Engineering Electromagnetics

Preface
Introduction to Electromagnetics
	A Simple View of Electromagnetics
	Units
		Derived Units
		Supplementary Units
		Customary Units
		Prefixes
	Other Units and Measures
		Units of Information
		The Decibel (dB) and Its Use
Contents
Chapter 1: Vector Algebra
	1.1 Introduction
	1.2 Scalars and Vectors
		1.2.1 Magnitude and Direction of Vectors: The Unit Vector and Components of a Vector
		1.2.2 Vector Addition and Subtraction
		1.2.3 Vector Scaling
	1.3 Products of Vectors
		1.3.1 The Scalar Product
		1.3.2 The Vector Product
		1.3.3 Multiple Vector and Scalar Products
	1.4 Definition of Fields
		1.4.1 Scalar Fields
		1.4.2 Vector Fields
	1.5 Systems of Coordinates
		1.5.1 The Cartesian Coordinate System
		1.5.2 The Cylindrical Coordinate System
		1.5.3 The Spherical Coordinate System
		1.5.4 Transformation from Cylindrical to Spherical Coordinates
	1.6 Position Vectors
		Vectors and Scalars
		Addition and Subtraction of Vectors
		Sums and Scaling of Vectors
		Scalar and Vector Products
		Multiple Products
		Scalar and Vector Fields
		Systems of Coordinates
		Position Vectors
Chapter 2: Vector Calculus
	2.1 Introduction
	2.2 Integration of Scalar and Vector Functions
		2.2.1 Line Integrals
		2.2.2 Surface Integrals
		2.2.3 Volume Integrals
		2.2.4 Symbolic Versus Numerical Integration
	2.3 Differentiation of Scalar and Vector Functions
		2.3.1 The Gradient of a Scalar Function
			2.3.1.1 Gradient in Cylindrical Coordinates
			2.3.1.2 Gradient in Spherical Coordinates
		2.3.2 The Divergence of a Vector Field
			2.3.2.1 Divergence in Cartesian Coordinates
			2.3.2.2 Divergence in Cylindrical and Spherical Coordinates
		2.3.3 The Divergence Theorem
		2.3.4 Circulation of a Vector and the Curl
			2.3.4.1 Circulation of a Vector Field
		2.3.5 Stokes´ Theorem
	2.4 Conservative and Nonconservative Fields
	2.5 Null Vector Identities and Classification of Vector Fields
		2.5.1 The Helmholtz Theorem
		2.5.2 Second-Order Operators
		2.5.3 Other Vector Identities
		Surface Integrals (Closed and Open)
		Volume Integrals
		Other Regular Integrals
		The Gradient
		The Divergence
		The Divergence Theorem
		The Curl
		Stokes´ Theorem
		The Helmholtz Theorem and Vector Identities
Chapter 3: Coulomb´s Law and the Electric Field
	3.1 Introduction
	3.2 Charge and Charge Density
	3.3 Coulomb´s Law
	3.4 The Electric Field Intensity
		3.4.1 Electric Fields of Point Charges
			3.4.1.1 Superposition of Electric Fields
			3.4.1.2 Electric Field Lines
			3.4.1.3 The Electric Dipole
		3.4.2 Electric Fields of Charge Distributions
			3.4.2.1 Line Charge Distributions
			3.4.2.2 Surface Charge Distributions
			3.4.2.3 Volume Charge Distributions
	3.5 The Electric Flux Density and Electric Flux
	3.6 Applications
	3.7 Summary
		Point Charges, Forces and the Electric Field
		Line Charge Densities
		Surface Charge Densities
		Volume Charge Densities
		The Electric Flux Density
Chapter 4: Gauss´s Law and the Electric Potential
	4.1 Introduction
	4.2 The Electrostatic Field: Postulates
	4.3 Gauss´s Law
		4.3.1 Applications of Gauss´s Law
			4.3.1.1 Calculation of the Electric Field Intensity
			4.3.1.2 Calculation of Equivalent Charges
	4.4 The Electric Potential
		4.4.1 Electric Potential Due to Point Charges
		4.4.2 Electric Potential Due to Distributed Charges
		4.4.3 Calculation of Electric Field Intensity from Potential
	4.5 Materials in the Electric Field
		4.5.1 Conductors
			4.5.1.1 Electric Field at the Surface of a Conductor
		4.5.2 Dielectric Materials
		4.5.3 Polarization and the Polarization Vector
		4.5.4 Electric Flux Density and Permittivity
			4.5.4.1 Linearity, Homogeneity, and Isotropy
		4.5.5 Dielectric Strength
	4.6 Interface Conditions
		4.6.1 Interface Conditions Between Two Dielectrics
		4.6.2 Interface Conditions Between Dielectrics and Conductors
	4.7 Capacitance
		4.7.1 The Parallel Plate Capacitor
		4.7.2 Capacitance of Infinite Structures
		4.7.3 Connection of Capacitors
	4.8 Energy in the Electrostatic Field: Point and Distributed Charges
		4.8.1 Energy in the Electrostatic Field: Field Variables
		4.8.2 Forces in the Electrostatic Field: The Principle of Virtual Work
	4.9 Applications
	4.10 Summary
		Postulates
		Gauss´s Law: Calculation of Electric Field Intensity from Charge Distributions
		Gauss´s Law: Calculation of Equivalent Charge from the Electric Field Intensity
		Potential: Point and Distributed Charges
		Electric Field from Potential
		Conductors in the Electric Field
		Polarization
		Dielectric Strength
		Interface Conditions
		Capacitance
		Energy in the Electric Field
		Forces
Chapter 5: Boundary Value Problems: Analytic Methods of Solution
	5.1 Introduction
	5.2 Poisson´s Equation for the Electrostatic Field
	5.3 Laplace´s Equation for the Electrostatic Field
	5.4 Solution Methods
		5.4.1 Uniqueness of Solution
		5.4.2 Solution by Direct Integration
		5.4.3 The Method of Images
			5.4.3.1 Point and Line Charges
			5.4.3.2 Charged Line over a Conducting Plane
			5.4.3.3 Charges Between Parallel Planes
			5.4.3.4 Images in Curved Geometries
		5.4.4 Separation of Variables: Solution to Laplace´s Equation
			5.4.4.1 Separation of Variables in Cartesian Coordinates
			5.4.4.2 Separation of Variables in Cylindrical Coordinates
	5.5 Summary
		Laplace´s and Poisson´s Equations
		Direct Integration
		Method of Images: Point and Line Charges in Planar Configurations
		Method of Images: Multiple Planes
		Method of Images in Curved Geometries
		Separation of Variables in Planar Geometries
		Separation of Variables in Cylindrical Geometries
Chapter 6: Boundary Value Problems: Numerical (Approximate) Methods
	6.1 Introduction
		6.1.1 A Note on Scripts and Computer Programs
	6.2 The General Idea of Numerical Solutions
	6.3 The Finite Difference Method: Solution to the Laplace and Poisson Equations
		6.3.1 The Finite Difference Approximation: First-Order Derivative
		6.3.2 The Finite Difference Approximation: Second-Order Derivative
		6.3.3 Implementation
			6.3.3.1 Implicit Solution
			6.3.3.2 Explicit Solution
		6.3.4 Solution to Poisson´s Equation
	6.4 The Method of Moments: An Intuitive Approach
	6.5 The Finite Element Method: Introduction
		6.5.1 The Finite Element
			6.5.1.1 The Triangular Element
		6.5.2 Implementation of the Finite Element Method
			6.5.2.1 The Field Equations
			6.5.2.2 Discretization
			6.5.2.3 Minimization
			6.5.2.4 Assembly of the Elemental Matrices
			6.5.2.5 Application of Boundary Conditions
			6.5.2.6 Solution
	6.6 Summary
		Finite Differences
		Method of Moments
		Finite Elements
Chapter 7: The Steady Electric Current
	7.1 Introduction
	7.2 Conservation of Charge
	7.3 Conductors, Dielectrics, and Lossy Dielectrics
		7.3.1 Moving Charges in an Electric Field
		7.3.2 Convection Current and Convection Current Density
		7.3.3 Conduction Current and Conduction Current Density
	7.4 Ohm´s Law
	7.5 Power Dissipation and Joule´s Law
	7.6 The Continuity Equation and Kirchhoff´s Current Law
		7.6.1 Kirchhoff´s Current Law
	7.7 Current Density as a Field
		7.7.1 Sources of Steady Currents
		7.7.2 Kirchhoff´s Voltage Law
	7.8 Interface Conditions for Current Density
	7.9 Applications
	7.10 Summary
		Convection and Conduction Current
		Conductivity and Resistance
		Power Dissipation and Joule´s Law
		Continuity and Circuit Laws
		Interface Conditions
Chapter 8: The Static Magnetic Field
	8.1 Introduction
	8.2 The Magnetic Field, Magnetic Field Intensity, and Magnetic Flux Density
	8.3 The Biot-Savart Law
		8.3.1 Applications of the Biot-Savart Law to Distributed Currents
	8.4 Ampère´s Law
	8.5 Magnetic Flux Density and Magnetic Flux
	8.6 Postulates of the Static Magnetic Field
	8.7 Potential Functions
		8.7.1 The Magnetic Vector Potential
		8.7.2 The Magnetic Scalar Potential
	8.8 Applications
	8.9 Summary
		The Biot-Savart Law
		Ampère´s Law
		Ampère´s Law, Superposition
		Biot-Savart Law, Magnetic Vector Potential
		Magnetic Scalar Potential
Chapter 9: Magnetic Materials and Properties
	9.1 Introduction
	9.2 Magnetic Properties of Materials
		9.2.1 The Magnetic Dipole
		9.2.2 Magnetization: A Model of Magnetic Properties of Materials
		9.2.3 Behavior of Magnetic Materials
			9.2.3.1 Diamagnetic and Paramagnetic Materials
			9.2.3.2 Ferromagnetic Materials
			9.2.3.3 Other Magnetic Materials
	9.3 Magnetic Interface Conditions
		9.3.1 Interface Conditions for the Tangential and Normal Components of the Magnetic Field Intensity H
	9.4 Inductance and Inductors
		9.4.1 Inductance per Unit Length
		9.4.2 External and Internal Inductance
	9.5 Energy Stored in the Magnetic Field
		9.5.1 Magnetostatic Energy in Terms of Fields
	9.6 Magnetic Circuits
	9.7 Forces in the Magnetic Field
		9.7.1 Principle of Virtual Work: Energy in a Gap
	9.8 Torque
	9.9 Applications
	9.10 Summary
		Magnetic Dipoles and Magnetization
		Magnetic Interface Conditions
		Inductance
		Energy
		Magnetic Circuits
		Forces
		Torque
Chapter 10: Faraday´s Law and Induction
	10.1 Introduction
	10.2 Faraday´s Law
	10.3 Lenz´s Law
	10.4 Motional Electromotive Force: The DC Generator
	10.5 Induced emf Due to Transformer Action
	10.6 Combined Motional and Transformer Action Electromotive Force
		10.6.1 The Alternating Current Generator
	10.7 The Transformer
		10.7.1 The Ideal Transformer
		10.7.2 The Real Transformer: Finite Permeability
		10.7.3 The Real Transformer: Finite Permeability and Flux Leakage
	10.8 Eddy Currents
	10.9 Applications
	10.10 Summary
		Motional emf
		Induced emf
		Generator emf
		Transformers
Chapter 11: Maxwell´s Equations
	11.1 Introduction: The Electromagnetic Field
	11.2 Maxwell´s Equations
		11.2.1 Maxwell´s Equations in Differential Form
		11.2.2 Maxwell´s Equations in Integral Form
	11.3 Time-Dependent Potential Functions
		11.3.1 Scalar Potentials
		11.3.2 The Magnetic Vector Potential
		11.3.3 Other Potential Functions
	11.4 Interface Conditions for the Electromagnetic Field
		11.4.1 Interface Conditions for the Electric Field
		11.4.2 Interface Conditions for the Magnetic Field
	11.5 Particular Forms of Maxwell´s Equations
		11.5.1 Time-Harmonic Representation
		11.5.2 Maxwell´s Equations: The Time-Harmonic Form
		11.5.3 Source-Free Equations
	11.6 Summary
		Maxwell´s Equations, Displacement Current, and Continuity
		Maxwell´s Equations
		Potential Functions
		Interface Conditions for General Fields
		Time-Harmonic Equations/Phasors
Chapter 12: Electromagnetic Waves and Propagation
	12.1 Introduction
	12.2 The Wave
	12.3 The Electromagnetic Wave Equation and Its Solution
		12.3.1 The Time-Dependent Wave Equation
		12.3.2 Time-Harmonic Wave Equations
		12.3.3 Solution of the Wave Equation
		12.3.4 Solution for Uniform Plane Waves
		12.3.5 The One-Dimensional Wave Equation in Free-Space and Perfect Dielectrics
	12.4 The Electromagnetic Spectrum
	12.5 The Poynting Theorem and Electromagnetic Power
	12.6 The Complex Poynting Vector
	12.7 Propagation of Plane Waves in Materials
		12.7.1 Propagation of Plane Waves in Lossy Dielectrics
		12.7.2 Propagation of Plane Waves in Low-Loss Dielectrics
		12.7.3 Propagation of Plane Waves in Conductors
		12.7.4 The Speed of Propagation of Waves and Dispersion
			12.7.4.1 Group Velocity
			12.7.4.2 Velocity of Energy Transport
			12.7.4.3 Dispersion
	12.8 Polarization of Plane Waves
		12.8.1 Linear Polarization
		12.8.2 Elliptical and Circular Polarization
	12.9 Applications
	12.10 Summary
		The Time-Dependent Wave Equation
		The Time-Harmonic Wave Equation
		Solution for Uniform Plane Waves
		The Poynting Vector
		Propagation in Lossless, Low-Loss, and Lossy Dielectrics
		Propagation in High-Loss Dielectrics and Conductors
		Dispersion and Group Velocity
		Polarization of Plane Waves
Chapter 13: Reflection and Transmission of Plane Waves
	13.1 Introduction
	13.2 Reflection and Transmission at a General Dielectric Interface: Normal Incidence
		13.2.1 Reflection and Transmission at an Air-Lossy Dielectric Interface: Normal Incidence
		13.2.2 Reflection and Transmission at an Air-Lossless Dielectric Interface: Normal Incidence
		13.2.3 Reflection and Transmission at an Air-Conductor Interface: Normal Incidence
	13.3 Reflection and Transmission at an Interface: Oblique Incidence on a Perfect Conductor
		13.3.1 Oblique Incidence on a Perfectly Conducting Interface: Perpendicular Polarization
		13.3.2 Oblique Incidence on a Perfectly Conducting Interface: Parallel Polarization
	13.4 Oblique Incidence on Dielectric Interfaces
		13.4.1 Oblique Incidence on a Dielectric Interface: Perpendicular Polarization
		13.4.2 Oblique Incidence on a Dielectric Interface: Parallel Polarization
		13.4.3 Brewster´s Angle
			13.4.3.1 Brewster´s Angle for Parallel Polarization
			13.4.3.2 Brewster´s Angle for Perpendicular Polarization
		13.4.4 Total Reflection
	13.5 Reflection and Transmission for Layered Materials at Normal Incidence
	13.6 Applications
	13.7 Summary
		Reflection and Transmission at a General Dielectric Interface: Normal Incidence
		Reflection and Transmission at a Dielectric Conductor Interface: Normal Incidence
		Oblique incidence on a Conducting Interface: Perpendicular Polarization
		Oblique Incidence on a Conducting Interface, Parallel Polarization
		Parallel and Perpendicular Polarization in Dielectrics
		Brewster's Angle
		Total Reflection
		Reflection and Transmission for Lossy and Lossless Dielectric Slabs at Normal Incidence
		Reflection and Transmission for a Dielectric Slab Backed by a Perfect Conductor: Normal Incidence
Chapter 14: Theory of Transmission Lines
	14.1 Introduction
	14.2 The Transmission Line
	14.3 Transmission Line Parameters
		14.3.1 Calculation of Line Parameters
			14.3.1.1 Resistance per Unit Length
			14.3.1.2 Inductance per Unit Length
			14.3.1.3 Capacitance per Unit Length
			14.3.1.4 Conductance per Unit Length
	14.4 The Transmission Line Equations
	14.5 Types of Transmission Lines
		14.5.1 The Lossless Transmission Line
		14.5.2 The Long Transmission Line
		14.5.3 The Distortionless Transmission Line
		14.5.4 The Low-Resistance Transmission Line
	14.6 The Field Approach to Transmission Lines
	14.7 Finite Transmission Lines
		14.7.1 The Load Reflection Coefficient
		14.7.2 Line Impedance and the Generalized Reflection Coefficient
		14.7.3 The Lossless, Terminated Transmission Line
		14.7.4 The Lossless, Matched Transmission Line
		14.7.5 The Lossless, Shorted Transmission Line
		14.7.6 The Lossless, Open Transmission Line
		14.7.7 The Lossless, Resistively Loaded Transmission Line
	14.8 Power Relations on a General Transmission Line
	14.9 Resonant Transmission Line Circuits
	14.10 Applications
	14.11 Summary
		Transmission Line Parameters
		Long, Lossless Lines
		The Distortionless Transmission Line
		The Low-Resistance Transmission Line
		The Field Approach to Transmission Lines
		Finite Transmission Lines
		Line Impedance, Reflection Coefficient, Etc
		Shorted and Open Transmission Lines
		Resistive Loads on Transmission Lines
		Capacitive and Inductive Loads on Transmission Lines
		Power Relations on Transmission Lines
		Resonant Transmission Lines
Chapter 15: The Smith Chart, Impedance Matching, and Transmission Line Circuits
	15.1 Introduction
	15.2 The Smith Chart
	15.3 The Smith Chart as an Admittance Chart
	15.4 Impedance Matching and the Smith Chart
		15.4.1 Impedance Matching
		15.4.2 Stub Matching
			15.4.2.1 Single Stub Matching
			15.4.2.2 Double Stub Matching
	15.5 Quarter-Wavelength Transformer Matching
	15.6 Summary
		General Design Using the Smith Chart
		Stub Matching
		Transformer Matching
Chapter 16: Transients on Transmission Lines
	16.1 Introduction
	16.2 Propagation of Narrow Pulses on Finite, Lossless Transmission Lines
	16.3 Propagation of Narrow Pulses on Finite, Distortionless Transmission Lines
	16.4 Transients on Transmission Lines: Long Pulses
	16.5 Transients on Transmission Lines: Finite-Length Pulses
	16.6 Reflections from Discontinuities
	16.7 Transients on Lines with Reactive Loading
		16.7.1 Capacitive Loading
		16.7.2 Inductive Loading
	16.8 Initial Conditions on Transmission Lines
	16.9 Summary
		Propagation of Narrow Pulses on Finite, Lossless, and Lossy Transmission Lines
		Transients on Transmission Lines: Long Pulses
		Transients on Transmission Lines: Finite-Length Pulses
		Reflections from Discontinuities
		Reactive Loading
		Initially Charged Lines
		Time Domain Reflectometry
Chapter 17: Waveguides and Resonators
	17.1 Introduction
	17.2 The Concept of a Waveguide
	17.3 Transverse Electromagnetic, Transverse Electric, and Transverse Magnetic Waves
		17.3.1 Transverse Electromagnetic Waves
		17.3.2 Transverse Electric (TE) Waves
		17.3.3 Transverse Magnetic (TM) Waves
	17.4 TE Propagation in Parallel Plate Waveguides
	17.5 TM Propagation in Parallel Plate Waveguides
	17.6 TEM Waves in Parallel Plate Waveguides
	17.7 Rectangular Waveguides
		17.7.1 TM Modes in Rectangular Waveguides
		17.7.2 TE Modes in Rectangular Waveguides
		17.7.3 Attenuation and Losses in Rectangular Waveguides
			17.7.3.1 Dielectric Losses
			17.7.3.2 Wall Losses
			17.7.3.3 Attenuation Below Cutoff
	17.8 Other Waveguides
	17.9 Cavity Resonators
		17.9.1 TM Modes in Cavity Resonators
		17.9.2 TE Modes in Cavity Resonators
	17.10 Energy Relations in a Cavity Resonator
	17.11 Quality Factor of a Cavity Resonator
	17.12 Applications
	17.13 Summary
		TE, TM, and TEM Propagation in Parallel Plate Waveguides
		TM/TE Modes in Rectangular Waveguides
		Attenuation and Losses in Rectangular Waveguides
		Cavity Resonators
Chapter 18: Antennas and Electromagnetic Radiation
	18.1 Introduction
	18.2 Electromagnetic Radiation and Radiation Safety
	18.3 Antennas
	18.4 The Electric Dipole
		18.4.1 The Near Field
		18.4.2 The Far Field
	18.5 Properties of Antennas
		18.5.1 Radiated Power
		18.5.2 Radiation Resistance
		18.5.3 Antenna Radiation Patterns
			18.5.3.1 Planar Antenna Radiation Pattern Plots
			18.5.3.2 Rectangular Radiation Pattern Plots
			18.5.3.3 Beamwidth
		18.5.4 Radiation Intensity and Average Radiation Intensity
		18.5.5 Antenna Directivity
		18.5.6 Antenna Gain and Radiation Efficiency
	18.6 The Magnetic Dipole
		18.6.1 Near Fields for the Magnetic Dipole
		18.6.2 Far Fields for the Magnetic Dipole
		18.6.3 Properties of the Magnetic Dipole
	18.7 Practical Antennas
		18.7.1 Linear Antennas of Arbitrary Length
			18.7.1.1 The Half-Wavelength Dipole Antenna
			18.7.1.2 Full- and Three-Halves-Wavelength Antennas
		18.7.2 The Monopole Antenna
	18.8 Antenna Arrays
		18.8.1 The Two-Element Array
			18.8.1.1 Two Element Parallel Antennas Array
			18.8.1.2 Two Element Colinear Antennas Array
		18.8.2 The n-Element Linear Array
	18.9 Reciprocity and Receiving Antennas
	18.10 Effective Aperture
	18.11 The Radar
		18.11.1 Types of Radar
	18.12 Other Antennas
	18.13 Applications
	18.14 Summary
		Fields of the Short Dipole-Hertzian Dipole (see Figure 18.3)
		Magnetic Dipole (Small-Loop Antenna, radius λ): See Figure 18.10
		Radar and Radar Cross Section
		Hertzian Dipole
		Magnetic Dipole
		Linear Antennas of Arbitrary Length
		The Half-Wave Dipole Antenna
		Various Length Dipole Antennas
		The Monopole Antenna
		Two-Element Image Antennas
		The n-Element Linear Array
		Reciprocity and Receiving Antennas
		Radar
Answers
	Chapter 1
	Chapter 2
	Chapter 3
	Chapter 4
	Chapter 5
	Chapter 6
	Chapter 7
	Chapter 8
	Chapter 9
	Chapter 10
	Chapter 11
	Chapter 12
	Chapter 13
	Chapter 14
	Chapter 15
	Chapter 16
	Chapter 17
	Chapter 18
Appendix: Summary of Vector Relations and Physical Constants
	Gradient, Divergence, Curl, and the Laplacian in Various Coordinates
Index