2016 Electromagnetic Fields and Waves

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Academic unit or major
Undergraduate major in Electrical and Electronic Engineering
Hirokawa Jiro  Nishikata Atsuhiro 
Class Format
Media-enhanced courses
Day/Period(Room No.)
Tue5-6(W541)  Fri5-6(W541)  
Course number
Academic year
Offered quarter
Syllabus updated
Lecture notes updated
Language used
Access Index

Course description and aims

This course focuses on plane-wave and its reflection and refraction, analyses of telegrapher's equation in distributed-element circuit. Topics include Maxwell's equation, plane-wave incidence to material, electromagnetic-wave radiation from source and current and voltage variation on distributed-element circuit. By combining lectures and exercises, the course enables students to understand and acquire the fundamentals of electromagnetic-wave radiation and propagation in space and in distribute-element circuit.
This course follows electricity and magnetism and explains the fundamentals on electromagnetic wave and wave-propagation mechanism for engineering applications. It is followed by other courses on signal system, waveguide engineering and the law and opto-electronics.

Student learning outcomes

By the end of this course, students will be able to:
1) Explain the meanings of Maxwell's equation and derive wave equations
2) Explain the meaning of plane wave and difference between travelling and standing waves.
3) Explain the operation in incidence of a plane wave to various material.
4) Explain how to determine the electromagnetic radiation and power flow from the source
5) Explain the relationship between the electromagnetic wave propagating along transmission lines and the current, voltage and power


wave equation, plane wave, reflection and refraction, antenna, distributed-element circuit, telegrapher's equation

Competencies that will be developed

Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

Class flow

Towards the end of class, students are given exercise problems related to the lecture given that day to solve. Also, students should submit a report summarizing the lecture after each class.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Maxwell's equation - Gauss law, Ampere's law, Faraday's law Explain the meaning of Maxwell's equation
Class 2 Wave equation, plane wave Derive wave equation and explain meaning of plane wave
Class 3 Standing wave, polarization, boundary condition - Travelling and standing waves, perpendicular and parallel polarizations, continuous condition for electromagnetic field Explain the difference between travelling and standing waves, the meaning of polarization, derive the continuous condition for electromagnetic wave
Class 4 Reflection and transmission in vertically incidence of wave - Dielectric case and perfect electric conductor case Explain the operation of vertical incidence of wave
Class 5 Reflection and refraction in oblique incidence of perpendicular polarization wave - Snell's law, total reflection and critical angle Explain the operation of oblique incidence of perpendicular polarization wave
Class 6 Reflection and refraction in oblique incidence of parallel polarization wave - Brewster's angle Explain the operation of oblique incidence of parallel polarization wave
Class 7 Plane wave incidence to lossy material - Attenuation in lossy material Explain the operation of plane wave incidence to lossy material
Class 8 Test level of understanding with exercise problems and summary of the first part of the course - Solve exercise problems covering the contents of classes 1–7. Test level of understanding and self-evaluate achievement for classes 1–7.
Class 9 Radiation of electromagnetic wave from a source - infinitesimal dipole, infinitesimal loop current, antenna's far field Explain the relation between point source field and antenna far-field.
Class 10 Poynting vector and uniqueness theorem - energy flow, uniqueness of boundary-value problem Explain the meaning of Poynting vector and the significance of uniqueness theorem.
Class 11 Distributed-element circuit and telegrapher's equation - TEM wave, transmission line, telegrapher's equation Explain the electromagnetic field around the transmissin line (Lecher wire and coaxial line).
Class 12 Solution of telegrapher's equation via Laplace transform - time-domain solution for lossless case, forward wave, backward wave Derive time-domain solution to the telegrapher's equation.
Class 13 Sinusoidal signal input to the distributed-element circuit - frequency-domain solution for lossy case, characterstic impedance Explain the characteristics of travelling wave on a distributed-element circuit with sinusoidal input.
Class 14 Analysis for finite-length distributed-element circuit - reflection coefficient, multiple reflections, impedance matching Explain the signal transmission between signal source and load connected via a finite-length distributed-element circuit.
Class 15 Standing wave ratio, scattering matrix - standing wave ratio and scattering matrix, scattering matrix and the example Explan the relationship between reflection coefficeint and standing wave ratio, the definition of scattering matrix.


Text is delivered at OCW-i.

Reference books, course materials, etc.

Yoji Kotsuka and Kimitoshi Murano "Basic electromagnetic-wave engineering" (ISBN: 978-4-86481-006-7). Students are strongly recommended to buy it.

Assessment criteria and methods

Students' knowledge of plane wave and its reflection and refraction, electromagnetic-wave radiation from source and distributed-element circuit, and their ability to apply them to problems will be assessed.
Midterm and final exams 80%, reports and exercise problems 20%.

Related courses

  • EEE.S351 : Signal System
  • EEE.S301 : Waveguide Engineering and the Radio Law
  • EEE.S361 : Opto-electronics Opto-electronics

Prerequisites (i.e., required knowledge, skills, courses, etc.)

Students must have successfully completed Electricity and Magnetism I and II (EEE.E201 and EEE.E202) and Electric Circuit I (EEE.C201) or have equivalent knowledge.

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