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Chapter I - Transient and Harmonic Analysis of Linear Systems

Introduction

Time Domain and Frequency Domain

States and Languages

Phasors and Frequency Domain (Harmonic) Analysis

Addition and Subtraction

Multiplication by a “real” Constant

Time Derivatives

Electric Power in Time Harmonic Circuits

Use of Phasors in Circuit Analysis

Demonstration of Circuit Analysis in the Frequency Domain

Starting with the time domain form

Starting with the frequency domain form

The Frequency Domain and the Laplace Transform

Addendum: The Mystery of j and Imaginary Numbers

Chapter II - Transmission Lines - Wave Equations

Transmission Lines Overview

Transmission Line Analysis (Theory)

Circuit Theory Analysis of a Two Conductor Controlled Geometry TL

RLGC Model

Transmission Line Circuit Analysis Using the Distributed RLGC Model

Steady-State Harmonic Analysis

Physical Implications of Solution Parameters

Two Special Cases: The Infinite Line and the Matched Load Line

Standing Waves and Standing Wave Ratio

Standing Waves and the Bounce Diagram

The Issues of Reflections and Standing Waves

Power Delivery

Signal Delivery

Combined Power and Signal Delivery Constraints

Addendum A: Driving Point Impedance

TL Driving Point Impedance and Input Impedance

Some Special Cases

Addendum B: Impedance Matching

How to Achieve Matching

L-PI-T Matching Networks

Stub Matching

The Quarter Wave Transformer as a Matching Network

The Half Wave Transformer as a Matching Network

Addendum C: The Bounce Diagram in Frequency Domain

Addendum D: The Time Domain Bounce Diagram

Time Domain Bounce Diagram for Lossless Lines and Resistive Discontinuities

Time Domain Reflectometry and the Bounce Diagram

Time-Domain Reflectometry for Ideal Step Waveform Excitations

Time-Domain Reflectometry for Ideal Dirac-Delta Impulse Waveform Excitations

Addendum E: The Smith Chart

Scales on the Smith Chart

The magnitude of the reflection coefficient (|Γ|) scale

The phase angle of the reflection coefficient (/Γ) scale

Normalized distance moved scale

Transmission Line Trace on the Smith Chart

Case of Lossless TL, α=0

Case of Lossy TL, α≠0

How Does the Smith Chart Work?

The Admittance Smith chart

Smith chart Features and Short Cuts

Matching using the Smith Chart

Chapter III - Transition to Electrostatics

Introduction

Why study EM

RLCG, Models and Parasitics

Addendum A: Review of coordinate systems

Cartesian, Cylindrical, and Spherical

Differential elements in coordinate systems

Length, area, and volume increments

Unit vectors in different coordinate systems

Relationships between coordinate systems

Addendum B: Review of vector Calculus

Vector Definition and Examples

Vector Representations in Coordinate Systems

Vector Operations

Addendum C: Spatial Distributions and DensitiesStatic Quantities

Static Distributions and Densities

Dynamic Distributions and Densities

Concentrations, Line, Area, and Volume Distributions

Conversions between density expressions

Addendum D: Line, Surface, and Volume Integrations

Integrating vector quantities

Integrating scalar quantities

Chapter IV - Electrostatic Fields – The Electric Flux and Gauss’ Law

The Electric Charge

Electric Flux

Electric Flux Density

Gauss’ Law – The Integral form

Application of Gauss’ Law in the Integral Form - Electric flux due to symmetrical charge distributions

Gauss’ Law in the Point Form (Differential Form)

Point form vs Integral Form

Cartesian coordinates Differential form of Gauss’ Law

The Divergence Theorem

Application of Gauss’ Law in the Point Form

Addendum A: Application of the Integral Form of Gauss’ Law to Symmetrical Charge Distributions     

Electric flux distributions for charges of spherical symmetries

Case of point charge located at the origin

Case of spherical surface charge distribution

Case of spherical shell charge distribution

Case of spherical volume charge distribution

Electric flux distributions for charges of cylindrical symmetries

Case of an infinite line charge uniformly stretched along the z-axis

Case of an infinite height cylindrical surface charge distribution

Case of a cylindrical shell of charge distribution with infinite height

Case of “full” cylindrical charge distribution with infinite height

Electric flux distributions for charges of planar symmetries

Case of Planar Surface Charge distribution

Case of Planar “slab” of charge distribution

Flux Density Distribution in some Familiar Combinations of Symmetrical Charge Distributions  

Two concentric spherical surfaces (Spherical Capacitor)

Two coaxial cylindrical surfaces (Coaxial Capacitor)

Two parallel planar surfaces (Parallel Plate Capacitor)

Chapter V - Electric Force, Field, Energy, and Potential

Introduction

Coulomb’s Forces

The Electric Field

Electric Field Evaluation using the “Incrementation” Scheme

Electric Field due to Famous Examples of Charge Distributions

Case of Charges distributed uniformly in a finite length straight line

Case of Charges distributed uniformly in an infinite length straight line

Energy in a System of Charges

Examples of Energy in a system of charges

Energy in a System of Point Charges

Energy in other forms of charge distributions

The Electric Potential

The Electric Potential due to the field of a point charge

Potential Gradient

Electric Potential Evaluation using the “Incrementation” Scheme

Conservative Nature of Electrostatic Potential

Energy Density in Electrostatic Fields

Addendum A: Electric Field due to Famous Examples of Charge Distributions

Charges distributed uniformly in a circular ring

Charges distributed uniformly in a circular disc

Alternative integration approaches to the finite disc case

Charges distributed uniformly in an infinitely extended sheet of charges

Important Remark

Addendum B: Electric Potential (and Field) due to Famous Examples of Charge Distributions

Charges distributed uniformly in a circular ring

Charges distributed uniformly in a circular disc

Electric Dipole (field and potential)

Chapter VI - Materials: Conductors and Dielectrics

Conductors

Conductors under static conditions

Conductors under dynamic conditions

Electric Current, Current Densities, and Resistance

Line, Surface, and Volume Current

Linear Density of Surface Current

Surface Density of Volume Current

Ohm’s Law

Dielectrics

Polarization Vector

Bound charge volumetric density: Surface density: Volumetric energy density

Energy stored

Capacitance

Parallel Plate capacitance

Coaxial TL capacitance

Boundary Conditions

Dielectric‐ Dielectric

Conductor‐Conductor

Conductor‐Dielectric

Resistors and Capacitors as Circuit Elements

Chapter VII - Poisson’s and Laplace’s Equations:
Uniqueness Theorem and Graphical and Numerical Solutions

Introduction

Poisson’s and Laplace’s Equations

The Laplacian Operator

Demonstration of solving Poisson’s Equation

Solving Poisson’s Equation for non-symmetrical Charge Distributions

Addendum A: The Method of Images

Uniqueness Theorem

The Uniqueness Theorem for Poisson's equation

Examples of the Use of the Method of Images

Addendum B: Further insight into the Uniqueness Theorem

Addendum C: Numerical Methods

Introduction

Numerical Analysis of Electrostatic Problems

Demonstration of Numerical Solution of Laplace’s Equation in 2D Problems

Demonstration of Iterative Solution of Laplace’s Equation in 2-D

Graphical Methods

Field Intensity and Flux Density Evaluation

Capacitance Evaluation

Chapter VIII - Magnetic Fields and Flux

Magnetostatics – Basic Laws

Ampere’s Law for Magnetic Force

Biot‐Savart Law: Magnetic Field Intensity and Magnetic Flux Density

The Magnetic Flux and Gauss’ Law for Magnetism

Ampere’s Circuital Law

Magnetic Field Evaluation Using the “Incrementation” Scheme and Biot‐Savart Law     

A finite length thin straight current‐carrying conductor

An infinite length thin straight current‐carrying conductor

A thin circular current‐carrying (loop) conductor

A finite height circular solenoid

Magnetic Field Evaluation Using Ampere's Circuital Law Scheme

Cylindrical (axial/coaxial) symmetries

An infinite length thin straight current‐carrying conductor

An infinite length thick straight current‐carrying conductor

An infinite length coaxial transmission line

Planar symmetries

An infinite extension thin current sheet

Toroidal & Solenoidal symmetries

Toroid

An infinite height solenoid

Magnetostatic Differential (Point) Forms

Point form of Gauss’ Law in Magnetism

Point form of Ampere’s Circuital Law

The Curl

Stoke’s Theorem

Static Form of Maxwell’s Equations

Scalar and Vector Magnetic Potential

Electrostatic – Magnetostatic Analogies

Chapter IX - Magnetic Material, Magnetic Circuits,  and Inductance

Magnetic Force and Torque

Magnetic force on moving charge

Magnetic force and torque on current loop

Energy storage in magnetic fields

Magnetic Properties of Materials

Dipole Moments and Magnetization Vector

Paramagnetism

Diamagnetism

Ferromagnetism

Residual magnetism and permanent magnets

Magnetic Boundary Conditions

Interface between two different magnetic materials

Interface between two nonmagnetic materials

Interface between nonmagnetic and magnetic materials

Magnetic flux confinement in magnetic materials

Magnetic Circuits

Magnetic circuit analysis using the electrical circuit analogy

Magnetic reluctance

Examples of magnetic circuit analysis

Inductance

Flux‐Linkage

Self and mutual inductances

Inductance relationship to reluctance

Energy stored in inductances

Addendum A: Evaluation of Self‐Inductance

Inductance evaluation using flux‐linkage

Inductance evaluation using magnetic reluctance

Inductance evaluation using magnetic energy storage

Examples of self‐inductance evaluation

Addendum B: Evaluation of Mutual Inductance

Mutual Inductance evaluation using flux‐linkage

Mutual Inductance evaluation using magnetic reluctance

Examples of mutual inductance evaluation

Addendum C: Magnetic Forces in Air Gaps: Magnetic Pull

Magnetic Forces in Air Gaps

Magnetic Lift

Examples of permanent magnet circuit analysis

Chapter X - Time‐Varying Fields – Faraday’s law

Introduction

Charge Trajectory in Magnetic Fields

Hall Effect

Faraday’s Law

Faraday’s Disk

An Example of a moving conductor in a time‐varying magnetic field

The Electric Generator

The Transformer

Faraday’s Maxwell’s Equation

Integral Form

Differential Form

Revisiting Field and Potential Formulae

Revisiting Ampere’s law – The Displacement Current

Revisiting Field and Potential Formulae: The Retarded Potentials

Derivation and justifications for the time‐varying modifications of the above field and potential relationships      

Summary of Maxwell’s Equations

Addendum A: Inductance under Time‐Varying Currents

Current‐Voltage relationship

Inductances in series and parallel

Energy stored and power in inductances

Energy stored in magnetic fields

Chapter XI - Wave Propagation - Transmission Lines Revisited

Introduction

Maxwell’s Equations and the Wave Equation

Solving the wave equation

Physical insight in the obtained wave equation solution

Source‐Free case of lossless media (perfect dielectric)

Case of Source‐Free lossy media σ≠0 (general material properties)

Special Cases (nonmagnetic)

Physical Insight into the Obtained Solutions for Wave Propagation Parameters in Dielectrics and Conductors       

Plane Waves in Good Dielectric

Uniform Plane Waves in Good Conductor

Poynting Vector ‐ Poynting Theorem

The Complex Poynting Theorem

The Complex Poynting Vector

Plane Waves Power Flow

Plane Waves in Controlled‐Geometry Transmission Lines

Case of Coaxial Line

Power Flow in Coaxial Lines

Important Observation

Electromagnetic Power Flows in Dielectric Media

Conductors provide Guidance (and Confinement)

Addendum A: Derivation of the Wave Equation’s Laplacian Form

Addendum B: Skin Effect and Shielding

Addendum C: Skin Effect in Coaxial Transmission Lines

High Frequency Coaxial Line Parameters

Addendum D: Loss Tangent for Energy‐Storage Media (Materials) & Devices

Chapter XII - Wave Polarization and Propagation in Multiple layers

Introduction

Wave Polarization

Linear Polarization

Circular Polarization

Elliptical Polarization

Physical Insight

Transmission and Reflection of Uniform Plane Waves in Multi‐Layer Media

Transmission and Reflection of Uniform Plane Waves: Normal Incidence

Case of two perfect dielectrics

Case of two lossy dielectrics

Case of a dielectric‐conductor interface

Reflection of Uniform Plane Waves: Normal Incidence on Multiple Layers

The Field Analysis Approach for Normal Incidence on Multiple Layers

Reflection of Uniform Plane Waves: Oblique Incidence

Total Reflection: Critical Angle

Physical Insight

Analysis of Wave Reflection and Refraction for Oblique Incidence

Case of Oblique Incidence with Parallel Polarization

Case of Oblique Incidence with Perpendicular Polarization

The Brewster Angle

Physical Insight

Addendum A: Derivation of Reflection and Transmission Coefficients for Normal Incidence on Multiple Layers              

The impedance approach

The bounce diagram approach

Addendum B: Derivation of Snell’s Law

Graphical Derivation of Snell’s Law

Wave Propagation Derivation of Snell’s Law

Addendum C: Total Reflection: Physical Applications

Addendum D: Derivation of Brewster Angle Expressions

Brewster Angle for the Parallel Polarization Case

Brewster Angle for the Perpendicular Polarization Case

Addendum E: The “Complex” Snell’s Law and the Mystery of the “Complex” Angle of Refraction

Oblique Incidence: the Case of Perfect Dielectric Interface to a Lossy Dielectric

Low Loss Approximations

Numerical Demonstration

Chapter XIII - Waveguides

Introduction

Why Waveguides

Typical Waveguide Configurations

Field Analysis of Guide Filling/Core Region

Metallic Rectangular Waveguides

Modes and Cut‐off Frequencies

Propagations Modes vs Cut‐off Modes

Physical Insight: Guide Wavelength & Phase Velocity

Continuation of the field analysis

Waveguides and TEM Modes

Transverse Electric, TE, Modes  

Example of TE modes: TE10 mode

Transverse Magnetic, TM, Modes

Example of TM modes: TM11 mode

Waveguide Impedance

Active and Dominant Mode Identification

Wave Propagation: Power Flow

Power Flow for the TE10 Dominant Mode

Time domain derivation of the power flow density for the TE10 mode

A Physical View of Wave Propagation and Power Flow in Waveguides

Modal Dispersion and Waveguide Bandwidth

Addendum A: Wave Equation Solution for Metallic Rectangular Waveguides: The Longitudinal Component of the Electric Field Phasor  

(Metallic) Rectangular Waveguides

Solution of the Generic Wave Equation

Addendum B: Can the phase velocity exceed the velocity of light?

Phase Velocity

Group Velocity

Alternate definition and derivation of the group velocity

Physical Insight: Can the Phase Velocity Exceed the Velocity of Light?

Addendum C: Wave Equation Solution for Metallic Rectangular Waveguides: Continuation for All Field Components    

Continuation of the Field Analysis

Addendum D: Field Maps for the TE10 and TM11 Modes

Field Maps for the TE10 Mode

Field Maps for the TM11 Mode

Addendum E: Active and Dominant Mode Identification

TheTabulation Approach for Mode Identification

Addendum F: Physical View of Wave Propagation and Power Flow in Waveguides     

A Physical View of Wave Propagation and Power Flow in Waveguides

APPENDIX A: Symbols and Units

APPENDIX B: Constants and SI Units

Constants

Fundamental SI Units

Power of 10 Prefixes

APPENDIX C: Material Properties

Material Conductivities

Material Permittivities

Material Permeabilities

APPENDIX D: Summary of EM Relationships

Maxwell’s Equations

Static Form of Maxwell’s Equations

Dynamic Form of Maxwell’s Equations

Constitutive Relationships

Potential Relationships

The Divergence Theorem

Stoke’s Theorem

Complex Material Properties

Complex Wave Parameters

Skin Depth

Poynting Vector

Coaxial Transmission Line Parameters

Normal Incidence Relationships

Oblique Incidence Relationships

Snell’s Law

The Brewster Angle

Rectangular Waveguide Relationships

APPENDIX E: Vector Identities

The Gradient

The Divergence

The Curl

The Laplacian Operator

Other Vector Identities