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:F. T. Ulaby “Fundamentals of Applied Electromagnetics”,

Fifth Edition, Prentice Hall, 2007

Recommended: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.)
  • 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 #1:20%

Hour Examination #2:20%

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 / C: Detailed instructions for the solution of EE problems
H: Homework graded by TA (20 %)
E: 2 hour exams (40%), final (40%)
1.2 Laboratory &computing tools / See the charter for the required lab ECE U441
1.3 Design/conduct experiments, analyze data / See the charter for the required lab ECE U441
1.4 Design systems, components, or processes / CHE: Design of transmission systems & phased arrays
1.5 (CE) Design and implement computer programs / H: MATLAB used in homeworks
2.1 Understand/apply mathematics
2.1.1 Differential calculus / CHE: Extensive use of differential calculus
2.1.2 Integral calculus / CHE: Extensive use of integral calculus
2.1.3 Complex algebra/analysis / CHE: Use of scalar and vector complex phasors
2.1.4 Differential/Difference equations / CHE: Solution of ordinary and partial differential equations
2.1.5 Linear algebra / C: S-parameters to analyze data
2.1.6 Multivariate calculus / CHE: Extensive use of multivariate calculus
2.1.7 Probability/Stochastic processes / N/A
2.2 Understand/apply physics
2.2.1 Solid state physics / N/A
2.2.2 Electricity & Magnetism / CHE: Extensive presentation of Electricity and Magnetism
2.3 (EE) Understand knowledge of programming
(CE) Solve engineering problems using programming
2.3.1 Flow charting/program design / N/A
2.3.2 Language syntax/debugging / CH: MatLab used in class and for homeworks
2.3.3 Output analysis / N/A
2.4 Connect ECE subfields / 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.
2.5 Information sources/literacy / CO: Use of several references
2.6 Connection between theory & application / CHE: Application of the theory to many practical applications
2.7 Connection between classroom & work/co-op / N/A
3.1 Effective written communication / H: Correct presentation (language, grammar, syntax) is emphasized for the preparation of the homework
3.2 Effective oral communications / N/A
3.3 Analyze information/compare alternatives / N/A
3.4 Multidisciplinary teams / N/A
3.5 (CE) Document engineering work appropriately / N/A
4.1 Professional/ethical issues / C: They are discussed in class
4.2 Lifelong learning / C: It is continuously emphasized in class
4.3 Career management / N/A
4.4 (CE) Copyright and privacy standards specific to computer hardware ad software / N/A
5.1 Social/cultural context of engineering / N/A
5.2 Historical/temporary issues of ECE / C: Historical background about electricity, magnetism, Faraday, Ampere, Maxwell, Hertz, et al.
5.3 Esthetics in engineering / N/A
5.4 Esthetics in written/oral expression / C: Comments for the improvement of the written presentations (homework)