In this example, XFdtd is used to simulate the performance of a substrate integrated waveguide (SIW) leaky wave antenna with transverse slots. The design was taken from the paper by Liu, Jackson, and Long . The antenna operates like a transverse slotted rectangular waveguide, but is designed in SIW for reduced cost, size, and for easier integration with planar circuits. Results for S-parameter performance, antenna gain, and efficiency are computed.
Device Design and Simulation
A top view of the entire antenna is shown in Figure 1 where the green material represents copper and the red is a dielectric (relative permittivity = 2.25 and loss tangent of 0.001). The device is approximately 310 mm in length, 40 mm in width, and 1 mm in height. The copper microstrip layer at the top of the device has transverse slots spaced at regular intervals and tapered at the ends. At each end of the device a nodal waveguide port is connected to a tapered microstrip line that connects to the SIW portion. In the top layer are a number of transverse slots, more easily seen in Figure 2. The edges of the top microstrip layer are terminated with vias. The layers are shown in angled views in Figures 3 through 5 where all parts are shown in Figure 3, the substrate is visible in Figure 4, and the vias in Figure 5.
The device is simulated by applying a frequency-limited signal to the waveguide port at one end. The S-parameter results are shown in Figure 6 and it can be seen that the device has good operating performance from 10.4-12.5 GHz and a few smaller frequency bands below 10.4 GHz. Below 10 GHz the response is cutoff.
The antenna produces several beams which range from near broadside to near end fire depending on the frequency. These beams are generally narrow and fan-shaped. At 10.2 GHz, the beam is quite narrow and peaks at about 8.6 dBi at theta=70 degrees in the YZ plane as shown in Figure 7 in a polar plot. The 10.2 GHz pattern is shown as a three-dimensional plot from the same angle as the polar plot of Figure 7 in Figure 8. A different perspective of the 10.2 GHz three-dimensional pattern is shown in Figure 9. At 10.8 GHz, the peak gain increases to 11.1 dBi and the beam shifts to a peak at theta=49 degrees in the YZ plane as shown in Figures 10, 11, and 12. The pattern broadens slightly and increases in peak gain at 11.5 GHz where the main lobe direction changes to theta=28 degrees and the maximum gain is 12.7 dBi as shown in Figures 13, 14, and 15. At 11.7 GHz the maximum gain is 14 dBi at an angle of theta=19 degrees as shown in Figures 16, 17, and 18. Finally, at 12 GHz, the maximum gain is 14.2 dBi at an angle of theta=13 degrees as shown in Figures 19, 20, and 21.
The radiation efficiency is computed in the paper using a theoretical approach for a slotted rectangular waveguide which does not consider the system mismatch or the power lost in other ports. A value comparable to this theoretical one is computed in XFdtd and is labeled the standalone radiation efficiency. The theoretical radiation efficiency from the paper is plotted in Figure 22 along with the standalone radiation efficiency from XFdtd and the XFdtd system efficiency, which includes both the mismatch loss and the power lost in the second waveguide port.
 J. Liu, D. R. Jackson, and Y. Long, “Substrate Integrated Waveguide (SIW) Leaky-Wave Antenna With Transverse Slots,” IEEE Trans. Antennas Propag., vol. 60, no. 1, pp. 20-29, Jan. 2012.