Catalog Entry (2012-2013):

3280 Applied Fields and Lines I(3) Transmission lines. Discontinuities, different termination, and matching methods. Application of vector analysis to Maxwell's equations. Uniform plane waves including reflection/transmission. S-parameters. Principles of antennas. LW, MW, SW, USW propagation. Prereq: MATH 1970, MATH 2350.


Elements of Engineering Electromagnetics, Rao N. N., 5th ed., 2000, Prentice-Hall.


Fields and Waves in Communications Electronics, Ramo, S., Whinnery, J., Van Duzer, T.,

Class Schedule:

The lectures will meet for three university hours each week. An optional problem session will meet for two university hours each week.

Course Outcomes:

In order to successfully complete and pass this course, the student will be able to:

  1. Employ concepts and formulas of vector analysis in 3 coordinate systems (1)
  2. Get refreshed and employ terms, formulas, parameters, and properties of electric and magnetic fields in dielectric, magnetic, and conductive materials (1, 3, 9a, 9d, 9f, 9g, 13, 15)
  3. Understand and employ Faraday, Ampere, and Gauss laws, and demonstrate the principle of magnetic levitation, and that of condenser microphone (1, 3, 4, 5, 6, 7, 9a, 9d, 9f, 9g, 13, 15)
  4. Understand and employ the Maxwell's equations in integral and differential form, including the concepts of vector analysis such as curl, div, grad, Laplacian, as well, as Stokes' and div theorems (1, 5, 9a, 9f, 9g)
  5. Understand and calculate scalar and vector potentials, the relation between E and V, and equipotential surfaces for static fields, and demonstrate their principal application for electrocardiograms (1, 3, 4, 5, 6, 7, 9a, 9d, 9f, 9g, 13, 15)
  6. Employ Maxwell's equations for time-varying fields to calculate parameters (8, (, T, f, 0o, ,o, :o) electromagnetic wave, especially sinusoidal, uniform, plane wave produced by a current and surface current density on metal sheets and cylinders, and propagating in the free space
  7. Investigate and determine the parameters of a lossy and lossfree electromagnetic wave in: perfect and imperfect dielectrics, and in good and perfect conductors, including the skin depth, and demonstrate wave's behavior through coax shielding, underwater communication
  8. Investigate and calculate the power flow and Poynting vector in different media, and demonstrate its working using microwave oven heating
  9. Investigate and calculate wave reflection and/or transmission at the dielectric-dielectric and conductor-dielectric boundary, using boundary conditions, calculate reflection and transmission factors at normal, and at oblique incidence
  10. Calculate the distributed parameters of a transmission line, using as an example L', R', G' and R' of a coax cable, the propagation constant (, and the characteristic impedance Zo
  11. Demonstrate the equivalence of E/H and V/I wave for a transmission line, calculate the phase velocity vp of forward and reflected V/I waves
  12. Investigate the reflection and calculate the reflection and transmission coefficient and the SWR for attenuated and loss-free V/I waves, for different types of termination: resistive, reactive, non-linear, digital; predict the variations of the input resistance, and the cross-talk
  13. Determine and find the transmission line matching, using single, and/or double stub
  14. Be familiar with, and use fluently the Smith Chart

Course Topics:

  1. Vectors and Fields
    1. Vector Algebra
    2. Three Coordinate Systems
    3. Scalar and Vector Fields
  2. Fields and Materials
    1. Electric and Magnetic Fields
    2. Conductors, Dielectrics, Magnetic Materials
  3. Maxwell's Equations in Integral Form
    1. Faraday Law
    2. Ampere Circuital Law
    3. Gauss Law
  4. Maxwell's Equations in Differential Form
    1. Sinusoidal Time-Varying Conditions
    2. Curl, Divergence, Gradient
    3. Laplacian, Potential Functions
  5. Sinusoidal Time-Varying, Uniform, Plane, Electromagnetic Wave
    1. Propagation in Free Space
    2. Propagation in Dielectrics and Conductors and Power Flow
    3. Reflection and Transmission at Boundaries, Boundary Conditions
    4. Wave Polarization, Normal and Oblique Incidence
  6. Transmission Lines
    1. Parameters of a Transmission Line
    2. Resistive Terminations and Discontinuities
    3. Termination by Arbitrary incl. Digital Gates Load; Crosstalk
    4. Transmission Line Matching
    5. Smith Chart Theory and Applications

The Reason this Course is in the Program:

High frequency/high speed/ wireless communications, based on time-varying electromagnetic fields belong to the most important areas of electrical/electronics/computer engineering. Our students need a good theoretical background for design and applications in those areas. This class is designed to provide the students with that background, together with a basis for further study.

Prepared by:

Thad Kulik - February 28, 2001