2024 Faculty Courses School of Engineering Department of Electrical and Electronic Engineering Graduate major in Electrical and Electronic Engineering
Advanced Electromagnetic Waves
- Academic unit or major
- Graduate major in Electrical and Electronic Engineering
- Instructor(s)
- Jiro Hirokawa / Takashi Tomura
- Class Format
- Lecture
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 5-6 Tue / 5-6 Fri
- Class
- -
- Course Code
- EEE.S401
- Number of credits
- 200
- Course offered
- 2024
- Offered quarter
- 1Q
- Syllabus updated
- Mar 14, 2025
- Language
- English
Syllabus
Course overview and goals
This course focuses on direct solution to Maxwell's equation, diffraction and scattering of electromagnetic wave. Topics include the derivation and the interpretation of solution to wave equation, field equivalent theorem, and scattering in cylindrical coordinate system and its interpretation. By combining lectures and reports, the course enables students to understand the analysis methods of electromagnetic wave and their interpretations.
The course follows electricity and magnetism, electromagnetic fields and waves and waveguide engineering and gives students deep interpretations on radiation and scattering of electromagnetic waves and is followed by advanced courses such as guided waveguide circuit theory, electrical modelling and simulations and RF measurement engineering.
Course description and aims
By the end of this course, students will be able to:
1) Derive wave equation from Maxwell's equation and understand the meaning of its solution.
2) Understand the meaning of field equivalent theorem.
3) Solve scattering problems in cylindrical coordinate system.
4) Understand the meaning of diffraction and scattering of electromagnetic wave.
Keywords
wave equation, field equivalence theorem, cylindrical coordinate system, diffraction and scattering
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
Students should submit homework summarizing the contents of the lecture after each class. Homework, etc. will be distributed and submitted at T2SCHOLA.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Derivation of the Helmholtz equation (Sec.1.1.1) | Derive using vector potential |
| Class 2 | Solutions to Helmholtz equation (Sec.1.1.2) | Explain the meaning of the solution to wave equation |
| Class 3 | Duality of electric and magnetic fields in Maxwell's equations (Sec.1.2), Uniqueness theorem (Sec.2.1) | Explain the structure of solution to wave equation and the meaning of uniqueness theorem |
| Class 4 | Application of the equivalence theorem (Sec.2.2) | Explain the meaning of field equivalence theorem |
| Class 5 | Understanding the equivalence theorem (Sec.2.3) | Explain the application of field equivalence theorem to plane wave propagation |
| Class 6 | Solutions and features for boundary value problems (Chap.3) | Explain how to solve boundary value problems |
| Class 7 | Expressions of complementary solutions in rectangular coordinates (Sec.4.1) | Derive homogeneous solution in rectangular coordinate system |
| Class 8 | Scattering problem (summation expression) due to a current in a one-end terminated parallel plate conductor (Sec.4.2.1) | Derive the summation expression for electromagnetic field in shorted parallel plates |
| Class 9 | Scattering problem (integral expression) due to a current in a one-end terminated parallel plate conductor (Sec.4.2.2) | Derive the integral expression for electromagnetic field in shorted parallel plates |
| Class 10 | Proof of agreement between the summation and integral expressions (Sec.4.2.3) | Derive equivalence between the summation and integral expressions for electromagnetic field in shorted parallel plates |
| Class 11 | Expressions of complementary solutions in cylindrical coordinates (Sec.5.1) | Compare with the solution in rectangular coordinate system |
| Class 12 | Scattering problem due to an electric current near a cylindrical conductor (Sec.5.2) | Derive radiation by line current |
| Class 13 | Scattering problem due to an electric current near a wedge conductor (Sec.5.3.1) | Derive scattering electromagnetic field by a half plane |
| Class 14 | Scattering problem of a plane wave incident to a semi-infinite plate conductor (Sec.5.3.2) | Explain diffraction phenomena of electromagnetic field by a half plane. |
Study advice (preparation and review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
J. Hirokawa and M. Ando, "Electromagnetic wave analysis" (In English)
Paperback, Design Egg Inc. (ISDN 978-4815022310)
https://www.amazon.co.jp/dp/4815022313?language=en_US
Amazon Kindle e-book (In English)
https://www.amazon.co.jp/dp/B08HL7GDRP?languaage=en_US
The paperback version and the e-book version have the same content.
Reference books, course materials, etc.
J. Hirokawa and M. Ando, "Waveguide slot antenna analysis using eigenfunction expansion method" (in Japanese)
Paperback, Design Egg Inc. (ISDN 978-4815022303)
https://www.amazon.co.jp/dp/4815022305?language=ja_JP
Amazon Kindle e-book (in Japanese)
https://www.amazon.co.jp/dp/B08HL57X25?language=ja_JP
The paperback version and the e-book version have the same content.
J.A.Stratton, "Electromagnetic Theory," IEEE Press, ISBN: 978-0-470-13153-4
R.F.Harrington, "Time-Harmonic Electromagnetic Fields," McGraw Hill, ISBN 978-0-471-20806-8
C.A.Balanis, ”Advanced Engineering Electromagnetics," Wiley, ISBN 978-0-470-58948-9
Evaluation methods and criteria
Students' knowledge of analysis methods for wave equations, and their ability to apply them to problems will be assessed.
1 exam (in-person written exam without using references) about 70%, homework about 30%.
Related courses
- EEE.S411 ： Guided Wave Circuit Theory
- EEE.G411 ： Electrical Modeling and Simulation
- EEE.C451 ： RF Measurement Engineering
Prerequisites
Students must have successfully completed Electricity and Magnetism I and II (EEE.E201 and EEE.E202), electromagnetic fields and waves (EEE.E211), waveguide engineering and the radio law (EEE.S301) or have equivalent knowledge.