讲解Propagation留学生、辅导MATLAB Electromagnetics, Antennas and Propagation程序

Electromagnetics, Antennas and Propagation – assignment #1

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, 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

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.

Learn how to use the Partial Differential Equation Toolbox of Matlab and use it to compare

your results.

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.

εr = 9, μr = 1

Point S(3,1)

x Coordinate origin (0,0)

Upper plate potential 15V

Outer box at potential 0V

Point Q(7,2)

Point P(5,3) 6 mm

12 mm

Point T(-1,1)

Point R(8,1)

εr = 1, μr = 1 (Air)

(0,2) x

Dr Miguel Navarro-Cía

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:

7. Repeat (1) and (2) and compare the results.

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.

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

penalised.

The report should be submitted via Canvas before 14 January 2019, 12:00 noon.

Marking criteria

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.

[1] M. N.O. Sadiku, Computational Electromagnetics with MATLAB, CRC Press, 2018.

[2] X.-Q Sheng and W. Song, Essentials of Computational Electromagnetics, WileyBlackwell,

2012.

[3] D. B. Davidson, Computational Electromagnetics for RF and Microwave Engineering,

Cambridge University Press, 2010.