Circuit Analysis with PSpice A Simplified Approach

Electric circuits, and their electronic circuit extensions, are found in all electrical and electronic equipment; including: household equipment, lighting, heating, air conditioning, control systems in both homes and commercial buildings, computers, consumer electronics, and means of transportation, such as cars, buses, trains, ships, and airplanes. Electric circuit analysis is essential for designing all these systems.

Electric circuit analysis is a foundation for all hardware courses taken by students in electrical engineering and allied fields, such as electronics, computer hardware, communications and control systems, and electric power. This book is intended to help students master basic electric circuit analysis, as an essential component of their professional education. Furthermore, the objective of this book is to approach circuit analysis by developing a sound understanding of fundamentals and a problem-solving methodology that encourages critical thinking.

Contents

Page

List of PSpice Simulations x

Preface x

Convention for Voltage and Current Symbols x

Part I: Basic Concepts in Circuit Analysis

Chapter 1 Preliminaries to Circuit Analysis

Objective and Overview x

1.1 What are electric circuits and what are they used for? x

1.2 What laws govern the behavior of electric circuits? x

1.3 What is electric current? x

1.4 What is the direction of current? x

1.5 What is voltage? x

1.6 What is voltage polarity?

1.7 How are energy and power related to voltage and current? x

Positive and Negative Values of Circuit Variables

1.8 What are ideal circuit elements and how do they handle energy?

1.9 Why resistance, capacitance, and inductance?

1.10 What are the approximations implicit in basic electric circuits?

Learning Checklist: What should be learned from this chapter

Problem-Solving Tips

Exercises and Problems

Chapter 2 Fundamentals of Resistive Circuits

Objective and Overview x

2.1Nature of Resistance x

2.2Ideal Resistors x

2.3 Short Circuit and Open Circuit x

2.4Ideal, Independent Voltage Source x

2.5Ideal, Independent Current Source x

2.6 Ideal, Dependent Sources x

Ideal, Dependent Voltage Sources x

Ideal, Dependent Current Sources x

2.7Nomenclature and Analysis of Resistive Circuits x

2.8Kirchhoff’s Laws x

Kirchhoff’s Current Law x

Kirchhoff’s Voltage Law x

2.9 Series and Parallel Connections x

Series Connection x

Parallel Connection x

2.10 Problem-Solving Approach x

Learning Checklist: What should be learned from this chapter x

Problem-Solving Tips x

Exercises and Problems x

Chapter 3 Circuit Equivalence

Objective and Overview x

3.1 Circuit Equivalence and its Implications x

3.2 Series and Parallel Connection of Resistors x

Series Connection of Resistors x

Parallel Connection of Resistors x

3.3Resistivity x

3.4 Star-Delta Transformation x

3.5Series and Parallel Connection of Ideal Sources x

Ideal Voltage Sources x

Ideal Current Sources x

3.6 Linear-Output Sources x

Linear-Output Voltage Source x

Transformation of Linear-Output Sources x

3.7 Problem-Solving Approach Updated x

Learning Checklist: What should be learned from this chapter x

Problem-Solving Tips x

Exercises and Problems x

Chapter 4 Circuit Theorems

Objective and Overview x

4.1 Excitation by Dependent Sources x

4.2Thevenin’s Theorem x

Derivation of TEC c

Derivation of TEC with PSpice x

4.3Norton’s Theorem x

Derivation of NEC with PSpice x

4.4 Substitution Theorem x

4.5 Source Absorption Theorem x

4.6 Problem-Solving Approach Updated x

Learning Checklist: What should be learned from this chapter x

Problem-Solving Tips x

Exercises and Problems x

Chapter 5 Circuit Simplification

Objective and Overview x

5.1 Superposition x

Dependent Sources x

Procedure for Applying Superposition x

Power with Superposition x

5.2 Output Scaling x

5.3 Redundant Resistors x

Redundant Resistors Connected to Sources x

Resistors not Carrying Current x

5.4 Partitioning of Circuits by Ideal Sources x

5.5 Source Rearrangement x

5.6 Exploitation of Symmetry x

5.6 Problem-Solving Approach Updated x

Learning Checklist: What should be learned from this chapter x

Problem-Solving Tips x

Appendix 5A Wheatstone Bridge x

Exercises and Problems x

Chapter 6 Circuit Equations

Objective and Overview x

6.1 Node-Voltage Method x

Change of Reference Node x

Non-Transformable Voltage Source x

6.2 Dependent Sources in Node-Voltage Method x

6.3 Mesh-Current Method x

Generalization of Mesh-Current Method x

Non-Transformable Current Source x

6.4 Dependent Sources in Mesh-Current Method x

6.5 Problem-Solving Approach Updated x

Learning Checklist: What should be learned from this chapter x

Problem-Solving Tips x

Exercises and Problems x

Chapter 7 Capacitors, Inductors, and Duality

Objective and Overview x

7.1 Voltage-Current Relation of a Capacitor x

Sign Convention x

Steady Capacitor Voltage x

Stored Energy x

7.2 Voltage-Current Relation of an Inductor x

Magnetic Fields and Related Quantities x

Magnetic Flux Linkage x

Inductance x

Voltage-Current Relation x

Steady Inductor Current x

Stored Energy x

7.3 Series and Parallel Connections of Initially-Uncharged Capacitors x

Series Connection of Initially-Uncharged Capacitors x

Parallel Connection of Initially-Uncharged Capacitors x

7.4 Series and Parallel Connections of Initially-Uncharged Inductors x

Series Connection of Initially-Uncharged Inductors x

Parallel Connection of Initially-Uncharged Inductors x

7.5 Duality x

Learning Checklist: What should be learned from this chapter x

Problem-Solving Tips x

Appendix 7A Derivation of the Dual of a Planar Circuit x

Exercises and Problems x

Chapter 8 Sinusoidal Steady State

Objective and Overview x

8.1 The Sinusoidal Function x

8.2 Responses to Sinusoidal Excitation x

Excitation in Trigonometric Form x

Complex Sinusoidal Excitation x

8.3 Phasors x

Phasor Notation x

Properties of Phasors x

8.4 Phasor Relations of Circuit Elements x

Phasor Relations for a Resistor x

Phasor Relations for a Capacitor x

Phasor Relations for an Inductor x

8.5 Impedance and Reactance x

8.6 Governing Equations x

8.7 Representation in the Frequency Domain x

8.8 Phasor Diagrams x

Learning Checklist: What should be learned from this chapter x

Problem-Solving Tips x

Appendix 8A ac Bridges x

Exercises and Problems x

Chapter 9 Linear Transformer

Objective and Overview x

9.1 Magnetic Coupling x

Dot Convention x

9.2 Mutual Inductance x

Coupling Coefficient x

9.3 Linear Transformer x

9.4 T-Equivalent Circuit x

Learning Checklist: What should be learned from this chapter x

Problem-Solving Tips x

Appendix 9A Energy Stored in Magnetically-Coupled Coils x

Exercises and Problems x

Chapter 10 Ideal Transformer

Objective and Overview x

10.1 Magnetic Circuit x

10.2 Ideal Transformer x

Definition x

Phasor Relations x

Reflection of Impedance x

Applications of Transformers x

10.3 Reflection of Circuits x

10.4 Ideal Autotransformer x

10.5 Transformer Imperfections x

Finite Inductance of Windings x

Finite Leakage flux x

Frequency Range x

Core Losses x

Construction of Small Inductors and Transformers x

Learning Checklist: What should be learned from this chapter x

Problem-Solving Tips x

Exercises and Problems x

Chapter 11 Basic Responses of First-Order Circuits

Objective and Overview x

11.1 Capacitor Discharge x

11.2 Capacitor Charging x

Charging with Initial energy Storage x

11.3 Inductor Discharge x

11.4 Inductor Charging x

11.5 Generalized First-Order Circuits x

Generalized Response x

Determining Initial and Final Values x

Effect of Sources on Time Constant x

Effective Values of Circuit Elements x

11.6 Role of Transient x

Learning Checklist: What should be learned from this chapter x

Problem-Solving Tips x

Exercises and Problems x

Chapter 12 Basic Responses of Second-Order Circuits

Objective and Overview x

12.1 Natural Responses of Series RLC Circuit x

Overdamped Responses x

Underdamped Responses x

Critically-Damped Responses x

Sustained Oscillations x

12.2 Natural Response of Parallel GCL Circuit x

12.3 Charging of Series RLC Circuit x

Underdamped Response x

Critically-Damped Response x

Comparison of Responses x

Charging of Parallel GCL Circuit x

12.4 Procedure for Analyzing Prototypical Second-Order Circuits x

Learning Checklist: What should be learned from this chapter x

Problem-Solving Tips x

Appendix 12A More General Second-Order Circuits x

Exercises and Problems x

Part II: Topics in Circuit Analysis

Chapter 13 Ideal Operational Amplifier

Objective and Overview x

13.1 Basic Properties x

Almost-Ideal Op Amp x

Equivalent Circuit x

13.2 Feedback x

13.3 Noninverting Configuration x

Unity-Gain Amplifier x

13.4 Inverting Configuration x

13.5 Applications of the Inverting Configuration x

Current-Source-to-Voltage-Source Converter x

Perfect Integrator

Perfect Differentiator x

Adder x

13.6 Difference Amplifier x

13.7 Solving Problems on Operational Amplifiers x

Learning Checklist: What should be learned from this chapter x

Problem-Solving Tips x

Exercises and Problems x

Chapter 14 Frequency Responses

Objective and Overview x

14.1 Analysis of Filters x

14.2 Ideal Frequency Responses x

14.3 First-Order Responses x

Parallel First-Order Filters x

14.4 Bode Plots x

Lowpass Response x

Highpass Response x

14.5 Second-Order Bandpass Response x

14.6 Second-Order Bandstop Response x

14.7 Second-Order Lowpass and Highpass Responses x

Lowpass Response x

Highpass Response x

14.8 Parallel Circuit x

14.9 Summary of Second-Order Responses x

Learning Checklist: What should be learned from this chapter x

Problem-Solving Tips x

Exercises and Problems x

Chapter 15 Butterworth and Active Filters

Objective and Overview x

15.1 Scaling x

15.2 Butterworth Response x

Product of Transfer Functions x

15.3 First-Order Active Filters x

Lowpass Filter x

Highpass Filter x

15.4 Non-Inverting Second-Order Active Filters x

Highpass Filter x

Lowpass Filter x

Bandpass Filter x

15.5 Inverting Second-Order Active Filters x

Bandpass Filter x

Highpass Filter x

Lowpass Filter x

15.6 Universal Filter x

Learning Checklist: What should be learned from this chapter x

Problem-Solving Tips x

Exercises and Problems x

Chapter 16 Responses to Periodic Inputs

Objective and Overview x

16.1 Fourier Series x

16.2 Fourier Analysis x

Exponential Form x

Frequency Spectrum x

Translation in Time x

16.3 Symmetry Properties of Fourier Series x

Even-Function Symmetry x

Odd-Function Symmetry x

Half-Wave Symmetry x

Quarter-Wave Symmetry x

16.4 Derivation of FSEs from those of Other Functions x

Addition/Subtraction/Multiplication x

Differentiation/Integration x

16.5 Concluding Remarks on FSEs x

Rate of Attenuation of Harmonics x

Application to Nonperiodic Functions x

Shifting Horizontal and Vertical Axes x

16.6 Circuit Responses to Periodic Functions x

16.7 Average Power and rms Values x

rms Value x

Learning Checklist: What should be learned from this chapter x

Problem-Solving Tips x

Exercises and Problems x

Chapter 17 Real, Reactive and Complex Power

Objective and Overview x

17.1 Instantaneous and Real Power x

Resistor x

Inductor x

Capacitor x

General Case x

17.2 Complex Power x

Complex Power Triangle x

Conservation of Complex Power x

17.3 Power Factor Correction x

Power Measurementsx

17.4 Maximum Power Transfer x

Purely Resistive Circuit x

Source and Load Impedances x

Admittance Relations x

Learning Checklist: What should be learned from this chapter x

Problem-Solving Tips x

Exercises and Problems x

Chapter 18 Responses to Step and Impulse Inputs

Objective and Overview x

18.1 Capacitor Response to Current Pulse x

18.2 The Impulse Function x

18.3 Response of Capacitive Circuits to Step and impulse inputs x

Single Capacitor x

RC Circuit x

Summary of Responses of Capacitive Circuits x

18.4 Inductor Response to Voltage Pulse x

18.5 Response of Inductive Circuits to Step and impulse inputs x

Single Inductor x

RL Circuit x

Summary of Responses of Inductive Circuits x

18.6 Response of RLC Circuits to Step and Impulse Inputs x

Learning Checklist: What should be learned from this chapter x

Problem-Solving Tips x

Exercises and Problems x

Chapter 19 Switched Circuits with Initial Energy Storage

Objective and Overview x

19.1 Series and Parallel Connections of Inductors with Initial Charges x

Capacitors in Parallel x

Capacitors in Series x

19.2 Series and Parallel Connections of Inductors with Initial Currents x

Inductors in Series x

Inductors in Parallel x

19.3 Switched Circuits x

Learning Checklist: What should be learned from this chapter x

Problem-Solving Tips x

Exercises and Problems x

Chapter 20 Convolution

Objective and Overview x

20.1 Shifting in Time and Folding x

Shifting in Time x

Folding around the Vertical axis x

20.2 The Convolution Integral x

Graphical Interpretation x

Procedure Based on Graphical Interpretation x

20.3 Operational Properties of Convolution x

Commutative Property x

Distributive property x

Associative property x

Invariance with Inverse Integration and Differentiation x

20.4 Special Cases of Convolution x

Convolution of Staircase Functions x

Convolution with Impulse Function x

Convolution with Step Function x

20.5 Some General Properties of the Convolution Integral x

Learning Checklist: What should be learned from this chapter x

Problem-Solving Tips x

Exercises and Problems x

Chapter 21 Properties of the Laplace Transform

Objective and Overview x

21.1 General x

21.2 Operational Properties of the LT x

21.3 Solution of Ordinary, Linear Differential Equations x

Inverse Laplace Transform x

Partial Fraction Expansion x

21.4 Theorems on the Laplace Transform x

Final Value Theorem x

Initial Value Theorem x

Convolution Theorem x

Learning Checklist: What should be learned from this chapter x

Problem-Solving Tips x

Appendix 21A Simplification of Rational Functions of s x

Exercises and Problems x

Chapter 22 The Laplace Transform in Circuit Analysis

Objective and Overview x

22.1 Representation of Circuit Elements in the s Domain x

Resistor x

Capacitor x

Inductor x

Magnetically-Coupled Coils x

22.2 Solution of Circuit Problems in the s Domain x

Switching x

22.3 Transfer Function x

Stability x

Sinusoidal Steady-State Response x

Interpretation of zeros and poles x

22.4 Interpretations of Circuit Responses in the s-Domain x

Natural Response of First-Order Circuits x

Natural Response of Second-Order Circuits x

Learning Checklist: What should be learned from this chapter x

Problem-Solving Tips x

Exercises and Problems x

Chapter 23 Fourier Transform

Objective and Overview x

23.1 Derivation of the Fourier Transform x

23.2 Some General Properties of the Fourier Transform x

Real and Imaginary Parts x

Fourier Transform at Zero Frequency x

Duality x

23.3 Operational Properties of the Fourier Transform x

23.4 Circuit Applications of the Fourier Transform x

23.5 Parseval’s Theorem x

Learning Checklist: What should be learned from this chapter x

Exercises and Problems x

Chapter 24 Two-Port Circuits

Objective and Overview x

24.1 Circuit Description x

24.2 Parameter Interpretation and Relations x

Interpretation of Parameters x

Inverse Relations x

Reciprocal Circuits x

Symmetric Circuits x

24.3 Equivalent Circuits x

24.4 Composite Two-Port Circuits x

Cascade Connection x

Parallel Connection x

Series Connection x

Series-Parallel Connection x

Parallel-Series Connection x

24.5 Analysis of Terminated Two-Port Circuits x

Learning Checklist: What should be learned from this chapter x

Exercises and Problems x

Chapter 25 Balanced Three-Phase Systems

Objective and Overview x

25.1 Three-Phase Variables x

Sum of Balanced Variables x

Phase Sequence x

25.2 The Balanced Y Connection x

Voltage relations x

Current Relations x

Power Relations x

25.3 The Balanced D Connection x

Voltage relations x

Current Relations x

Power Relations x

25.4 Analysis of Balanced Three-Phase Systems x

Y-Y System x

D -D System x

25.5 Power in Balanced Three-Phase Systems x

Instantaneous Power x

Complex Power x

Two-Wattmeter Method of Power Measurement x

25.6 Advantages of Three-Phase Systems x

25.7 Power Generation, Transmission, and Distribution x

Learning Checklist: What should be learned from this chapter x

Exercises and Problems x

Appendices

Appendix A SI Units, Symbols, and Prefixes x

Appendix B Useful Mathematical Relations x

Appendix C PSpice Simulation x

Appendix D Complex Numbers and Algebra x

Appendix E Solution of Linear Simultaneous Equations x

Nassir Sabah is a Professor of Electrical and Computer Engineering at the American University of Beirut, Lebanon. He received his B.Sc. (Hons. Class I) and his M.Sc. in Electrical Engineering from the University of Birmingham, U.K., and his Ph.D. in biophysical sciences from the State University of New York (SUNY/Buffalo). He has served as Chairman of the Electrical Engineering Department, Director of the Institute of Computer Studies, and Dean of the Faculty of Engineering and Architecture, at the American University of Beirut. In these capacities, he was responsible for the development of programs, curricula, and courses in electrical, biomedical, communications, and computer engineering. Professor Sabah has extensive professional experience in the fields of electrical engineering, electronics, and computer systems, with more than 35 years teaching experience in electric circuits, electronics, neuroengineering, and biomedical engineering. He has over 100 technical publications, mainly in neurophysiology, biophysics, and biomedical instrumentation. He has served on numerous committees and panels in Lebanon and the region. Professor Sabah is a Fellow of the IET, U.K., and a member of the American Society of Engineering Education.