Aperture Antenna FDTD Simulation

Introduction:

This was my introductory project to learn to use OpenEMS¹ as a Finite Difference Time Domain Method (FDTD) solver and teach myself fundamentals of the FDTD² algorithm along with relearning some fundamental antenna theory.

Using the FDTD simulation software OpenEMS¹ via MATLAB, I attempt to recreate and compare the results from the TE₁₀ mode of a square aperture antenna given by Balanis³ with a real world rectangular aperture composed of a rectangular waveguide with a large conducting ground plane surrounding the waveguide opening.

Using the already written script of a Horn Antenna in the OpenEMS tutorials, I edited the script to form an open ended waveguide aperture antenna as seen in Figure 1 below. The center frequency (test frequency) of this aperture antenna was set to 15GHz making the aperture opening:

a = 3λ = 60mm by b = 2λ = 40mm

The entire ground plane around the aperture is is 200mm by 200mm.

Figure 1. Open End Waveguide Aperture Structure (a = 3λ, b = 2λ)

Results:

Figure 2(a,b) shows the electric field magnitude of the results calculated using OpenEMS and the results given in Balanis³ (chapter 12, figure 12.12).

As one can see, the OpenEMS simulation results show the same comparative number of lobes in both the E-plane and H-plane. As is explained by Balanis, the E-plane shows similar and equivalent characteristics to that of a constant field aperture of the same dimensions but the H-plane does not because the TE₁₀ mode is not constant in the H-plane and thus the number of lobes is different to that of a constant field aperture.

Figure 2a. Relative Magnitude of Electric field calculated via OpenEMS

Figure 2b. Relative Magnitude of Electric field given in Antenna Theory by Balanis

Take Away:

I learned how to properly use OpenEMS to model antennas via the FDTD algorithm by setting up proper mesh and boundary conditions and other parameters. I was able to reproduce a well known solution to a problem to test my understanding and proper usage of OpenEMS and FDTD.

To do this, I had to manipulate already published script/code to obtain data which is otherwise not an already written function/script output.

Extras:

Figure 3 shows the directivity of the waveguide aperture and you can find the FDTD simulation in Figure 4, which shows a movie of the actual electric field magnitude squared simulation being pulsed (initially a Gaussian pulse with center frequency at 15GHz and cutoffs at 10GHz and 20GHz). The directivity shows what seems to be one main back lobe. In addition, there seems to be some non-uniform continuity in the back. I believe this is caused by the diffraction and fringing of the aperture which is not taken into account by Balanis in his analysis of a waveguide aperture.

Figure 3. Directivity of Waveguide Aperture Antenna

Figure 4. OpenEMS FDTD simulation of Electric Field magnitude squared

Citations:

1. OpenEMS. (2015, October 10). openEMS, . Retrieved 02:29, October 26, 2015 from http://openems.de/index.php?title=OpenEMS&oldid=934.
2. Understanding the Finite-Difference Time-Domain Method, John B. Schneider, www.eecs.wsu.edu/~schneidj/ufdtd, 2010.
3. Balanis, C. A., 1938. (2005). Antenna theory: Analysis and design (3rd ed.). Hoboken, N.J: Wiley-Interscience.