EMP-4305
Electromagnetic Field Theory
Welcome to the amazing world of Electromagnetics! This course will introduce you to the branch of science that deals with forces that occur around electrically charged particles and the relation between those forces. Electromagnetics is the single topic in electrical engineering that connects all other topics.
The Amazing World of Electromagnetics!
This course is taught in English, but we have created a really neat overview of all of electromagnetics that introduces the concepts with graphics and animations instead of complicated math equations. This overview has been translated into different languages below. Please enjoy!
Course Materials
Homework
- Homework #1 — Graphics & MATLAB (due 25 Jan 2023)
- Homework #2 — Maxwell’s Equations (due 1 Feb 2023)
- Homework #3 — Electromagnetic Waves (due 13 Feb 2023)
- Homework #4 — Wave Scattering (due 6 Mar 2023)
- Homework #5 — Transmission Lines (due 3 Apr 2023)
- Homework #6 — Waveguides (due 24 Apr 2023)
Help
Final Project
Presentations will be given during the final exam period, Friday 12 May 2023 at 10:00am. All documents, media, codes, and other electronic files must be submitted to the course instructor no later than 24 hours prior to your presentation.
Resources
- Graphics Checklist
- Checklist For Technical Writing
- Checklist For Presentations
- (PDF) Summary of Trigonometric Identities
Course Topics
Topic 1 — Course Introduction
Topic 2 — Review of Vector Calculus
Lectures & Notes
- (PDF) (Video) Lecture 2a — Mathematical Preliminaries
- (PDF) (Video) Lecture 2b — Math with Vectors
- (PDF) (Video) Lecture 2c — Coordinate Systems
- (PDF) (Video) Lecture 2d — Differential Length, Area & Volume
- (PDF) (Video) Lecture 2e — Integrations & Constant Coordinate Lines and Areas
- (PDF) (Video) Lecture 2f — Del Operator & Field Operations
- (PDF) (Video) Lecture 2g — Important Concepts
Summaries
- (PDF) Summary of Vector Calculus for Electromagnetics
Supplemental Information
- (Video) Gradients & Partial Derivatives
- (Video) Divergence & Curl
- (Video) Cross Product & Dot Product – Visual Explanation
- Vector Calculus Identities
Topic 3 — Maxwell's Equations
Lectures & Notes
- (PDF) (Video) Lecture 3a — Terms & Definitions
- (PDF) (Video) Lecture 3b — Gauss’ Law
- (PDF) (Video) Lecture 3c — Gauss’ Law for Magnetic Fields
- (PDF) (Video) Lecture 3d — Faraday’s Law
- (PDF) (Video) Lecture 3e — Ampere’s Circuit Law
- (PDF) (Video) Lecture 3f — Constitutive Relations
- (PDF) (Video) Lecture 3g — Statics & Dynamics
- (PDF) (Video) Lecture 3h — Romeo & Juliet Model of Oscillation and Waves
Animations from Notes
- Animation of Faraday’s experiment
- Animation of Faraday’s law in differential form
- Animation of Ampere’s experiment
- Animation of Ampere’s circuit law in differential form (no J)
- Animation of Ampere’s experiment
- Animation of conduction current
Summaries
- (PDF) Summary of Maxwell’s Equations
- (PDF) Summary of Sign Conventions
- (PDF) Summary of Electromagnetic Material Properties
Supplemental Information
Topic 4 — Electrostatics
Lectures & Notes
- (PDF) (Video) Lecture 4a — Conditions for Electrostatics
- Point Charges
- Electric Charge Distributions
- (PDF) (Video) Lecture 4f — Charge Distributions
- (PDF) (Video) Example 1 — Uniform Finite Line Charge
- (PDF) (Video) Example 2 — Uniform Infinite Line Charge
- (PDF) (Video) Example 3 — Uniform Circular Plate Charge
- (PDF) (Video) Example 4 — Uniform Infinite Plate Charge
- (PDF) (Video) Example 5 — Uniform Spherical Charge
- (PDF) (Video) Example 6 — Calculating the Field via Gauss’ Law
- Electric Potential
- Electrostatic Energy
- Electric Materials and Boundary Conditions
- Electrostatic Devices: Resistors and Capacitors
- (PDF) (Video) Lecture 4o — Laplace’s Equation
- (PDF) (Video) Lecture 4p — Solving Laplace’s Equation
- (PDF) (Video) Lecture 4q — Analyzing Resistors
- (PDF) (Video) Lecture 4r — Analyzing Capacitors
- (PDF) (Video) Example — Resistor
- (PDF) (Video) Example — Capacitor
- (PDF) (Video) Example — Capacitor Simulation Example
Summaries
Supplemental Information
- (PDF) Rigorous Capacitor Modeling
Topic 5 — Magnetostatics
Lectures & Notes
- (PDF) (Video) Lecture 5a — Conditions for Magnetostatics
- (PDF) (Video) Lecture 5b — Biot-Savart Law (point currents?)
- Current Distributions
- (PDF) (Video) Lecture 5c — Current Distributions: Point, Line, Surface, and Volume
- (PDF) (Video) Example 1 – Magnetic Field Around a Finite-Length Wire
- (PDF) (Video) Example 2 – Magnetic Field Around an Infinite-Length Wire
- (PDF) (Video) Example 3 – Get a Feel for the Numbers
- (PDF) (Video) Example 4 – Magnetic Field Outside of a Coaxial Cable
- Lorentz Force Law
- Forces on Current Elements
- (PDF) (Video) Lecture 5e — Force on a Current Element
- (PDF) (Video) Example 1 — Force on a Wire
- (PDF) (Video) Lecture 5f — Force Between Two Current Elements
- (PDF) (Video) Example 2 — Force Between Current Elements
- (PDF) (Video) Examples 3 and 4 — Get a Feel for the Numbers
- (PDF) (Video) Lecture 5g — Force Between Two Current Loops
- (PDF) (Video) Lecture 5h — Magnetic Torque and Moment
- (PDF) (Video) Example 5 — Magnetic Moment
- (PDF) (Video) Lecture 5i — Magnetic Dipole
- (PDF) (Video) Lecture 5j — Magnetostatic Boundary Conditions
- Magnetostatic Devices
- (PDF) (Video) Lecture 5k — Preliminary Concepts: Magnetic Flux Linkage, Inductance, and Energy in an Inductor
- (PDF) (Video) Lecture 5l — Energy in the Magnetic Field
- (PDF) (Video) Lecture 5m — Recipe for Analyzing Inductors
- (PDF) (Video) Example 1 — The Solenoid
- (PDF) (Video) Example 2 — MacDonald’s Straw Inductor
- (PDF) (Video) Example 3 — Inductance of a Coaxial Line
- (PDF) (Video) Example 4 — RG-59 Coaxial Transmission Line
Summaries
Topic 6 — Electromagnetic Waves
Lectures & Notes
- (PDF) (Video) Lecture 6a — Electromagnetic Waves
- (PDF) (Video) Lecture 6b — Wave Parameters
- (PDF) (Video) Lecture 6c — Dispersion Relation
- (PDF) (Video) Lecture 6d — EM Wave Polarization
- (PDF) (Video) Lecture 6e — Wave Examples
- (PDF) (Video) Lecture 6f — Lossy Dielectrics
- (PDF) (Video) Lecture 6g — Skin Depth & Power Flow
Animations from the Notes
- (Video) Animation of a wave changing speed and wavelength after entering a second material
- (Video) Animation of the definition of a wave vector
- (Video) Animation of a wave propagating in a vacuum
- (Video) Animation of a wave propagating in a lossless dielectric
- (Video) Animation of a wave propagating in a lossy dielectric
- (Video) Animation of instantaneous Poynting vector
Summaries
- (PDF) Summary of Electromagnetic Waves
Topic 7 — Wave Scattering
Lectures & Notes
- (PDF) (Video) Lecture 7a — Scattering from an Interface — Normal Incidence
- (PDF) (Video) Lecture 7b — Scattering from an Interface — Oblique Incidence
- (PDF) (Video) Lecture 7c — Phase Matching & Special Angles
- (PDF) (Video) Lecture 7d — Examples & Applications
- (PDF) (Video) Lecture 7e — Standing Waves
- (PDF) (Video) Lecture 7f — Multiple Scattering
Animations from the Notes
- (Zip) MATLAB Figure (gives you ability to orbit) of Geometry of Scattering at an Interface
- (Video) Animation of Snell’s Law — low index to high index
- (Video) Animation of Snell’s Law — high index to low index
- (Video) Animation of Standing Waves — high to low impedance interface
- (Video) Animation of Standing Waves — low to high impedance interface
- (Video) More Mathematical Animation of Standing Waves — high to low impedance interface
- (Video) More Mathematical Animation of Standing Waves — low to high impedance interface
- (Video) Animation of Standing Wave Ratio
Refraction Demonstration Cards
Fresnel Visualization Tool
Supplemental Information
- (YouTube) Why does total internal reflection happen?
Summaries
- (PDF) Summary of Scattering at an Interface
Topic 8 — Transmission Lines
Lectures & Notes
- (PDF) (Video) Lecture 8a — Transmission Line Equations
- (PDF) (Video) Lecture 8b — Transmission Line Parameters
- (PDF) (Video) Lecture 8c — Transmission Line Examples
- (PDF) (Video) Lecture 8d — Scattering on a Transmission Line
- (PDF) (Video) Lecture 8e — Impedance Transformation and Parameter Relations
- (PDF) (Video) Lecture 8f — Multi-Segment Transmission Line Devices
- (PDF) (Video) Lecture 8g — Analysis & Design of Multi-Segment Transmission Line Devices
Animations from the Notes
- (Video) Animation of Impedance Transformation
- (Video) Animation of VSWR with an open-circuit load
- (Video) Animation of VSWR with a short-circuit load
- (Video) Animation of VSWR with Z0 > ZL
- (Video) Animation of VSWR with Z0 < ZL
- (Video) Animation of VSWR terminated with an RL circuit
- (Video) Animation of VSWR terminated with an RC circuit
Online Calculators
- Transmission Lines
- Other
Summaries
- (PDF) Summary of Transmission Lines
Topic 9 — Waveguides
Lectures & Notes
- (PDF) (Video) Lecture 9a — Waveguide Introduction
- Waveguide Analysis Setup
- (PDF) (Video) Lecture 9b — Governing Equations for Waveguides
- (PDF) (Video) Lecture 9c — Equations for LHI Waveguide Analysis
- (PDF) (Video) Lecture 9d — Full Wave Analysis Setup for Waveguides
- (PDF) (Video) Lecture 9e — TEM Analysis Setup for Waveguides
- (PDF) (Video) Lecture 9f — TE and TM Analysis Setup for Waveguides
- (PDF) (Video) Lecture 9g — Slab Waveguide Analysis Setup
- Parallel Plate Waveguide
- Rectangular Metal Waveguide
- (PDF) Lecture 9p — Other Waveguides
Animations from the Notes
- (Video) Animation of TM0 (TEM) mode in a parallel plate waveguide
- (Video) Animation of TM1 mode in a parallel plate waveguide
- (Video) Animation of TM2 mode in a parallel plate waveguide
- (Video) Animation of TE1 mode in a parallel plate waveguide
- (Video) Animation of TE2 mode in a parallel plate waveguide
- (Video) Animation of TE3 mode in a parallel plate waveguide
- (Zip) Movies of modes in a rectangular waveguide
Topic 10 — Computational Electromagnetics
Numerical Analysis of Transmission Lines
- (PDF) (Video) Lecture 10a — Numerical Analysis of Transmission Lines
- (PDF) (Video) Lecture 10b — Using tlcalc()
- (Video) MATLAB Session — Analyzing a microstrip transmission line using tlcalc()
Finite-Difference Analysis of Slab Waveguides
- (PDF) (Video) Lecture 10c — 1D Finite-Difference Method
- (PDF) (Video) Lecture 10d — Numerical Analysis of Slab Waveguides
Getting Started in Computational Electromagnetics
- Electromagnetic and Photonic Simulation for the Beginner: Finite-Difference Frequency-Domain in MATLAB
Perfect book to get started in computational electromagnetics. Includes theory, derivations, and all MATLAB codes for simulating waveguides, transmission liens, diffraction gratings, guided-mode resonance filters, frequency selective surfaces, metamaterials, metasurfaces, invisibility cloaks, surface waves and others. - ($$$) One-Dimensional FDTD with MATLAB
Having trouble getting started in computational electromagnetics? Don’t know where to start? This is your answer! Here is a complete online course intended for the complete beginner that covers every detail of 1D FDTD in simple terms and with high quality visualizations. In addition, all of the code is presented and explained to implement the 1D FDTD method in MATLAB. - ($$$) Two-Dimensional FDTD with MATLAB
This is a follow-on to the prerequisite course 1D-FDTD that is intended for the complete beginner. The course covers everything you need to develop your own 2D electromagnetic simulations. Every line of code in MATLAB is typed and explained.
Topic 11 — Smith Charts
Resources
MATLAB Resources
- Getting Started with MATLAB
- Download .zip file with MATLAB codes
- tlcalc.p — This is a MATLAB function that simulates any two-conductor transmission line. The dielectric can be anything isotroic.
- tlcalc_demo.m — This MATLAB program demonstrates the use of tlcalc() by calculating the paramters for a microstrip transmission line.
- Note: Some of the above items are protected function files and have a “.p” extension. They work just like “.m” files, but they cannot be opened to view the code inside of them.