COMS7309 Computational Techniques in Electromagnetics
Assignment 2, S2 2024
BACKGROUNDS
Microwave system have now been widely used in our life since it was first introduced in the 1950s. One of the most prominent applications for modern society is satellite communication which forms the foundation of information-sharing systems such as mobile phones, radio and the Internet. In recent years, low earth orbit (LEO) satellite systems have been developed to provide continuous coverage for on-the-move platforms such as vehicles or aircraft in remote areas that are rarely covered by traditional terrestrial systems. Since signals are directly transferred between user terminals and the satellite (as illustrated in Figure 1) to enable wireless communications, precise alignments between the user terminals and the orbiting satellites are required to establish a stable communication link.
Traditional satellite communication systems use mechanical components to enable a tracking capability. Mechanical systems can provide wide scanning angles with negligible gain loss. However, they are not suitable for modern satellite communication systems because of their slow scanning speed. Moreover, the large size and high cost of maintenance also prevent them from being used in portable applications such as mobile phones or vehicles. To overcome these challenges, electrical beam-forming phased arrays (Figure 2) are proposed to provide a fast-tracking capability with features of compactness and cost-effectiveness.
The tracking capability of a beam-forming phased array is obtained by using signals with different phases to stimulate different antenna elements in the array. As illustrated in Figure 2, the phase excitation of each antenna element is controlled using a tunable phase-shifting system. By changing the phase of the excitation, the radiated overall beam can be focused towards a desired direction, realising a tracking capability.
MATERIALS
In this assignment, a framework of 2D FDTD code is provided. Based on this framework, a complete 2D FDTD code is required to be programmed.
The simulation configuration is shown in Figure 3.
In this assignment, a computation domain with the size of 500 mm × 500 mm is defined. This computation domain is surrounded by a perfect matching layer (PML). The PML has 10 layers (detailed parameters regarding the PML can be found in the code framework).
In total 25 transmitting antennas (Tx) modelled as ideal line sources are evenly distributed on a line parallel to the x direction and with y coordinate of 180 mm. The distance between adjacent transmitting antennas is λ/2. The first Tx antenna is located at (-90 mm, 180 mm) and the last Tx antenna is located at (90 mm, 180 mm).
In total 55 receiving antennas (Rx) are evenly distributed on a line parallel to the x direction with y coordinate of -180 mm. The distance between adjacent receiving antennas is λ/2. The first Rx antenna is located at (-200 mm, -180 mm) and the last Rx antenna is located at (205 mm, -180 mm).
The line sources are propagating TMz waves. The source signals are modelled using modulated sinusoidal waves. A Gaussian waveform. is used to modulate the sinusoidal waves. The sinusoidal waves have a single frequency of 20 GHz.
TASKS
Task I: Please build the 2D-FDTD code to simulate the wave propagation in the simulation configuration shown in Figure 3. In the simulations, you will need to simulate the wave propagation with different beam-forming angles (0°, 15°, 30°, and 45°). The beam-forming angle is defined by a parameter named “beamforming_angle” in the code framework. The default value is π/6 (30°). Please note that the beamforming angle is represented by φ as shown in Figure 3. Please also note that the “beamforming_angle” variable in the code uses radiance as the unit of the angle.
Task II: Please show the Ez field distribution in the frequency domain at a frequency of 20 GHz for different beam-forming angles (0°, 15°, 30°, and 45°).
Task III: Please show the Ez field distribution in the time domain at different time steps (the 750th time
step, the 1000th time step, the 1250th time step, and the 1500th time step) for different beam-forming angles (0°, 15°, 30°, and 45°).
Task IV: Please record and show the frequency domain signals of Ez field at the frequency of 20 GHz at the positions of the receiving antennas (indicated by the circles with red dots in Figure 3).
Please note that the positions of the transmitting and receiving antennas have been defined in the code framework. The waveforms of all Tx antennas are also defined in the code framework.
Please provide your MATLAB (or any other programming language) code with detailed comments.
Marking Criteria for the codes (65%):
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Sections
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Weight
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Comments
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Structure of the codes
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20%
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Build the correct structure of the 2D-FDTD algorithm
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Complete the missing codes
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35%
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Complete the missing codes in the code framework
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Comments
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15%
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Have detailed comments for the developed codes
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Results
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30%
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The developed codes can produce the correct results
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Requirements for the report (35%):
1. Basic introductions of the beam-forming using a phased array system and the 2D-FDTD.
2. Relevant math formulations and corresponding illustrations.
3. A flowchart of your code.
4. Pseudocode of your codes (for the format of pseudocode, please refer to https://en.wikipedia.org/wiki/Pseudocode).
5. Figures of the results as required in Tasks I-IV.
6. Conclusion and inspiration from the results of your simulation. Some physical interpretations can gain your additional marks!