Introduction

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 solutions [1].

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 (FD), finite elements, or methods of moments [2],[3]. The students are referred to the Lectures on “Numerical Methods” and references therein for further details about different methods and commercial software.

Assignment

Task 1 (80%)

Write a computer program to implement the FD method that will solve the scenario shown in the figure. Notice that the potential difference between the infinitely thin central metal plates on either side of the 0.5 mm thick dielectric slab is +5V and outer box is at potential 2.5V. Thus, there is an infinitesimally small gap between the central metal plates and the outer box. If the structure extends into the page, it is known as a fin-line. 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, FREEFEM (https://freefem.org/) or CST Microwave Studio® (E-Static Solver) available in the School of Engineering’s PCs.

Using your programme:

1. Calculate the potential at points P, Q, R, and S when the length of the central plates M = 2.5.

2. Draw a contour map showing the potential.

3. Draw the electric field distribution and calculate the magnitude of the electric field |E| and the flux density |D| at P, Q, R and S.

4. Calculate the capacitance per unit length between the central plates and compare it   with the theoretical capacitance of a parallel plate capacitor of the same length as the overlapping length between the two central plates. Discuss the

agreement/disagreement.

5. Compute the velocity of the electromagnetic wave propagating along the line. Using the Partial Differential Equation Toolbox of Matlab, FREEFEM or CST MWS:

6. Repeat (1) and (2) assuming that the dielectric slab does not exist and compare the results. State any approximation that you may have used.

Task 2 (5%)

Go tohttps://rogerscorp.com/, find a suitable substrate to fabricate the structure and state it

in your report.

Task 3 (15%)

Survey the developments of planar transmission lines beyond X band (> 12 GHz) in the technical literature. Create a graph with 3 points showing measured attenuation against frequency for microstrips, and 3 more points for any other transmission line (e.g., coplanar   waveguide, coplanar strip line, slotline, fin-line, etc.). Indicate clearly the year of the reported data and cite the technical paper appropriately.

Submission details

A report is required with a description of how you tackled the problem along with the answers to all questions and tasks.

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. Do not include any code for Matlab Partial Differential Equation Toolbox, FREEFEM or CST MWS.

The report should be no more than 6 sides of A4 excluding the reference list and the appendix with your code. Use 11 point Sans Serif font (e.g. Arial), single line spacing and 1.5 cm margins all round. Results at the different requested points should be tabulated.

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 and using someone else code will be penalised and reported to the School Plagiarism Officer.

The report should be submitted in Acrobat PDF format via Canvas by the deadline set on the EMAP module’s Canvas page.

Marking criteria (task 1)

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 Matlab Partial Differential Equation Toolbox, FREEFEM or CST MWS 5%

7.   Good programming practice – annotated source code 5%