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 finite difference method that will solve the         scenario shown in the figure below. Notice that the potential difference between the             enclosing box and the central metal plate is 15V and the background is air unless otherwise stated. The program can be in any computer language that is available within the School.

12 mm

Outer box at potential 0V

Learn how to use the Partial Differential Equation Toolbox of Matlab or FREEFEM (https://freefem.org/).

Using your programme:

1. Calculate the potential at points P, Q, R, S and T when the background is air (as shown in the sketch) or a dielectric εr = 2.

2. Draw a contour map showing the potential.

3. Calculate the magnitude of the electric field |E| and the flux density |D| at P, Q, R, S and T.

4. Calculate the capacitance per unit length (i) between the central metal plate and the  bottom boundary and (ii) between the central metal plate and the top boundary using your finite difference data and compare them with those of parallel plate capacitors of the same size neglecting fringing fields (i.e., fields outside the capacitor are                neglected).

5. Using the capacitances per unit length from 4, calculate the total capacitance per unit length of the stripline neglecting fringing fields.

6.  If the structure were a transmission line extending into the page, what is the velocity of the electromagnetic wave along the line? Do this using your finite difference data as    well as using the simple parallel plate assumption.

Using the Partial Differential Equation Toolbox of Matlab or FREEFEM:

7. Repeat (1) and (2) and compare the results. State any approximation that you may have used.

Task 2 (20%)

Survey the developments of microstrip transmission lines for millimetre-waves (f = 30 to 300 GHz) in the technical literature. Create a graph with at least 5 points showing measured       attenuation against frequency. Indicate clearly the source of the data points (e.g. cite            technical paper).

Submission details

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

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 or FREEFEM.

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.

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 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