Circuit Analysis I

618 Pages·2009·5.03 MB·English

by  Karris, Steven T.

Circuit Analysis I
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Steven T. Karris
Orchard Publications
www.orchardpublications.com
Circuit Analysis I

with MATLAB® Computing and
Simulink® / SimPowerSystems®
Modeling
Steven T. Karris
Orchard Publications, Fremont, California
www.orchardpublications.com
Circuit Analysis I with MATLAB® Computing and Simulink® / SimPowerSystems® Modeling
Copyright  2009 Orchard Publications. All rights reserved. Printed in USA. 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: 2009923770
ISBN10: 1934404187
ISBN13: 9781934404188
TX 5737590
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.
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 employed by the electrical engineering and computer
engineering departments as adjunct instructor at various colleges and universities. Many of the
examples and problems are based on the author’s industrial experience. The text is an expansion
of our previous publication, Circuit Analysis I with MATLAB® Applications, ISBN 9780
970951120, and this text, in addition to MATLAB scripts for problem solution, includes
several Simulink® and SimPowerSystems® models. The pages where these models appear are
indicated n the Table of Contents.
The 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 D and E provide a thorough review of
complex numbers and matrices respectively.
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, the
answers to these questions and detailed solutions of all problems are provided at the end of each
chapter. The rationale 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, primary, or supplementary textbook, it provides the reader with a
resource to test the reader’s knowledge.
A previous knowledge of MATLAB® would be very helpful. However he material of this text can
be learned without MATLAB, Simulink and SimPowerSystems. This author highly recommends
that the reader studies this material in conjunction with the inexpensive Student Versions of The
MathWorks™ Inc., the developers of these outstanding products, available from:
The MathWorks, Inc.
3 Apple Hill Drive
Natick, MA, 01760
Phone: [phone],
www.mathworks.com
[email protected].
Appendix A of this text provides a practical introduction to MATLAB, Appendix B is an
introduction to Simulink, and Appendix C is an introduction to SimPowerSystems. These
packages will be invaluable in later studies such as the design of analog and digital filters.
Preface
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
39510 Paseo Padre Parkway
Suite 315
Fremont, California 94538
www.orchardpublications.com
[email protected]
Table of Contents
1
Basic Concepts and Definitions 11
1.1 The Coulomb........................................................................................................11
1.2 Electric Current and Ampere ...............................................................................11
1.3 Two Terminal Devices .........................................................................................14
1.4 Voltage (Potential Difference) .............................................................................15
1.5 Power and Energy .................................................................................................18
1.6 Active and Passive Devices ................................................................................111
1.7 Circuits and Networks ........................................................................................113
1.8 Active and Passive Networks .............................................................................113
1.9 Necessary Conditions for Current Flow .............................................................113
1.10 International System of Units ............................................................................114
1.11 Sources of Energy ...............................................................................................117
1.12 Summary .............................................................................................................119
1.13 Exercises .............................................................................................................121
1.14 Answers / Solutions to EndofChapter Exercises ............................................124
MATLAB Computing: Pages 16 through 18
2
Analysis of Simple Circuits 21
2.1 Conventions .........................................................................................................21
2.2 Ohm’s Law ............................................................................................................21
2.3 Power Absorbed by a Resistor ..............................................................................23
2.4 Energy Dissipated in a Resistor ............................................................................24
2.5 Nodes, Branches, Loops and Meshes ...................................................................25
2.6 Kirchhoff’s Current Law (KCL) ...........................................................................26
2.7 Kirchhoff’s Voltage Law (KVL)............................................................................27
2.8 Single Mesh Circuit Analysis .............................................................................210
2.9 Single NodePair Circuit Analysis ....................................................................214
2.10 Voltage and Current Source Combinations .......................................................217
2.11 Resistance and Conductance Combinations .....................................................218
2.12 Voltage Division Expressions .............................................................................222
2.13 Current Division Expressions .............................................................................224
2.14 Standards for Electrical and Electronic Devices ................................................226
2.15 Resistor Color Code ...........................................................................................226
2.16 Power Rating of Resistors ...................................................................................228
2.17 Temperature Coefficient of Resistance ..............................................................228
2.18 Ampere Capacity of Wires .................................................................................229
Circuit Analysis I with MATLAB  Computing and Simulink / SimPowerSystems Modeling i
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2.19 Current Ratings for Electronic Equipment.........................................................229
2.20 Copper Conductor Sizes for Interior Wiring ......................................................231
2.21 Summary .............................................................................................................236
2.22 Exercises ..............................................................................................................239
2.23 Answers / Solutions to EndofChapter Exercises ............................................247
Simulink / SimPowerSystems models: Pages 224, 226
3
Nodal and Mesh Equations - Circuit Theorems 31
3.1 Nodal, Mesh, and Loop Equations.......................................................................31
3.2 Analysis with Nodal Equations............................................................................31
3.3 Analysis with Mesh or Loop Equations................................................................38
3.4 Transformation between Voltage and Current Sources....................................320
3.5 Thevenin’s Theorem..........................................................................................323
3.6 Norton’s Theorem..............................................................................................333
3.7 Maximum Power Transfer Theorem..................................................................335
3.8 Linearity..............................................................................................................337
3.9 Superposition Principle.......................................................................................338
3.10 Circuits with Non-Linear Devices......................................................................342
3.11 Efficiency............................................................................................................344
3.12 Regulation...........................................................................................................345
3.13 Summary.............................................................................................................347
3.14 Exercises.............................................................................................................349
3.15 Answers / Solutions to EndofChapter Exercises............................................360
MATLAB Computing: Pages 3-4, 37, 311, 314, 316, 318, 332, 366,
370, 372, 374, 376, 380, 390
Simulink / SimPowerSystems models: Pages 38, 319
4
Introduction to Operational Amplifiers 41
4.1 Signals...................................................................................................................41
4.2 Amplifiers.............................................................................................................41
4.3 Decibels................................................................................................................42
4.4 Bandwidth and Frequency Response....................................................................44
4.5 The Operational Amplifier...................................................................................45
4.6 An Overview of the Op Amp...............................................................................45
4.7 Active Filters......................................................................................................413
4.8 Analysis of Op Amp Circuits..............................................................................416
4.9 Input and Output Resistance.............................................................................428
4.10 Summary.............................................................................................................432
4.11 Exercises.............................................................................................................434
ii Circuit Analysis I with MATLAB  Computing and Simulink / SimPowerSystems Modeling
Copyright © Orchard Publications
4.12 Answers / Solutions to EndofChapter Exercises............................................443
MATLAB Computing: Page 4-47
Simulink / SimPowerSystems models: Pages 452
5
Inductance and Capacitance 51
5.1 Energy Storage Devices.......................................................................................51
5.2 Inductance...........................................................................................................51
5.3 Power and Energy in an Inductor......................................................................511
5.4 Combinations of Inductors in Series and in Parallel.........................................514
5.5 Capacitance.......................................................................................................516
5.6 Power and Energy in a Capacitor......................................................................521
5.7 Combinations of Capacitors in Series and in Parallel.......................................524
5.8 Nodal and Mesh Equations in General Terms..................................................526
5.9 Summary............................................................................................................529
5.10 Exercises............................................................................................................531
5.11 Answers / Solutions to EndofChapter Exercises...........................................536
MATLAB Computing: Pages 513, 523, 540
6
Sinusoidal Circuit Analysis 61
6.1 Excitation Functions...........................................................................................61
6.2 Circuit Response to Sinusoidal Inputs................................................................61
6.3 The Complex Excitation Function.....................................................................63
6.4 Phasors in R, L, and C Circuits...........................................................................68
6.5 Impedance.........................................................................................................614
6.6 Admittance.......................................................................................................617
6.7 Summary...........................................................................................................623
6.8 Exercises............................................................................................................626
6.9 Solutions to EndofChapter Exercises............................................................632
MATLAB Computing: Pages 621, 632, 635
Simulink / SimPowerSystems models: Pages 622, 637, 638
7
Phasor Circuit Analysis 71
7.1 Nodal Analysis....................................................................................................71
7.2 Mesh Analysis......................................................................................................75
7.3 Application of Superposition Principle...............................................................76
7.4 Thevenin’s and Norton’s Theorems.................................................................710
7.5 Phasor Analysis in Amplifier Circuits...............................................................714
Circuit Analysis I with MATLAB  Computing and Simulink / SimPowerSystems Modeling iii
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7.6 Phasor Diagrams................................................................................................717
7.7 Electric Filters....................................................................................................722
7.8 Basic Analog Filters...........................................................................................723
7.9 Active Filter Analysis........................................................................................728
7.10 Summary............................................................................................................731
7.11 Exercises.............................................................................................................732
7.12 Answers to EndofChapter Exercises..............................................................739
MATLAB Computing: Pages 7-4, 76, 78, 712, 713, 715, 717, 721, 730,
744, 745, 746, 748, 750, 751, 755, 756, 758
Simulink models: Pages 79, 710
8
Average and RMS Values, Complex Power, and Instruments 81
8.1 Periodic Time Functions......................................................................................81
8.2 Average Values....................................................................................................82
8.3 Effective Values....................................................................................................84
8.4 Effective (RMS) Value of Sinusoids.....................................................................85
8.5 RMS Values of Sinusoids with Different Frequencies.........................................87
8.6 Average Power and Power Factor........................................................................89
8.7 Average Power in a Resistive Load....................................................................811
8.8 Average Power in Inductive and Capacitive Loads...........................................811
8.9 Average Power in NonSinusoidal Waveforms.................................................814
8.10 Lagging and Leading Power Factors...................................................................815
8.11 Complex Power  Power Triangle......................................................................816
8.12 Power Factor Correction....................................................................................818
8.13 Instruments.........................................................................................................820
8.14 Summary.............................................................................................................831
8.15 Exercises.............................................................................................................834
8.16 Answers to EndofChapter Exercises..............................................................840
MATLAB Computing: Page 8-3 continued on Page 84
9
Natural Response 91
9.1 Natural Response of a Series RL circuit...............................................................91
9.2 Natural Response of a Series RC Circuit..............................................................99
9.3 Summary.............................................................................................................917
9.4 Exercises..............................................................................................................918
9.5 Answers to EndofChapter Exercises...............................................................925
MATLAB Computing: Page 927
Simulink / SimPowerSystems models: Page 924
iv Circuit Analysis I with MATLAB  Computing and Simulink / SimPowerSystems Modeling
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10
Forced and Total Response in RL and RC Circuits 101
10.1 Unit Step Function.............................................................................................101
10.2 Unit Ramp Function..........................................................................................10 6
10.3 Delta Function...................................................................................................10 7
10.4 Forced and Total Response in an RL Circuit...................................................1014
10.5 Forced and Total Response in an RC Circuit...................................................1021
10.6 Summary............................................................................................................1031
10.7 Exercises............................................................................................................1033
10.8 Answers to EndofChapter Exercises.............................................................1040
MATLAB Computing: Pages 1018, 1030
Simulink / SimPowerSystems models: Page 1051
A
Introduction to MATLAB A1
A.1 Command Window ..............................................................................................A1
A.2 Roots of Polynomials ............................................................................................A3
A.3 Polynomial Construction from Known Roots ......................................................A4
A.4 Evaluation of a Polynomial at Specified Values ..................................................A5
A.5 Rational Polynomials ...........................................................................................A8
A.6 Using MATLAB to Make Plots ..........................................................................A9
A.7 Subplots .............................................................................................................A18
A.8 Multiplication, Division and Exponentiation ...................................................A19
A.9 Script and Function Files ..................................................................................A26
A.10 Display Formats .................................................................................................A31
MATLAB Computations: Entire Appendix A
B
Introduction to Simulink B1
B.1 Simulink and its Relation to MATLAB ...............................................................B1
B.2 Simulink Demos .................................................................................................B20
Simulink Modeling: Entire Appendix B
C
Introduction to SimPowerSystems C1
C.1 Simulation of Electric Circuits with SimPowerSystems......................................C1
SimPowerSystems Modeling: Entire Appendix C
D
A Review of Complex Numbers D1
D.1 Definition of a Complex Number........................................................................D1
Circuit Analysis I with MATLAB  Computing and Simulink / SimPowerSystems Modeling v
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