## Table of Contents

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