## ECE 5106 Electromagnetic Waves

#### Spring 2015 textbook list

The Spring 2015 ECE textbook list is available online for students.

#### Current Prerequisites & Course Offering

For current prerequisites for a particular course, and to view course offerings for a particular semester, see the Virginia Tech Course Timetables.

### ECE 5106 Electromagnetic Waves (3C)

Maxwell's electromagnetic field theory and its applications to engineering problems. 5106: Analytical techniques (Green's theory, modal analysis, etc.) pertaining to guided wave propagation and to scattering and diffraction by discontinuties and inhomogeneties in metallic and dielectric waveguiding structures.

What is the reason for this course?

The design of microwave and optical components, such as antennas, waveguides, etc., as well as the effective exploitation of diverse types of communication channels, is based upon the theory of electromagnetic fields, expressed most efficiently by Maxwellâ€™s equations. However, the solution of these equations requires an in-depth understanding of a number of diverse techniques.

Typically offered: Spring. Program Area: Electromagnetics.

Why are these prerequisites or corequisites required?

Engineering: Proficiency in undergraduate electromagnetic fields. (Knowledge of the material covered in ECE 3106 is mandatory). Mathematics: Differential equations and Fourier concepts. Also Graduate standing.

### Department Syllabus Information:

Major Measurable Learning Objectives:
• Apply the basic concepts of Green's theory, potential function theory, and equivalence theory to the development of EM problem analysis and solution.
• Evaluate basic near zone, Fresnel zone, and far field radiation properties of antenna current distributions
• Apply the basic theorems of electromagnetics to homogenize the medium and enable the use of the free space (vacuum) Green function.
• Carryout the application of an eigenvalue decompositions to the solutions of source free Maxwell's equations to setup and solve problems involving both open and closed geometries.
• Apply the method of separation of variables in rectangular, cylindrical, and spherical coordinates to solve radiation and scattering problems in these geometries.

Course Topics
Topic Percentage
a. Solving Maxwell's equations with sources %
b. The vector wave equation vs. the Helmhnoltz equation %
c. Green's Theory (capabilities and limitations) %
d. Potential Theory (capabilities and limiations) %
e. Current to potential to fields %
f. Deriving the free space Green function %
g. Solution for radiation by an elemental dipole %
h. Zones of radiation and behavior of the fields %
2. Behavior of the far and Fresnel zone fields 8%
a. Focusing of an antenna %
b. Importance of Fourier transforms %
3. Simple equivalent sources 12%
a. Weyl representation for the free space Green's function %
b. Relation to Huygen's Principle %
c. Method of stationary phase and the far fields %
d. Comparison of far zone fields from Weyl and vector potential approaches %
4. Basic electromagnetic theorems 10%
a. Duality %
b. Reciprocity %
c. Uniqueness & image theory %
5. Equivalence theory 20%
a. Basic concept %
b. Importance of radiation condition %
c. Use in simple problems %
d. Use in problems to set up integral equaitons for the currents %
e. Perfectly conducting bodies (MFIE & EFIE equations) %
f. Dielectric bodies %
g. Multiple bodies %
6. Green functions 15%