ECE U440: Electromagnetic Fields and Waves (4 SH)
Required course (Third year)
This course is an introduction to electromagnetics and to high frequency applications. It
covers the following topics. Transmission lines: Transmission line model with
distributed circuit elements, analytical and graphical solutions, one dimensional
traveling and standing waves, and applications. Vector calculus and vector phasors.
Electromagnetic field theory: Lorentz force equation, Maxwell’s equations, Poynting
theorem, and application to the transmission line’s TEM waves. Uniform plane wave
polarization and propagation in lossless and dissipative media. Reflection and refraction
of uniform plane waves by conducting and dielectric surfaces in the cases of normal and
oblique incidence. The special cases of total transmission (Brewster angle) and total
reflection (non-uniform plane waves). Applications to waveguides, resonators and
optical fibers. Radiation, elementary antennas (transmitters and receivers) and phased
arrays.
Prerequisites: MTH U341 and PHY U155
Co-requisite: ECE U441 must be taken concurrently
Textbooks:
Required:
Recommended:
F. T. Ulaby “Fundamentals of Applied Electromagnetics”,
Fifth Edition, Prentice Hall, 2007
1. Kraus and Fleisch, “Electromagnetics with Applications,”
Fifth Edition, McGraw-Hill, 1995
2. Nasar, “2000 Solved Problems in Electromagnetics,”
Schaum’s Series, McGraw-Hill, 1992
3. Fogiel (Ed.), “The Electromagnetics Problem Solver”,
Research and Education Association, 1993
Course objectives:
The students will learn the following topics:
 Transmission lines
 Physics of wave propagation (retardation, etc.)
 Models for transmission systems using circuits with distributed parameters
 Mathematical solution for the transmission line and wave equations (time domain and
frequency domain)
 Reflection, standing wave ratio, transmission into another line, impedance, excitation,
etc.
 Practical transmission line applications (matching, location of short, resonators, etc.)
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Fundamental electromagnetic field equations in differential form:
 Lorentz’s force equation (definition of the electromagnetic field)
 Maxwell’s equations (electromagnetic field in terms of the sources)
 Conservation of charge (restriction on the sources)
 Constitutive relations (flux densities in terms of the electromagnetic field)
 Poynting’s theorem (calculation and conservation of energy)
Uniform plane waves:
 Physics of electromagnetic waves
 Polarization
 Derivation from Maxwell’s equations (no boundaries)
 Transmission line model for TEM waves
Reflection and transmission of uniform plane waves:
 Derivation of the boundary conditions
 Normal incidence
 Oblique incidence (Snell’s Law)
 Total transmission – Brewster angle
 Total reflection - Optical Fibers
 Parallel plate waveguide and resonator
Wireless transmission
 Radiation (solution of Maxwell’s equations in unbounded media)
 Electric dipole antenna
 General characteristics for transmitters
 General characteristics for receivers
 Friis transmission formula
 Phased arrays
COURSE OUTLINE:
Chapter 1: Introduction
Overview of electromagnetic fields and forces. Traveling waves. The electromagnetic
spectrum. Review of complex numbers and phasors. (3 classes)
Chapter 2: Transmission Lines
Transmission line model based on distributed circuit elements. Transmission line
equations and solutions. Sinusoidal steady state analysis. The lossless line. Traveling
and standing waves. Impedances, admittances, reflection coefficients, and power flow.
Standing wave ratio. Smith chart. Transmission line matching. Lossy lines. (10 classes)
Chapter 3: Vector Analysis
Review of vector algebra-addition, subtraction, multiplication, division, scalar and vector
products. Cartesian coordinate systems. Vector differential operators: divergence and
curl of vector fields. (3 classes)
Chapter 6: Maxwell’s Equations for Time-Varying Fields
Lorentz force equation. Constitutive parameters. Integral relations and point relations
(differential relations and boundary conditions) for the two Gauss’s laws, Faraday’s law,
and Ampere’s law. Poynting theorem. (6 classes)
Chapter 7: Plane–Wave Propagation
Application of Maxwell’s equations to uniform plane waves in unbounded media. Plane
wave propagation and polarization in lossless media. Propagation in dissipative media.
(4 classes)
Chapter 8: Wave Reflection and Transmission
Reflection and transmission of waves at interface between two media. Snell’s law.
Reflectivity and transmissivity. Brewster angle. Total reflection. Applications to
waveguides, resonators, and optical fibers. (7 classes)
Chapter 9: Radiation and Antennas
The short dipole. Antenna radiation characteristics. Half wave and longer dipoles.
Receivers. Friis transmission formula. Antenna arrays. (7 classes)
EXAMINATION POLICY AND COURSE CREDITS:
Homework:
20%
Problem sets, which are completed on time, will be
graded by the Teaching Assistant. Solutions will be
distributed.
Hour Examination #1:
Hour Examination #2:
20%
20%
Final Examination:
40%
Contribution of course to meeting professional component:
Basic science / Math: 2.5 SH
Engineering topics: 1.5 SH
General Engineering:
Relationship of course to program objectives
ECE U440
1.1 Formulate &solve ECE problems
1.2 Laboratory &computing tools
1.3 Design/conduct experiments, analyze data
1.4 Design systems, components, or processes
1.5 (CE) Design and implement computer
programs
2.1 Understand/apply mathematics
2.1.1 Differential calculus
2.1.2 Integral calculus
2.1.3 Complex algebra/analysis
2.1.4 Differential/Difference equations
2.1.5 Linear algebra
2.1.6 Multivariate calculus
2.1.7 Probability/Stochastic processes
2.2 Understand/apply physics
2.2.1 Solid state physics
2.2.2 Electricity & Magnetism
2.3 (EE) Understand knowledge of programming
(CE) Solve engineering problems using
programming
2.3.1 Flow charting/program design
2.3.2 Language syntax/debugging
2.3.3 Output analysis
2.4 Connect ECE subfields
2.5 Information sources/literacy
2.6 Connection between theory & application
2.7 Connection between classroom & work/co-op
3.1 Effective written communication
3.2 Effective oral communications
3.3 Analyze information/compare alternatives
3.4 Multidisciplinary teams
3.5 (CE) Document engineering work
appropriately
4.1 Professional/ethical issues
4.2 Lifelong learning
4.3 Career management
4.4 (CE) Copyright and privacy standards specific
to computer hardware ad software
C: Detailed instructions for the solution of EE
problems
H: Homework graded by TA (20 %)
E: 2 hour exams (40%), final (40%)
See the charter for the required lab ECE U441
See the charter for the required lab ECE U441
CHE: Design of transmission systems & phased
arrays
H: MATLAB used in homeworks
CHE: Extensive use of differential calculus
CHE: Extensive use of integral calculus
CHE: Use of scalar and vector complex phasors
CHE: Solution of ordinary and partial differential
equations
C: S-parameters to analyze data
CHE: Extensive use of multivariate calculus
N/A
N/A
CHE: Extensive presentation of Electricity and
Magnetism
N/A
CH: MatLab used in class and for homeworks
N/A
CHE: Use of transmission line theory as an extension
of circuit theory. Extension of Linear Systems
concepts to include spatial as well as time variation.
CO: Use of several references
CHE: Application of the theory to many practical
applications
N/A
H: Correct presentation (language, grammar, syntax)
is emphasized for the preparation of the homework
N/A
N/A
N/A
N/A
C: They are discussed in class
C: It is continuously emphasized in class
N/A
N/A
5.1 Social/cultural context of engineering
5.2 Historical/temporary issues of ECE
5.3 Esthetics in engineering
5.4 Esthetics in written/oral expression
N/A
C: Historical background about electricity,
magnetism, Faraday, Ampere, Maxwell, Hertz, et al.
N/A
C: Comments for the improvement of the written
presentations (homework)