Circuit Analysis II with MATLAB Applications

501 Pages·2004·7.2 MB·English

by  Steven T. Karris

Circuit Analysis II
with MATLAB® Applications
Steven T. Karris
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Orchard Publications, Fremont, California
www.orchardpublications.com
Circuit Analysis II Students and working professionals will find Circuit
Analysis II with MATLAB® Applications to be a con-
with MATLAB® Applications cise and easy-to-learn text. It provides complete,
clear, and detailed explanations of advanced electri-
cal engineering concepts illustrated with numerous
practical examples.
This text includes the following chapters and appendices:
• Second Order Circuits • Resonance • Elementary Signals • The Laplace Transformation
• The Inverse Laplace Transformation • Circuit Analysis with Laplace Transforms • Frequency
Response and Bode Plots • Self and Mutual Inductances - Transformers • One and Two Port
Networks • Three Phase Systems • Introduction to MATLAB • Differential Equations • Matrices
and Determinants • Constructing Semilog Plots with Microsoft Excel • Scaling
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 masters
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 addition, he
has over 25 years of teaching experience that he acquired at several educational institutions as
an adjunct professor. He is currently with UC Berkeley Extension.
Orchard Publications, Fremont, California
Visit us on the Internet
www.orchardpublications.com
or email us: [email protected]
ISBN 0-9709511-9-1
$39.95 U.S.A.
Circuit Analysis II
with MATLAB® Applications
Steven T. Karris
Orchard Publications
www.orchardpublications.com
Circuit Analysis II with MATLAB® Applications
Copyright (cid:148) 2003 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(cid:147), Inc., and Microsoft(cid:147)
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: 2003094467
Copyright Number TX-745-064
ISBN 0-9709511-9-1
Disclaimer
The publisher has used his best effort to prepare this text. However, the publisher and author makes no warranty of any
kind, expressed or implied with regard to the accuracy, completeness, and computer codes contained in this book, and
shall not be liable in any event for incidental or consequential damages in connection with, or arising out of, the
performance or use of these programs.
This book was created electronically using Adobe Framemaker(cid:147).
Preface
This text is written for use in a second course in circuit analysis. The reader of this book should have
the traditional undergraduate knowledge of an introductory circuit analysis material such as Circuit
Analysis I with MATLAB® Applications by this author. Another prerequisite would be knowledge of
differential equations, and in most cases, engineering students at this level have taken all required
mathematics courses. It encompasses a spectrum of subjects ranging from the most abstract to the
most practical, and the material can be covered in one semester or two quarters. Appendix B serves as
a review of differential equations with emphasis on engineering related topics and it is recommended
for readers who may need a review of this subject.
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.
Chapter 1 is an introduction to second order circuits and it is essentially a sequel to first order circuits
that were discussed in the last chapter of as Circuit Analysis I with MATLAB® Applications. Chapter 2
is devoted to resonance, and Chapter 3 presents practical methods of expressing signals in terms of
the elementary functions, i.e., unit step, unit ramp, and unit impulse functions. Thus, any signal can be
represented in the compex frequency domain using the Laplace transformation.
Chapters 4 and 5 are introductions to the unilateral Laplace transform and Inverse Laplace transform
respectively, while Chapter 6 presents several examples of analyzing electric circuits using Laplace
transformation methods. Chapter 7 begins with the frequency response concept and Bode magnitude
and frequency plots. Chapter 8 is devoted to transformers with an introduction to self and mutual
inductances. Chapter 9 is an introduction to one- and two-terminal devices and presents several
practical examples. Chapter 10 is an introduction to three-phase circuits.
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 of this text the magnitude and phase plots can be easily
obtained with a one line MATLAB code. Moreover, MATLAB will be invaluable in later studies such
as the design of analog and digital filters.
Circuit Analysis II with MATLAB Applications
Orchard Publications
As stated above, Appendix B is a review of differential equations. Appendix C is an introduction
to matrices, Appendix D provides instructions on constructing semilog templates to be used with
Bode plots, and Appendix E discusses scaling methods.
In addition to numerous real-world examples, this text contains several exercises at the end of
each chapter. Detailed solutions of all exercises are provided at the end of each chapter. The
rationale is to encourage the reader to solve all exercises 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.
The author is indebted to the class of the Spring semester of 2001 at San Jose State University,
San Jose, California, for providing several of the examples and exercises of this text.
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
[email protected]
Circuit Analysis II with MATLAB Applications
Orchard Publications
Contents
Chapter 1
Second Order Circuits
The Response of a Second Order Circuit....................................................................................1-1
The Series RLC Circuit with DC Excitation...............................................................................1-2
Response of Series RLC Circuits with DC Excitation................................................................1-5
Response of Series RLC Circuits with AC Excitation..............................................................1-11
The Parallel GLC Circuit...........................................................................................................1-14
Response of Parallel GLC Circuits with DC Excitation............................................................1-16
Response of Parallel GLC Circuits with AC Excitation............................................................1-26
Other Second Order Circuits.....................................................................................................1-29
Summary....................................................................................................................................1-36
Exercises....................................................................................................................................1-38
Solutions to Exercises................................................................................................................1-40
Chapter 2
Resonance
Series Resonance.........................................................................................................................2-1
Quality Factor Q in Series Resonance.......................................................................................2-4
0s
Parallel Resonance.......................................................................................................................2-6
Quality Factor Q in Parallel Resonance....................................................................................2-9
0p
General Definition of Q.............................................................................................................2-10
Energy in L and C at Resonance...............................................................................................2-11
Half-Power Frequencies - Bandwidth.......................................................................................2-12
A Practical Parallel Resonant Circuit........................................................................................2-16
Radio and Television Receivers................................................................................................2-17
Summary....................................................................................................................................2-20
Exercises....................................................................................................................................2-22
Solutions to Exercises................................................................................................................2-24
Chapter 3
Elementary Signals
Signals Described in Math Form.................................................................................................3-1
The Unit Step Function ...............................................................................................................3-2
The Unit Ramp Function...........................................................................................................3-10
Circuit Analysis II with MATLAB Applications i
Orchard Publications
The Delta Function....................................................................................................................3-12
Sampling Property of the Delta Function..................................................................................3-12
Sifting Property of the Delta Function......................................................................................3-13
Higher Order Delta Functions...................................................................................................3-15
Summary....................................................................................................................................3-19
Exercises....................................................................................................................................3-20
Solutions to Exercises................................................................................................................3-21
Chapter 4
The Laplace Transformation
Definition of the Laplace Transformation...................................................................................4-1
Properties of the Laplace Transform...........................................................................................4-2
The Laplace Transform of Common Functions of Time...........................................................4-12
The Laplace Transform of Common Waveforms......................................................................4-23
Summary....................................................................................................................................4-29
Exercises....................................................................................................................................4-34
Solutions to Exercises................................................................................................................4-37
Chapter 5
The Inverse Laplace Transformation
The Inverse Laplace Transform Integral.....................................................................................5-1
Partial Fraction Expansion...........................................................................................................5-1
Case for m (cid:116) n............................................................................................................................5-13
Alternate Method of Partial Fraction Expansion.......................................................................5-15
Summary....................................................................................................................................5-18
Exercises....................................................................................................................................5-20
Solutions to Exercises................................................................................................................5-22
Chapter 6
Circuit Analysis with Laplace Transforms
Circuit Transformation from Time to Complex Frequency........................................................6-1
Complex Impedance Z(s)............................................................................................................6-8
Complex Admittance Y(s).........................................................................................................6-10
Transfer Functions.....................................................................................................................6-13
Summary....................................................................................................................................6-17
Exercises....................................................................................................................................6-18
Solutions to Exercises................................................................................................................6-21
ii Circuit Analysis II with MATLAB Applications
Orchard Publications
Chapter 7
Frequency Response and Bode Plots
Decibel.............................................................................................................................................................7-1
Bandwidth and Frequency Response..........................................................................................................7-3
Octave and Decade........................................................................................................................................7-4
Bode Plot Scales and Asymptotic Approximations..................................................................................7-5
Construction of Bode Plots when the Zeros and Poles are Real............................................................7-6
Construction of Bode Plots when the Zeros and Poles are Complex.................................................7-12
Corrected Amplitude Plots.........................................................................................................................7-25
Summary........................................................................................................................................................7-36
Exercises........................................................................................................................................................7-38
Solutions to Exercises..................................................................................................................................7-39
Chapter 8
Self and Mutual Inductances - Transformers
Self-Inductance............................................................................................................................8-1
The Nature of Inductance............................................................................................................8-1
Lenz’s Law..................................................................................................................................8-3
Mutually Coupled Coils...............................................................................................................8-3
Establishing Polarity Markings..................................................................................................8-11
Energy Stored in a Pair of Mutually Coupled Inductors...........................................................8-14
Circuits with Linear Transformers.............................................................................................8-20
Reflected Impedance in Transformers.......................................................................................8-25
The Ideal Transformer...............................................................................................................8-28
Impedance Matching..................................................................................................................8-32
A Simplified Transformer Equivalent Circuit...........................................................................8-33
Thevenin Equivalent Circuit......................................................................................................8-34
Summary....................................................................................................................................8-38
Exercises....................................................................................................................................8-42
Solutions to Exercises................................................................................................................8-44
Chapter 9
One- and Two-port Networks
Introduction and Definitions.......................................................................................................................9-1
One-port Driving-point and Transfer Admittances.................................................................................9-2
One-port Driving-point and Transfer Impedances..................................................................................9-7
Two-Port Networks.....................................................................................................................................9-12
Circuit Analysis II with MATLAB Applications iii
Orchard Publications
The y Parameters..........................................................................................................................................9-12
The z parameters..........................................................................................................................................9-19
The h Parameters.........................................................................................................................................9-24
The g Parameters.........................................................................................................................................9-29
Reciprocal Two-Port Networks.................................................................................................................9-34
Summary........................................................................................................................................................9-38
Exercises........................................................................................................................................................9-43
Solutions to Exercises.................................................................................................................................9-45
Chapter 10
Three-Phase Systems
Advantages of Three-Phase Systems.........................................................................................10-1
Three-Phase Connections..........................................................................................................10-1
Transformer Connections in Three-Phase Systems...................................................................10-4
Line-to-Line and Line-to-Neutral Voltages and Currents.........................................................10-5
Equivalent Y and (cid:39) Loads.......................................................................................................10-10
Computation by Reduction to Single Phase............................................................................10-20
Three-Phase Power..................................................................................................................10-21
Instantaneous Power in Three-Phase Systems.........................................................................10-23
Measuring Three-Phase Power................................................................................................10-27
Summary..................................................................................................................................10-30
Exercises..................................................................................................................................10-32
Solutions to Exercises..............................................................................................................10-33
Appendix A
Introduction to MATLAB®
MATLAB® and Simulink®.......................................................................................................A-1
Command Window.....................................................................................................................A-1
Roots of Polynomials..................................................................................................................A-3
Polynomial Construction from Known Roots............................................................................A-4
Evaluation of a Polynomial at Specified Values........................................................................A-6
Rational Polynomials..................................................................................................................A-8
Using MATLAB to Make Plots................................................................................................A-10
Subplots....................................................................................................................................A-19
Multiplication, Division and Exponentiation...........................................................................A-20
Script and Function Files..........................................................................................................A-26
Display Formats........................................................................................................................A-31
iv Circuit Analysis II with MATLAB Applications
Orchard Publications