## 3 Antenna Design and Parameters Study
### Design and Simulation of the EBG MPAs
In Figure 4b, two square-shaped slots are etched along the right diagonal line of the center patch to create Right Hand Circular Polarization (RHCP), which is similar to one of the structures introduced in [13]. By embedding these slots like this, the antenna's current distribution is perturbed, leading to the excitation of two orthogonal resonant modes with the same amplitude but with a 90-degree phase difference, which is necessary to produce circular polarization. The placement and dimensions ratio of the square slots, as well as the location of the probe feed are optimized to reach good circularly polarized radiation. The minimum antenna design requirements are tabulated in Table 1. These requirements are for maintaining a data rate of 10 Msps when using a QPSK modulated signal for our CubeSat's X-band transmitter module. The antennas are simulated and optimized using CST Studio Suite 2019 software. The Time-domain solver is used for full-wave electromagnetic simulations. The antenna design procedure is summarized as follows:  
1. Design and simulate the original CP MPA in the available surface area with only the center radiator, at the target frequency of 8.483 GHz;
2. Design and simulate the MPA with the mushroom-like EBG structure added;
3. Optimize the related parameters to satisfy the requirements of gain and CP. The parameters of the CP EBG MPA are listed in Table 2. The units are millimeters. The important antenna parameters such as the input reflection coefficient (S\({}_{\mathbf{11}}\)), antenna gain (S\({}_{\mathbf{21}}\)), and the antenna far-field radiation pattern are simulated. In addition, simulation of the axial ratio (AR) at the operating frequency of 8.483 GHz and the 3 dB axial ratio bandwidth (ARBW) over frequencies will be carried out to evaluate the circular polarization quality of the antenna. Figure 5 shows the simulated S\({}_{\mathbf{11}}\) values of the original MPA and the CP EBG MPA. At 8.483 GHz, the S\({}_{\mathbf{11}}\) values of the original MPA and the CP EBG MPA are \(-21.9\) dB and \(-18.2\) dB, respectively. However, it is evident in Figure 5 that the circular \begin{table}
\begin{tabular}{c c} \hline \hline
**Name** & **Value** \\ \hline Gain Bandwidth & 10 dBi \\ Gain Bandwidth & 13 MHz \\ S\({}_{\mathbf{11}}\) Bandwidth & 13 MHz \\ AR Bandwidth & 13 MHz \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The minimum antenna design requirements. Figure 4: The design of X-band EBG MPAs for circular polarization: (**a**) overview and (**b**) zoom-in of the center patch radiator. The grey circle is the contacting part of the SMA probe feed. polarization antenna has the better \(-10\) dB operation bandwidth, which is around 0.7 GHz in comparison to the \(-10\) dB bandwidth value of 0.47 GHz of the original antenna. The gains over frequencies of these antennas are presented In Figure 6. From this figure, we can see that the gains at 8.483 GHz of the original and the CP EBG MPAs are, in turn, 8.27 dBi and 11.72 dBi. This means that a gain increment of around 3.5 dB is achieved after adding the mushroom-like EBG ring to the original antenna structure. \begin{table}
\begin{tabular}{c c c} \hline
**Name** & **Value** & **Description** \\ \hline Lp & 10 & Patch length \\ Wp & 10 & Patch width \\ Lg & 91.3 & Ground length \\ Wg & 91.3 & Ground width \\ Lebg & 10 & Length of an EBG element \\ Webg & 10 & Width of an EBG element \\ gebg & 2 & Gap between two adjacent EBGs \\ lsl1 & 4 & Length of the upper square \\ wsl1 & 4 & Width of the upper square \\ lsl2 & 3 & Length of the lower square \\ wsl2 & 3 & Width of the lower square \\ le1 & 0.5 & Distance from the upper square to the upper edge \\ we1 & 0.5 & Distance from the upper square to the right edge \\ le2 & 1 & Distance from the lower square to the lower edge \\ we2 & 1 & Distance from the lower square to the left edge \\ lcor & 15 & Truncated corner length \\ wcor & 15 & Truncated corner width \\ h & 1.6 & Substrate thickness \\ hc & 0.035 & Conductive part thickness \\ \hline \end{tabular}
\end{table}