Practical Electromagnetics: From Biomedical Sciences to Wireless Communication

517 Pages·2006·8.688 MB·English

by  Devendra K. Misra

PRACTICAL
ELECTROMAGNETICS

PRACTICAL
ELECTROMAGNETICS
FROM BIOMEDICAL SCIENCES
TO WIRELESS COMMUNICATION
DEVENDRA K. MISRA
University ofWisconsin —Milwaukee
Milwaukee,Wisconsin
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LibraryofCongressCataloging-in-PublicationData:
Misra,Devendra,1949-
Practicalelectromagnetics:frombiomedicalsciencestowireless
communication/byDevendraK.Misra
p.cm.
Includesbibliographicalreferencesandindex.
ISBN-130-471-74865-6
ISBN-100-471-74865-X(acid-freepaper)
1. Electromagnetism--Textbooks. I. Title.
QC760.2.M572006
537--dc22 2006008776
PrintedintheUnitedStatesofAmerica
10 9 8 7 6 5 4 3 2 1
CONTENTS
PREFACE ix
1 Introduction 1
1.1 Electrical Sourcesand Fundamental Quantities, 2
1.2 Static and Dynamic Fields, 5
1.3 Workingwith ComplexNumbers andFunctions, 10
Problems, 18
2 Vectors and Fields 19
2.1 Workingwith Vectors, 20
2.2 Coordinate Systems, 35
2.3 Differentiation andIntegration ofVectors, 44
2.4 Gradient ofthe Scalar Field, 53
2.5 Divergence ofthe Vector Field, 59
2.6 CURL of the Vector Field, 61
2.7 The Divergence Theorem, 65
2.8 StokesTheorem, 70
2.9 Other Operations Involving r, 73
2.10 Helmholtz Theorem, 74
Problems, 75
3 Basic Laws of Electromagnetics 80
3.1 Maxwell’s Equations in Large-Scale orIntegral Form, 81
3.2 Maxwell’s Equations in Point or Differential Form, 92
v
vi CONTENTS
3.3 Constitutive Relations, 96
3.4 Boundary Conditions, 99
3.5 Lorentz’sForce Equation, 102
3.6 Poynting’s Vector andPower Flow, 119
Problems, 127
4 Uniform Plane Waves 132
4.1 Wave Equation and Uniform Plane Wave Solutions, 132
4.2 Plane Electromagnetic Waves inLossyMedia, 149
4.3 Uniform Plane Wave Incident Normally on anInterface, 155
4.4 Uniform Plane Wave Incident Obliquelyon an Interface, 166
Problems, 177
5 TransmissionLines 185
5.1 Transmission Line Equations, 186
5.2 Finite Length TransmissionLine, 194
5.3 Smith Chart, 212
5.4 Transients on Transmission Lines, 222
Problems, 229
6 Modified Maxwell’s Equationsand Potential Functions 233
6.1 MagneticCharge andCurrent, 233
6.2 MagneticVector and Electric Scalar Potentials, 235
6.3 Electric Vector and Magnetic Scalar Potentials, 237
6.4 Constructionof aSolution inRectangular Coordinates, 238
6.5 Constructionof aSolution inCylindrical Coordinates, 253
6.6 Constructionof aSolution inSphericalCoordinates, 262
Problems, 270
7 Source inInfinite Space 271
7.1 Fields ofan Infinitesimal Source, 271
7.2 Antenna Parameters, 277
7.3 Linear Antennas, 286
7.4 Antenna Arrays, 290
7.5 FRIIS Transmission Formula and the Radar RangeEquation, 300
Problems, 307
8 Electrostatic Fields 310
8.1 Laws of Electrostatic Fields, 310
8.2 Gauss’sLaw, 316
8.3 Poisson’s andLaplace’s Equations, 317
8.4 Capacitorsand Energy Storage, 319
8.5 Further Applications ofPoisson’s and Laplace’sEquations, 332
Problems, 343
CONTENTS vii
9 Magnetostatic Fields 346
9.1 Laws of Magnetostatic Fields, 346
9.2 Inductors andEnergy Storage, 357
9.3 MagneticMaterials, 369
9.4 MagneticCircuits, 373
Problems, 378
10 Waveguidesand Cavity Resonators 380
10.1 MetallicRectangular Waveguide, 380
10.2 MetallicCircular Waveguide, 394
10.3 Rectangular Cavity Resonators, 399
10.4 CircularCylindrical Cavity Resonators, 405
Problems, 412
11 Numerical Techniques 414
11.1 Finite-Difference Methods, 415
11.2 Method of Moments, 446
11.3 Scattering ofPlanarEM WavesFrom an
InfinitelyLong Cylinder, 453
Problems, 462
AppendixA MathematicalFormulas 464
AppendixB Delta Functionand Evaluation ofFieldsin
Unbounded Media 471
AppendixC Bessel Functions 479
AppendixD Legendre Functions 488
AppendixE Characteristics of Selected Materials 493
AppendixF Physical Constants 495
AppendixG Decibels and Neper 496
AppendixH Nomenclature and Characteristics ofStandard
RectangularWaveguides 498
Selected Reference Books 500
Index 503
PREFACE
Electromagnetic fields is one of the classical disciplines that has been around for
some time. However, still today new scientific and technological applications in
this area keep on growing. Therefore electromagnetic fields is a core subject not
only for electrical engineering and physics majors, but also for students coming
from many other disciplines. There are a number of excellent textbooks that were
developed to meet the requirements of traditional curricula. These are mostly
suited for introductory one- and two-semester sequences in electrical engineering
or physics programs. Since many of the new areas developed lately warrant
integrationintotheelectricalengineeringcurriculum,itisoftendifficulttoaccom-
modateatraditionaltwo-semestersequenceinelectromagneticfieldsalongwiththe
suitableprerequisitecourses.Furtherthereisalmostnoroomleftforanupper-level
coursethatincludessomecontemporaryapplicationsofelectromagneticfields.This
bookis attempting toaddress these issues.
The subject matter of this book is arranged such that it is suitable for students
with the basic calculus and basic physics that are required at the college level.
After a brief review of the fundamental units and prefixes, electrical sources and
fundamentalquantitiesareintroducedinChapter1.Thisisfollowedbythecharac-
teristics of sinusoidal waves. A working introduction of complex numbers is also
included in this chapter. Chapter 2 begins with the definitions of vectors and
the manipulation techniques of vectors in rectangular, cylindrical, and spherical
coordinates. The concepts of scalar and vector fields are introduced. Vector
calculus is briefly reviewed along with the gradient of scalar fields, and the
divergence and curl of vector fields. The relevant theorems are covered as well in
thischapter.
ix
x PREFACE
Maxwell’s equations in their large-scale form are introduced in Chapter 3 as
experimental facts expressed mathematically. A number of examples are used to
illustratetheirimportance.Afterintroducingtheequationofcontinuity,Maxwell’s
equationsinpointformarefoundviathedivergenceandStokestheorems.Sections
on the constitutive relations andthe boundary conditions follow. The chapter ends
withintroductionsoftheLorentzforceequationandthePoyntingtheorem.Chapter
4presentsthepropagationcharacteristicsofuniformplanewavesalongwithsome
simple applications. The formulation of Helmholtz’s equation is summarized and
used in the construction of uniform plane waves propagating in various media of
infinite extent. The concepts of reflection and transmission of these waves at an
interface with another medium are alsodiscussed inthis chapter.
Chapter 5 begins with the fundamentals of signal propagation in frequency
domain. The Smith chart technique is presented for analyzing transmission line
circuits.Thischapterconcludeswithanintroductiontotime-domainanalysisofsig-
nalstravelingonatransmissionline.Theconceptsofmagneticcharge andcurrent
are the subject of Chapter 6. After a brief discussion of the modified Maxwell
equations, vector and scalar potentials are introduced. The techniques covered
in this chapter are used to construct solutions of electromagnetic problems in
rectangular, cylindrical, and spherical coordinate systems.
Chapter 7 begins with an analysis of electromagnetic fields produced by an
infinitesimal current element in an unbounded medium. After a discussion of
antennaparameters,theradiationbehaviorofalinearantennaispresented.Follow-
ing this, the concepts of antenna arrays are presented along with broadside and
end-fire arrays. This chapter includes a section on the Friis transmission formula
and the radarrange equation.
Electrostatic and magnetostatic fields are considered in Chapters 8 and 9 as a
specialcaseoftime-varyingelectricalsources.Anumberofelectrostaticproblems
are analyzed via Poisson’s and Laplace’s equations. Energy storage in electrical
capacitors and inductorsis introduced along with a fewapplication examples.The
fundamentals of magnetic materials and the magnetic circuits are also discussed
in Chapter 9.
FurtherapplicationsofthesolutiontechniquesofChapter6arefoundinChapter
10wherethesignalpropagationisstudiedincylindricalwaveguidesofrectangular
andcircularcrosssections.Thischapterincludessectionsonrectangularandcircu-
lar cylindrical cavity resonators. Chapter 11, the last chapter of this book briefly
explainstwowidelyusednumericaltechniquestosolveelectromagneticproblems.
Theconceptsoffinitedifferenceareillustratedbyafewsimpleexamples.Asection
on the method of moments is included in this chapter. The problem formulation
required for the method of moments is the topic of the last section of this chapter,
and it covers the scattering of a planar electromagnetic wave from a conducting
cylinder aswell.
There are eight appendixes providing relevant mathematical formulas, Bessel
functions, and Legendre functions. An appendix is also devoted to the concept of
the delta function along with its application in finding electromagnetic fields in an
unboundedmedium.
PREFACE xi
Some ofthe highlightsof the book are asfollows:
Thefundamentalsofcomplexnumbersandvectoranalysisarepresentedatthe
.
beginning along with a number of solved examples. Readers already familiar
with these topics can easily skip the first twochapters.
Maxwell’s equations are introduced early in Chapter 3 as mathematical rep-
.
resentationsofexperiments.Afterabriefpresentationofconstitutiverelations
andboundaryconditions,theLorentzforceequationisintroduced.Anumberof
examplesare used toillustrate applications ofthe various formulas.
Uniform plane waves are presented in Chapter 4. The chapter includes a
.
number ofsimpleapplication examples.
Transmission line circuits are presented in Chapter 5. This discussion can be
.
easilymovedtothebeginningofasemester’sworkifaninstructorprefersthat.
Therestofthematerialcanbeusedforupperleveltechnicalelectiveorabegin-
.
ning graduate level courses. Also the last section of Chapter 4 can be easily
replaced with Chapters 8 and 9 inafirst course.
There are some 170 fully solved examples that are closely connected to the
.
material presented in each chapter. The book includes over 225 practice
problems aswell.
ACKNOWLEDGMENTS
So many scientists, mathematicians, and engineers have enriched my studies of
electromagnetic fields over the years that it is not possible to list everyone here in
this short space. I have benefited also from many researchers and professionals
working in this area. I gratefully acknowledge the contributions of each and every
oneofthemfortheirgenerosityandkindness.AlsoIwouldliketothanktheanon-
ymousreviewerswhoprovidedseveralvaluablesuggestions.Ideeplyappreciatethe
support I received from my wife, Ila, son, Shashank, and daughter-in-law, Julie,
duringthecourseofthisproject.Thisprojectgotstartedbecauseoftheenthusiastic
support I received from Val Moliere and her staff at Wiley. I feel fortunate for
continued current support from Paul Petralia and his assistant WhitneyA. Lesch.
DEVENDRA K. MISRA
UniversityofWisconsin—Milwaukee