## 4 Flared SBF Antenna with a Superstrate Lid  
Some of the previous designs of waveguide-fed SBF antennas have utilized foam materials to support the sub-reflector at the required height from the main reflector. Although the foam material has been useful for prototyping, it is not strong enough to keep the sub-reflector permanently in place and could potentially be modified when installed for a practical application. For example, the foam could be pushed downward into the main reflector, and the optimized position of the sub-reflector would be compromised. To solve this issue, we developed a thin plastic-based superstrate that is rigid enough to maintain the position of the sub-reflector with minimal effect on the antenna's performance. Furthermore, the superstrate can be easily 3D printed. It is important to judiciously choose the right thickness and material of the superstrate to minimize the reflections that can negatively affect the antenna's performance. We carried out simulation studies to compare the performance of the antenna with and without the superstrate to ensure that excellent performance is maintained. The geometry of the flared SBF antenna with the substrate lid is shown in Figure 7. The lid consists of two parts that are connected together, a thin disk with a hole and a rim surrounding the hole on which the sub-reflector is placed. The dimensions \(\mathrm{t_{S1}}\), \(\mathrm{t_{S2}}\) and \(\mathrm{t_{sub}}\) refer to the thickness of the disk, the thickness of the lid's rim, and the thickness of the sub-reflector. The distance between the rim and the sub-reflector (\(\mathrm{Hr}\,-\,\mathrm{Hs}\,\)= 5.45 mm) is equal to \(\mathrm{t_{S1}}\) + \(\mathrm{t_{S2}}\), \(\mathrm{t_{Sub}}\) = 2 mm, while the diameter of the disk's hole is equal to 37.5 mm. For the simulation, we studied the effects of the lid on the behavior of the antenna by modeling it with two plastic materials with different dielectric constants. The first is the polylactic (PLA) plastic with a dielectric constant of 2.1, while the second plastic is the acrylonitrile butadiene styrene (ABS) plastic with a dielectric constant of 3.0. The thickness of the lid's disk (\(\mathrm{t_{S1}}\)) was also varied from 1-4 mm and studied to obtain the best design performance. Figure 7: Flared SBF antenna with a dielectric superstrate cover. Figure 8a,b gives the simulated S11 result of the flared antenna. From both plots, it can be seen that the antenna with the lid raised the S11 result compared to the antenna with no lid. The effect of the PLA lid with the lower dielectric constant on the antenna is not as significant as that of the ABS lid. While the S11 result for the PLA lid is raised between 4.3-5.6 GHz, the value does not go above \(-10\) dB, therefore the bandwidth does not change much. All the simulated impedance bandwidths were between 62.2% to 67.8% for 4 mm to 1 mm lid thickness, respectively. As the thickness of the ABS lid increases above 1 mm, the S11 result is raised above \(-10\) dB at the lower frequencies, which drastically reduced the impedance bandwidth. The bandwidth for the antenna with no lid is 66.7%, while the antenna with the ABS lid of 1 mm, 2 mm, 3 mm, and 4 mm had impedance bandwidths of 66.4%, 46.4%, 43.2%, and 45.7%, respectively. The peak realized gain for the SBF antenna with the PLA and ABS lids are compared to the antenna without the lid in Figure 9. There is a general trend of the gain reducing with increasing lid thickness. However, the gain loss experienced by the PLA lid is not as high as that of the ABS with the higher dielectric constant. This gain loss is most noticeable at 5.6 GHz and with a lid thickness of 4 mm. For example, at 5.6 GHz, the lidless antenna has a peak gain of 17.02 dBi, while the PLA and ABS lids with a lid thickness of 4 mm  
Figure 8: Simulated S11 result of the flared SBF antenna with: (**a**) PLA lid; (**b**) ABS lid. have peak gains of 15.7 dBi and 10.8 dBi, respectively. The gain loss is very minimal for the 1 mm lid thickness.