designing a Broadband Bandreject Op Amp Filter641

15.7 Designing a Fourth-Order Low-Pass Op Amp Filter645

15.8 Calculating Butterworth Transfer Functions■8

15.9 Designing a Fourth-Order Low-Pass Butterworth Filter651

15.10 Determining the Order of a Butterworth Filter654

15.11 An Alternate Approach to Determining the Order of a Butterworth Filter654

15.12 Designing a High-Q Bandpass Filter658

15.13 Designing a High-Q Bandreject Filter661

Chapter16

16.1 Finding the Fourier Series of a Triangular Waveform with No Symmetry680

16.2 Finding the Fourier Series of an Odd Function with Symmetry687

16.3 Calculating Forms of the Trigonometric Fourier Series for Periodic Voltage689

16.4 Calculating Average Power for a Circuit with a Periodic Voltage Source697

16.5 Estimating the rms Value of a Periodic Function699

16.6 Finding the Exponential Form of the Fourier Series701

Chapter17

17.1 Using the Fourier Transform to Find the Transient Response735

17.2 Using the Fourier Transform to Find the Sinusoidal Steady-State Response736

17.3 Applying Parseval's Theorem739

17.4 Applying Parseval's Theorem to an Ideal Bandpass Filter740

17.5 Applying Parseval's Theorem to a Low-Pass Filter741

Chapter18

18.1 Finding the z Parameters of a Two-Port Circuit753

18.2 Finding the a Parameters from Measurements755

18.3 Finding h Parameters from Measurements and Table 18.1758

18.4 Analyzing a Terminated Two-Port Circuit766

18.5 Analyzing Cascaded Two-Port Circuits770