Circuit analysis i with MATLAB applications

Orchard Publications, Fremont, California www.orchardpublications.com G=[35/50 −j*3/50; −1/5 1/10+j*1/10]; I=[1 0]'; V=G\I; Ix=5*V(2,1)/4; % Multiply Vc by 5 and divide by 4 to get current Ix magIx=abs(Ix); theta=angle(Ix)*180/pi; % Convert current Ix to polar form fprintf(' \n'); disp(' Ix = ' ); disp(Ix); fprintf('magIx = %4.2f A \t', magIx); fprintf('theta = %4.2f deg \t', theta); fprintf(' \n'); fprintf(' \n'); Ix = 2.1176-1.7546i magIx = 2.75 A theta = -39.64 deg Steven T. Karris Circuit Analysis I with MATLAB® Applications Students and working professionals will find Circuit Analysis I with MATLAB® Applications to be a con- cise and easy-to-learn text. It provides complete, clear, and detailed explanations of the principal elec- trical engineering concepts, and these are illustrated with numerous practical examples. This text includes the following chapters and appendices: • Basic Concepts and Definitions • Analysis of Simple Circuits • Nodal and Mesh Equations - Circuit Theorems • Introduction to Operational Amplifiers • Inductance and Capacitance • Sinusoidal Circuit Analysis • Phasor Circuit Analysis • Average and RMS Values, Complex Power, and Instruments • Natural Response • Forced and Total Response in RL and RC Circuits • Introduction to MATLAB • Review of Complex Numbers • Matrices and Determinants Each chapter contains numerous practical applications supplemented with detailed instructions for using MATLAB to obtain quick and accurate answers. Steven T. Karris is the president and founder of Orchard Publications. He earned a bachelors degree in electrical engineering at Christian Brothers University, Memphis, Tennessee, a mas- ters degree in electrical engineering at Florida Institute of Technology, Melbourne, Florida, and has done post-master work at the latter. He is a registered professional engineer in California and Florida. He has over 30 years of professional engineering experience in industry. In addi- tion, he has over 25 years of teaching experience that he acquired at several educational insti- tutions as an adjunct professor. He is currently with UC Berkeley Extension. Orchard Publications Visit us on the Internet www.orchardpublications.com or email us: info@orchardpublications.com ISBN 0-9744239-3-9 $39.95 Circuit Analysis I with MATLAB® Applications Circuit Analysis I with MATLAB® Applications Steven T. Karris Orchard Publications www.orchardpublications.com Circuit Analysis I with MATLAB® Applications Copyright © 2004 Orchard Publications. All rights reserved. Printed in Canada. No part of this publication may be reproduced or distributed in any form or by any means, or stored in a data base or retrieval system, without the prior written permission of the publisher. Direct all inquiries to Orchard Publications, 39510 Paseo Padre Parkway, Fremont, California 94538, U.S.A. URL: http://www.orchardpublications.com Product and corporate names are trademarks or registered trademarks of the MathWorks®, Inc., and Microsoft® Corporation. They are used only for identification and explanation, without intent to infringe. Library of Congress Cataloging-in-Publication Data Library of Congress Control Number 2004093171 ISBN 0-9744239-3-9 Disclaimer The author has made every effort to make this text as complete and accurate as possible, but no warranty is implied. The author and publisher shall have neither liability nor responsibility to any person or entity with respect to any loss or damages arising from the information contained in this text. This book was created electronically using Adobe Framemaker®. Circuit Analysis I with MATLAB Applications Orchard Publications Preface This text is an introduction to the basic principles of electrical engineering. It is the outgrowth of lecture notes prepared by this author while teaching for the electrical engineering and computer engineering departments at San José State University, DeAnza college, and the College of San Mateo, all in California. Many of the examples and problems are based on the author’s industrial experience. It can be used as a primary text or supplementary text. It is also ideal for self-study. This book is intended for students of college grade, both community colleges and universities. It presumes knowledge of first year differential and integral calculus and physics. While some knowledge of differential equations would be helpful, it is not absolutely necessary. Chapters 9 and 10 include step-by-step procedures for the solutions of simple differential equations used in the derivation of the natural and forces responses. Appendices B and C provide a thorough review of complex numbers and matrices respectively. There are several textbooks on the subject that have been used for years. The material of this book is not new, and this author claims no originality of its content. This book was written to fit the needs of the average student. Moreover, it is not restricted to computer oriented circuit analysis. While it is true that there is a great demand for electrical and computer engineers, especially in the internet field, the demand also exists for power engineers to work in electric utility companies, and facility engineers to work in the industrial areas. Circuit analysis is comprised of numerous topics. It would be impractical to include all related topics in a single text. This book, Circuit Analysis I with MATLAB® Applications, contains the standard subject matter of electrical engineering. Accordingly, it is intended as a first course in circuits and the material can be covered in one semester or two quarters. A sequel, Circuit Analysis II with MATLAB® Applications, is intended for use in a subsequent semester or two subsequent quarters. It is not necessary that the reader has previous knowledge of MATLAB®. The material of this text can be learned without MATLAB. However, this author highly recommends that the reader studies this material in conjunction with the inexpensive MATLAB Student Version package that is available at most college and university bookstores. Appendix A of this text provides a practical introduction to MATLAB. As shown on the front cover, a system of equations with complex coefficients can be solved with MATLAB very accurately and rapidly. MATLAB will be invaluable in later studies such as the design of analog and digital filters. In addition to several problems provided at the end of each chapter, this text includes multiple-choice questions to test and enhance the reader’s knowledge of this subject. Moreover, answers to these questions and detailed solutions of all problems are provided at the end of each chapter. The rationale Preface Circuit Analysis I with MATLAB Applications Orchard Publications is to encourage the reader to solve all problems and check his effort for correct solutions and appropriate steps in obtaining the correct solution. And since this text was written to serve as a self-study or supplementary textbook, it provides the reader with a resource to test his knowledge. The author has accumulated many additional problems for homework assignment and these are available to those instructors who adopt this text either as primary or supplementary text, and prefer to assign problems without the solutions. He also has accumulated many sample exams. Like any other new book, this text may contain some grammar and typographical errors. Accordingly, all feedback for errors, advice and comments will be most welcomed and greatly appreciated. Orchard Publications Fremont, California Circuit Analysis I with MATLAB Applications i Orchard Publications Contents Chapter 1 Basic Concepts and Definitions The Coulomb 1-1 Electric Current and Ampere 1-1 Two Terminal Devices 1-4 Voltage (Potential Difference) 1-5 Power and Energy 1-8 Active and Passive Devices 1-12 Circuits and Networks 1-12 Active and Passive Networks 1-12 Necessary Conditions for Current Flow 1-12 International System of Units 1-13 Sources of Energy 1-17 Summary 1-18 Exercises 1-21 Answers to Exercises 1-25 Chapter 2 Analysis of Simple Circuits Conventions 2-1 Ohm’s Law 2-1 Power Absorbed by a Resistor 2-3 Energy Dissipated by a Resistor 2-4 Nodes, Branches, Loops and Meshes 2-5 Kirchhoff’s Current Law (KCL) 2-6 Kirchhoff’s Voltage Law (KVL) 2-7 Analysis of Single Mesh (Loop) Series Circuits 2-10 Analysis of Single Node-Pair Parallel Circuits 2-14 Voltage and Current Source Combinations 2-16 Resistance and Conductance Combinations 2-18 Voltage Division Expressions 2-22 Current Division Expressions 2-24 Standards for Electrical and Electronic Devices 2-26 Resistor Color Code 2-27 Power Rating of Resistors 2-28 Contents ii Circuit Analysis I with MATLAB Applications Orchard Publications Temperature Coefficient of Resistance 2-29 Ampere Capacity of Wires 2-30 Current Ratings for Electronic Equipment 2-30 Copper Conductor Sizes for Interior Wiring 2-33 Summary 2-38 Exercises 2-41 Answers to Exercises 2-50 Chapter 3 Nodal and Mesh Equations - Circuit Theorems Nodal, Mesh, and Loop Equations 3-1 Analysis with Nodal Equations 3-1 Analysis with Mesh or Loop Equations 3-8 Transformation between Voltage and Current Sources 3-20 Thevenin’s Theorem 3-24 Norton’s Theorem 3-35 Maximum Power Transfer Theorem 3-38 Linearity 3-39 Superposition Principle 3-41 Circuits with Non-Linear Devices 3-45 Efficiency 3-47 Regulation 3-49 Summary 3-49 Exercises 3-52 Answers to Exercises 3-64 Chapter 4 Introduction to Operational Amplifiers Signals 4-1 Amplifiers 4-1 Decibels 4-2 Bandwidth and Frequency Response 4-4 The Operational Amplifier 4-5 An Overview of the Op Amp 4-5 Active Filters 4-13 Analysis of Op Amp Circuits 4-16 Input and Output Resistance 4-28 Summary 4-32 Circuit Analysis I with MATLAB Applications iii Orchard Publications Contents Exercises 4-34 Answers to Exercises 4-43 Chapter 5 Inductance and Capacitance Energy Storage Devices 5-1 Inductance 5-1 Power and Energy in an Inductor 5-11 Combinations of Series and Parallel Inductors 5-14 Capacitance 5- 17 Power and Energy in a Capacitor 5-22 Capacitance Combinations 5-25 Nodal and Mesh Equations in General Terms 5-28 Summary 5-29 Exercises 5-31 Answers to Exercises 5-36 Chapter 6 Sinusoidal Circuit Analysis Excitation Functions 6-1 Circuit Response to Sinusoidal Inputs 6-1 The Complex Excitation Function 6-3 Phasors in , , and Circuits 6-8 Impedance 6-14 Admittance 6- 17 Summary 6-21 Exercises 6-25 Answers to Exercises 6-30 Chapter 7 Phasor Circuit Analysis Nodal Analysis 7-1 Mesh Analysis 7-5 Application of Superposition Principle 7-7 Thevenin’s and Norton’s Theorems 7-8 Phasor Analysis in Amplifier Circuits 7-12 RL C Contents iv Circuit Analysis I with MATLAB Applications Orchard Publications Phasor Diagrams 7-15 Electric Filters 7-20 Basic Analog Filters 7-21 Active Filter Analysis 7-26 Summary 7- 28 Exercises 7-29 Answers to Exercises 7-37 Chapter 8 Average and RMS Values, Complex Power, and Instruments Periodic Time Functions 8-1 Average Values 8-2 Effective Values 8-3 Effective ( RMS) Value of Sinusoids 8-5 RMS Values of Sinusoids with Different Frequencies 8-7 Average Power and Power Factor 8-9 Average Power in a Resistive Load 8-10 Average Power in Inductive and Capacitive Loads 8-11 Average Power in Non-Sinusoidal Waveforms 8-14 Lagging and Leading Power Factors 8-15 Complex Power - Power Triangle 8-16 Power Factor Correction 8-18 Instruments 8-21 Summary 8-30 Exercises 8-33 Answers to Exercises 8-39 Chapter 9 Natural Response The Natural Response of a Series RL circuit 9-1 The Natural Response of a Series RC Circuit 9-10 Summary 9-17 Exercises 9-19 Answers to Exercises 9-25 [...]... Adjoint of a Matrix C-20 Singular and Non-Singular Matrices C-21 The Inverse of a Matrix C-21 Solution of Simultaneous Equations with Matrices C-23 Exercises C-30 vi Circuit Analysis I with MATLAB Applications Orchard Publications Chapter 1 Basic Concepts and Definitions T his chapter begins with the basic definitions in electric... MathWorks, Inc., 3 Apple Hill Drive, Natick, MA, 01760, www.mathworks.com An introduction to MATLAB is given in Appendix A 1-6 Circuit Analysis I with MATLAB Applications Orchard Publications Voltage (Potential Difference) We will use the MATLAB int(f,a,b) integration function where f is a symbolic expression, and a and b are the lower and upper limits of integration respectively Note When MATLAB cannot find... two-terminal devices which we will be concerned with in this text are shown in Figure 1.12 Linear devices are those in which there is a linear relationship between the voltage across that device and the current that flows through that device Diodes and Transistors are non-linear devices, that is, their voltage-current relationship is non-linear These will not be discussed in this text A simple circuit with. .. conditions which are necessary to set up and maintain a flow of current in a network or circuit These are: 1-12 Circuit Analysis I with MATLAB Applications Orchard Publications International System of Units 1 There must be a voltage source (potential difference) present to provide the electrical work which will force current to flow 2 The circuit must be closed These conditions are illustrated in Figures... charged bodies, the coulomb force decreases in proportion to the square of the distance between their charge centers • Electric current is defined as the instantaneous rate at which net positive charge is moving past this point in that specified direction, that is, dq i = - = lim ∆q dt ∆ t → 0 ∆t 1-18 Circuit Analysis I with MATLAB Applications Orchard Publications Summary • The unit of current is the... Kelvin Other units used in physical sciences and electronics are derived from the SI base units and the most common are listed in Table 1.6 1-14 Circuit Analysis I with MATLAB Applications Orchard Publications International System of Units TABLE 1.2 Most Commonly Used SI Prefixes Value 13.2 KV (Kilovolts) = 13.2 × 10 3 volts centi c 2.8 cm (centimeters) = 2.8 x 10 –2 meter milli m 4 mH (millihenries)... Conductance G sl iG ope iR v R = Ri R Inductance L iL L + vL − diL vL = L dt iG G p slo G= + vG − i G = Gv G e vG Capacitance C vL l op =s L iC e diL dt C + − vC iC l op =s C dv iC = C C dt e dvC dt Figure 1.12 Voltage and current sources and linear devices Circuit Analysis I with MATLAB Applications Orchard Publications 1-11 Chapter 1 Basic Concepts and Definitions 1.6 Active and Passive Devices Independent... present and the circuit is closed Therefore, both conditions are satisfied and current will flow R L vS + − C I Figure 1.17 A circuit in which current flows 1.10 International System of Units The International System of Units (abbreviated SI in all languages) was adopted by the General Conference on Weights and Measures in 1960 It is used extensively by the international scientific community It was formerly... where power is absorbed by a two-terminal device 1-8 Circuit Analysis I with MATLAB Applications Orchard Publications Power and Energy i= 6cos3t A + Two terminal device 1 B − A i= −5sin5t Two terminal device 2 − v=−18sin3t v=cos5t p = (−18sin3t)(6cos3t) = −54sin6t w B + p = (cos5t)(−5sin5t) = −2.5sin10t w Figure 1.10 Examples where power is delivered to a two-terminal device In Figure 1.9, power is absorbed... is convenient to think or consider the instantaneous current, that is, the direction of the current which flows at some particular instant As before, we assume a direction by placing an arrow next to the device in which the current flows, and if a negative value for the current i is obtained, we conclude that the actual direction is opposite of that of the arrow Circuit Analysis I with MATLAB Applications . MATLAB Applications Circuit Analysis I with MATLAB Applications Steven T. Karris Orchard Publications www.orchardpublications.com Circuit Analysis I with MATLAB . Analysis in Amplifier Circuits 7-12 RL C Contents iv Circuit Analysis I with MATLAB Applications Orchard Publications Phasor Diagrams 7-15 Electric Filters