Circuit Systems with MATLAB® and PSpice

Won Y. Yang and Seung C. Lee

Chung-Ang University, South Korea

B I C E N T E N N I A L

9 I C E N T E N N I A L

John Wiley & Sons(Asia) Pte Ltd

Contents

Preface xiii

Limits of Liability and Disclaimer of Warranty of Software xv

1 Basic Concepts on Electric Circuits 1 1.1 Symbols and Units 1 1.2 Network Variables 1

1.2.1 Voltage and Current 1 1.2.2 Electric Power and Energy 3 1.2.3 Reference Polarity and Direction of Voltage/Current 3 1.2.4 Passive Sign Convention 4

1.3 Circuit Elements 5 1.3.1 Passive Elements 5 1.3.2 Active Elements 9 1.3.3 Operational Amplifier 10 1.3.4 Transistor 13

1.4 Kirchhoff's Laws 13 1.4.1 Nodes, Branches, and Meshes/Loops 14 1.4.2 Kirchhoff's Current Law (KCL) 15 1.4.3 Kirchhoff's Voltage Law (KVL) 16 1.4.4 The Number of KCL/KVL Equations 18

1.5 Equivalent Transformation of Sources 19 1.5.1 Combination of Several Sources 19 1.5.2 Voltage-Current Source Transformation 21 1.5.3 Examples of Source Transformation 23

1.6 Series and Parallel Connections 25 Problems 25

2 Resistor Circuits 35 2.1 Combination of Resistors 35

2.1.1 Series Combination of Resistors 35 2.1.2 Parallel Combination of Resistors 36

2.2 Voltage/Current Divider 37 2.2.1 Voltage Divider 37 2.2.2 Current Divider 38

2.3 A-Y(II-T) Transformation 38 2.3.1 A-Y(II-T) Conversion Formula 39 2.3.2 Y-A(T-n) Conversion Formula 39

2.4 Node Analysis 40 2.4.1 Circuits Having No Dependent Sources 42

viii Contents

2.4.2 Circuits Having Dependent Sources 45 2.5 Mesh (Loop) Analysis 48

2.5.1 Circuits Having No Dependent Sources 49 2.5.2 Circuits Having Dependent Sources 53

2.6 Comparison of Node Analysis and Mesh Analysis 56 2.7 Thevenin/Norton Equivalent Circuits 63 2.8 Superposition Principle and Linearity 71 2.9 OP Amp Circuits with Resistors 72

2.9.1 Inverting OP Amp Circuit 72 2.9.2 Noninverting OP Amp Circuit 74 2.9.3 Voltage Follower 76 2.9.4 More Exact Analysis of OP Amp Circuits 77 2.9.5 OP Amp Circuits with Positive Feedback 78

2.10 Transistor Circuits 81 2.11 Loading Effect and Input/Output Resistance 81 2.12 Load Line Analysis of Nonlinear Resistor Circuits 82 2.13 More Examples of Resistor Circuits 86 Problems 95

First-Order Circuits 111 3.1 Characteristics of Inductors and Capacitors 111

3.1.1 Inductor 111 3.1.2 Capacitor 113

3.2 Series-Parallel Combination of Inductors/Capacitors 115 3.2.1 Series-Parallel Combination of Inductors 115 3.2.2 Series-Parallel Combination of Capacitors 116

3.3 Circuit Analysis Using the Laplace Transform 117 3.3.1 The Laplace Transform for a First-Order Differential Equation 118 3.3.2 Transformed Equivalent Circuits for R, L, and C 119

3.4 Analysis of First-Order Circuits 120 3.4.1 DC-Excited RL Circuits 120 3.4.2 DC-Excited RC Circuits 123 3.4.3 Time-Constant and Natural Responses of First-Order Circuits 125 3.4.4 Sequential Switching 133 3.4.5 AC-Excited First-Order Circuits 136

3.5 Analysis of First-Order OP Amp Circuits 138 3.5.1 First-Order OP Amp Circuits with Negative Feedback 138 3.5.2 First-Order OP Amp Circuits with Positive Feedback 140

3.6 LRL Circuits and CRC Circuits 144 3.6.1 An LRL Circuit 144 3.6.2 A CRC Circuit 146 3.6.3 Conservation of Flux Linkage and Charge 148 3.6.4 A Measure Against Violation of the Continuity Rule on

the Inductor Current 148 3.7 Simulation Using PSpice and MATLAB 149

3.7.1 An RC Circuit with Sequential Switching 149 3.7.2 An AC-Excited RL Circuit 151

3.8 Application and Design of First-Order Circuits 152 Problems 159

Contents ix

4 Second-Order Circuits 177 4.1 The Laplace Transform For Second-Order Differential Equations 177

4.1.1 Overdamped Case with Two Distinct Real Charactenstic Roots 178 4.1.2 Critically Damped Case with Double Real Charactenstic Roots 179 4.1.3 Underdamped Case with Two Distinct Complex

Characteristic Roots 179 4.1.4 Stability of a System and Location of its Characteristic Roots 180

4.2 Analysis of Second-Order Circuits 181 4.2.1 A Series RLC Circuit 181 4.2.2 A Parallel RLC Circuit 192 4.2.3 Two-Mesh/Node Circuit 198 4.2.4 Circuits Having Dependent Sources 200 4.2.5 Thevenin Equivalent Circuit 202

4.3 Second-Order OPAmp Circuits 203 4.4 Analogy and Duality 205

4.4.1 Analogy 205 4.4.2 Duality 206

4.5 Transfer Function, Impulse Response, and Convolution 207 4.5.1 Linear Systems 208 4.5.2 Time-Invariant Systems 208 4.5.3 The Pulse Response of a Linear Time-Invariant System 208 4.5.4 The Input-Output Relationship of a Linear

Time-Invariant System 209 4.6 The Steady-State Response to a Sinusoidal Input 211 4.7 An Example of MATLAB Analysis and PSpice Simulation 213 Problems 214

5 Magnetically Coupled Circuits 223 5.1 Self-Inductance 223 5.2 Mutual Inductance 225 5.3 Relative Polarity of Induced Voltages and Dot Convention 226

5.3.1 Dot Convention and Sign of Mutual Inductance Terms 226 5.3.2 Measurement of the Relative Winding Direction 226 5.3.3 Measurement of Mutual Inductance 227 5.3.4 Energy in Magnetically Coupled Coils 228

5.4 Equivalent Models of Magnetically Coupled Coils 228 5.4.1 T-Equivalent Circuit 229 5.4.2 II-Equivalent Circuit 234

5.5 Ideal Transformer 237 5.6 Linear Transformer 240 5.7 Autotransformers 241 Problems 243

6 AC Circuits 255 6.1 Sinusoidal Sources 255 6.2 Phasor and AC Analysis 256 6.3 AC Impedance of Passive Elements 261

6.3.1 Resistor 261 6.3.2 Inductor 261 6.3.3 Capacitor 262

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6.4 AC Circuit Examples 263 6.5 Instantaneous, Active, Reactive, and Complex Power 275 6.6 Power Factor 278 6.7 Maximum Power Transfer - Impedance Matching 283 6.8 Load Flow Calculation 285 6.9 Design and Simulation for Maximum Power Transfer 286 Problems 289

7 Three-Phase AC Circuits 299 7.1 Balanced Three-Phase Voltages 299 7.2 Power of Balanced Three-Phase Loads 302 7.3 Measurement of Three-Phase Power 303 7.4 Three-Phase Power System 304 7.5 Electric Shock and Grounding 310 Problems 313

8 Frequency Selective Circuit - Filter 319 8.1 Lowpass Filter (LPF) 319

8.1.1 Series LR Circuit 319 8.1.2 Series RC Circuit 320

8.2 Highpass Filter (HPF) 321 8.2.1 Series CR Circuit 321 8.2.2 Series RL Circuit 321

8.3 Bandpass Filter (BPF) 322 8.3.1 Series RLC Circuit and Series Resonance 322 8.3.2 Parallel RLC Circuit and Parallel Resonance 326

8.4 Bandstop Filter (BSF) 329 8.4.1 Series RLC Circuit 329 8.4.2 Parallel RLC Circuit 332

8.5 Active Filter 333 8.5.1 First-Order Active Filter 333 8.5.2 Second-Order Active LPF/HPF 334 8.5.3 Second-Order Active BPF 336 8.5.4 Second-Order Active BSF 337

8.6 Analog Filter Design 341 Problems 354

9 Circuits Analysis Using Fourier Series 373 9.1 Fourier Series 373 9.2 Computation of Fourier Coefficients Using Symmetry 375 9.3 Circuit Analysis Using Fourier Series 379 9.4 Fourier Series and Laplace Transform 387 9.5 RMS Value and Power of a Nonsinusoidal Periodic Signal 393

9.5.1 RMS Value and Distortion Factor of a Nonsinusoidal Periodic Signal 393

9.5.2 Power and Power Factor of a Nonsinusoidal Periodic Signal 394

Problems 395

Contents xi

10 Two-Port Networks 401 10.1 Definitions of Two-Port Parameters 401 10.2 Relationships Among Two-Port Parameters 406

10.2.1 The z-Parameters and a-Parameters 406 10.2.2 The a-Parameters and /i-Parameters 407 10.2.3 The z-Parameters and /j-Parameters 408

10.3 Reciprocity of a Two-Port Network 411 10.4 Interconnection of Two-Port Networks 413

10.4.1 Series Connection and z-Parameters 413 10.4.2 Parallel (Shunt) Connection and y-Parameters 414 10.4.3 Series-Parallel (Shunt) Connection and ^-Parameters 415 10.4.4 Parallel (Shunt)-Series Connection and g-Parameters 415 10.4.5 Cascade Connection and a-Parameters 416 10.4.6 Curse of the Port Condition (Current Requirement) 416

10.5 Two-Port Networks Having Source/Load 420 10.5.1 Input Impedance 422 10.5.2 Voltage Gain 423 10.5.3 Current Gain 423 10.5.4 (Thevenin) Equivalent Impedance Seen from the Output 424 10.5.5 (Thevenin) Equivalent Source Seen from the Output 424 10.5.6 The Parameters of an Overall Two-Port Network 425

10.6 Feedback Amplifiers as Two-Port Networks 430 10.6.1 Series-Parallel (Shunt) Feedback Amplifier 431 10.6.2 Series-Series Feedback Amplifier 431 10.6.3 Parallel-Parallel Feedback Amplifier 432 10.6.4 Parallel (Shunt)-Series Feedback Amplifier 433 10.6.5 General Feedback Structure 434

10.7 Circuit Models with Given Parameters 438 10.7.1 Circuit Model with Given z-Parameters 438 10.7.2 Circuit Model with Given y-Parameters 438 10.7.3 Circuit Model with Given h and g-Parameters 438 10.7.4 Circuit Model with Given a and ^-Parameters 438

Problems 440

Appendices 451 Appendix A: Laplace Transform 451 Appendix B: Matrix Operations with MATLAB 461 Appendix C: Complex Number Operations with MATLAB 466 Appendix D: Nonlinear/Differential Equations with MATLAB 468 Appendix E: Symbolic Computations with MATLAB 471 Appendix F: Useful Formulas (Reference [K-2]) 474 Appendix G: The Standard Values of Resistors, Capacitors, and Inductors 476 Appendix H: OrCAD/PSpice (References [K-l] and [R-2]) 481 Appendix I: MATLAB Introduction (Reference [K-2]) 511 Appendix J: Solutions to Problems 514

References 525

Index 527