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# Electromagnetics, Antennas and Propagation Assignment No. 1: Finite differences methods

UKUniversity of BirminghamElectromagnetics Antennas and PropagationFinite differences methodsMatlab

# 2022/23 Electromagnetics, Antennas and Propagation Assignment No. 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 .

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 ,. 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.

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:

1. 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 to https://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.

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