## 3 Antenna Design and Parameters Study
### Parameters Study  
This section discusses the influence on the antenna gain enhancement of the design parameters such as the shape and number of the EBG structures, as well as the size of the mushroom-like EBG elements. Each parameter will be varied separately while the other parameters remain unchanged to emphasize its effect on the antenna gain. Firstly, the effect of the EBG shape is considered. Figure 10 demonstrates the EBG ring configurations that we have designed simulated, and the distance from the center radiator to its nearest EBG elements is the same in all the configurations, which are labeled from Case (a) to Case (h). Figure 10a shows the original structure (Case (a)), which is a full two-layer EBG ring with the total number of 48 mushroom-like EBG elements. Apparently, this structure is not applicable to the 3U satellite model without modification, as explained in Section 3.1. As can be seen from Figure 10b-h, we gradually removed the outer-layer EBG elements, relocated some elements, and altered the structure of the inner-layer EBG elements until we found the optimal configuration. The effect of this structure alteration is shown in the increase in the antenna gains as depicted in Figure 11. In this figure, at 8.483 GHz, we can see that the gain of Case (a) is around 7.6 dBi, which is even lower than before adding the  
Figure 8: The surface current distribution at \(\omega t=90^{\circ}\) of (**a**) the original MPA and (**b**) the CP EBG MPA.  
Figure 9: The simulated 3 dB axial ratio bandwidth of the CP EBG MPA.  
EBG, but in Case (c), after removing 25 EBG elements of the outer layer, the gain is boosted to 9.4 dBi. In Case (f), we only keep two EBG elements of the outer ring and in Case (g), the outside EBG ring is totally removed, and the gain values continue to rise to approximately 10.9 dBi. However, the peaked gains in these cases are still not located at 8.483 GHz. Finally, in Case (h), the truncation at the four outer corners of the antenna resulted in a further gain increase of around 0.8 dB to reach the highest value of 11.72 dBi exactly at the target frequency 8.483 GHz. This can be explained as follows: By truncating the four corners, the surface wave, as well as the diffraction and scattering waves on these areas will be removed. Moreover, this leads to a shift in the bandgap center frequency, nudging it to align with the antenna target frequency. Consequently, more power is radiated into free space, leading to an improvement in the antenna gain. Therefore, cutting the four edge corners is not only structurally necessary to fit the antenna on the CubeSat surface, but also provides good electromagnetic effects in terms of gain enhancement and frequency tuning.  
Secondly, the effect on the gain enhancement when changing the dimensions of the EBG is studied. In this case, we use the Case (h) EBG configuration in Figure 10h. Only the dimensions of the EBG elements are varied while all other parameters remain unchanged. The length and width values are equal to ensure that each EBG element is always square with the ground via located in the center of the element. It is important in maintaining the rotational symmetry of the mushroom EBG elements, as well as the antenna structure, to guarantee polarization-independent reflection phase characteristics that are required for our CubeSat antenna application. Figure 12 illustrates the gain values when changing the EBG dimensions from 9 mm to 11 mm with a step size of 0.5 mm. As shown in this figure, the highest gain of 11.72 dBi at 8.483 GHz (denoted as the solid red line) is reached when the dimensions of the EBG elements are 10 mm, which is the same value as the size of the square center patch radiator. Deviations from this optimal size shift the bandgap away from the target operation frequency and reduce its effectiveness, leading to a decline in the antenna gain.  
Figure 10: The experimental EBG MPAs from Case (**a**), with the initial EBG, to Case (**h**), with the final EBG design.