Electromagnetics, Antennas and Propagation – assignment #1
Most real-life electromagnetic problems do not fall into a class that can be solved by
analytical methods. For these common situations, we must resort to numerical approximate
Numerical methods are becoming ubiquitous in engineering practice as digital computer
speed and memory capacity continue to increase. Among the powerful methods are those
using finite differences, finite elements, or methods of moments ,. The students are
referred to the Lectures on “Numerical Methods” and references therein for further details
about different methods and commercial software.
Write a computer program to implement the finite difference method that will solve the
scenario shown in the figure below. Notice that the potential difference between the 1 mm
width central metal plates is +10V or 0V and the rest of the metal boundaries are at potential
0V. If the structure extends into the page, it is known as an edge-coupled grounded coplanar
waveguide (inside a conducting enclosure). The program can be in any computer language
that is available within the School.
Learn how to use the Partial Differential Equation Toolbox of Matlab (or any electromagnetic
software available within the School) and use it to compare your results.
Using your programme:
1. Calculate the potential at points P, Q, R, S and T when the central right-hand side
metal plate is at -5V and also when it is at +5V.
2. Draw a contour map showing the potential for both bias situations.
3. Compare the results with those obtained with the Partial Differential Equation Toolbox
of Matlab (or any other electromagnetic software).
4. Calculate the magnitude of the electric field |E| and the flux density |D| at P, Q, R, S
and T for both bias conditions.
5. For both bias conditions, calculate the capacitance per unit length (i) between both
central plates and (ii) between each central plate and all the other metal boundaries
using your program and compare them with those of parallel plate capacitors of the
same size neglecting fringing fields (i.e., fields outside the capacitor are neglected).
εr = 9, μr = 1
x Coordinate origin (0,0)
Outer box at potential 0V
Point P(5,3) 6 mm
εr = 1, μr = 1 (Air)
Dr Miguel Navarro-Cía
6. Using the capacitances from 5, calculate the total capacitance of the edge-coupled
grounded coplanar waveguide neglecting fringing fields for both bias conditions.
7. If the structure were a transmission line extending into the page, what is the velocity of
the electromagnetic wave along the line for either of the bias conditions?
8. Research the literature of edge-coupled coplanar waveguides and find the expressions
for computing the total even- and odd-mode capacitance per unit length. Compare
your results with those obtained from such expressions.
A report is required with a description of how you tackled the problem and the answers to the
The report should be self-contained with a good description of the methods you used.
Your computer code (with comments) should be included as an appendix.
The report should be no more than 10 sides of A4 excluding the appendix with your code.
Use 11 point Sans Serif font (e.g. Arial), single line spacing and 1.5 cm margins all round.
In addition, you will need to add to a cover and feedback sheet to ensure you receive
targeted feedback that will support your learning. It is a requirement for students to include
the completed template as the first page of every assignment that is submitted for marking.
Plagiarism, which includes, but is not limited to, a failure to acknowledge sources will be
The report should be submitted in Acrobat PDF format, on Canvas, by 14:00 on 20 January
1. Introduction – a general description of the problem 5%
2. Methodology 30%
3. Results and discussion 40%
4. Use of references with full reference list provided 5%
5. Report and structure 10%
6. Good command of Partial Differential Equation Toolbox of Matlab 5%
7. Good programming practice – annotated source code 5%
Benchmark statements of expectations
An excellent report will present succinctly the theory behind the finite difference method with
pertinent citations to the literature, will explain the methodology followed to solve the
questions and will provide a suitable discussion when comparing the results obtained with
the student’s programme, the Matlab toolbox and the analytical solutions (under pertinent
assumptions), including your consideration of accuracy.
A failing report will be one that is not structured, misses questions, fails to provide the
computer code as an appendix, and lacks of discussion and details on how the assignment
has been tackled.
 M. N.O. Sadiku, Computational Electromagnetics with MATLAB, CRC Press, 2018.
 X.-Q Sheng and W. Song, Essentials of Computational Electromagnetics, WileyBlackwell, 2012.
 D. B. Davidson, Computational Electromagnetics for RF and Microwave Engineering,
Cambridge University Press, 2010.