## 4 Analysis of Numerical Results
### Graphite Resonator
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline \multicolumn{1}{c}{**Geometry**} & \(|\mathbf{S_{1}}|\) & **BW** & **MLM** & **HPBW** & **SLL** \\  & **(dB)** & **(MHz)** & **(dBi)** & **(c)** & **(dB)** \\ \hline Patch antenna & \(-\)34.30 & 60 & 2.79 & 148.2 & w/o \\ \hline Rectangular prism & \(-\)14.70 & 57 & 3.27 & 126.9 & \(-\)11.1 \\ \hline Hollow rectangular prism & \(-\)8.46 & 42 & 2.79 & 139.1 & w/o \\ \hline Cylindrical hemisphere & \(-\)14.84 & 62 & 3.09 & 149.1 & w/o \\ \hline Concave hemisphere & \(-\)11.97 & 54 & 4.25 & 121 & \(-\)10.6 \\ \hline Hollow concave hemisphere & \(-\)12.76 & 54 & 4.49 & 115.1 & \(-\)11.9 \\ \hline Hemisphere & \(-\)14.4 & w/o & \(-\)2.27 & 164.6 & w/o \\ \hline Inverted cone & \(-\)16.49 & 51 & 4.7 & 114 & \(-\)11.1 \\ \hline Hollow inverted cone & \(-\)16.74 & 49 & 5.04 & 102.1 & \(-\)6.4 \\ \hline Cone & \(-\)13.55 & 60 & 3.27 & 148.7 & w/o \\ \hline LPA Inverted half-cylinder & \(-\)4.19 & 9 & 1.84 & 129.8 & w/o \\ \hline LPA hollow inverted half-cylinder & \(-\)4.81 & 16 & 2.12 & 129.5 & w/o \\ \hline LPA half-cylinder & \(-\)2.32 & w/o & \(-\)0.65 & 135.3 & w/o \\ \hline WPA inverted half-cylinder & \(-\)16.27 & 59 & 3.59 & 143.3 & w/o \\ \hline WPA hollow inverted half-cylinder & \(-\)16.48 & 56 & 4.08 & 129.6 & \(-\)11.7 \\ \hline WPA half-cylinder & \(-\)10.76 & 50 & 3.47 & 146 & w/o \\ \hline LPA inverted trapezoidal prism & \(-\)5.76 & 3 & 3.35 & 128.2 & \(-\)7.6 \\ \hline LPA hollow inverted trapezoidal prism & \(-\)6.45 & 29 & 4.08 & 114.6 & \(-\)8.6 \\ \hline LPA trapezoidal prism & \(-\)7.97 & w/o & 2.82 & 164.3 & w/o \\ \hline WPA inverted trapezoidal prism & \(-\)7.68 & 39 & 3.69 & 120.4 & \(-\)11.2 \\ \hline WPA hollow inverted trapezoidal prism & \(-\)12.07 & 45 & 4.09 & 127.8 & w/o \\ \hline WPA trapezoidal prism & \(-\)12.43 & 52 & 3.58 & 143.3 & w/o \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Patch antenna with a graphite-made resonator: Key parameters values at the resonant frequency. Figure 15: Patch antenna with a graphite-made resonator: the radiation pattern plot of the 1D far-field realized gain (\(\phi=0\)). (**a**) half-cylinder-based; and (**b**) trapezoidal prism-based. the most pronounced change. Moreover, the BW values listed in Table 6 are relatively broader for both geometries, with those associated with the rectangular prism being the closest to the patch antenna without a resonator. According to the radiation pattern plots, as depicted in Figure 14b, the rectangular prism offers an MLM that exceeds the patch antenna with a resonator. In contrast, the hollow rectangular prism shows an MLM similar to the patch antenna a with a resonator. Paying attention to the HPBW and SLL parameters, the rectangular prism shows the highest reduction compared to the patch antenna without a resonator, Table 6.  
In relation to the cone-base shape geometries, similar \(|S_{11}|\) values are obtained, as shown in Figure 13c. All geometries exhibit a broader BW except the cone, which attains a value similar to the patch antenna without a resonator. Concerning the radiation pattern, as depicted in Figure 14c, all the geometries exceed the MLM value of the patch antenna without a resonator. The hollow inverted cone and inverted cone exhibit similar performance in terms of MLM and achieve a relevant reduction in both HPBW and SLL, Table 6, and, consequently, they can be advanced to improve antenna directionality. In regards to the half-cylinder geometries, \(|S_{11}|\) in Figure 13a shows distinct performance trends based on the type of alignment. Geometries with the LPA alignment exhibit similar behavior to one another, as do those using the WPA alignment. Using LPA offers a downshift in the resonant frequency, suggesting their potential for reducing antenna size. In terms of BW, as listed in Table 6, geometries with WPA achieve the highest BW values compared to the patch antenna without a resonator. In contrast, geometries using LPA reduce the BW values.