## 4 Analysis of Numerical Results
### Graphite Resonator
The radiation patterns in Figure 15a show geometries using WPA achieve MLM values higher than the patch antenna without a resonator. Conversely, geometries using LPA exhibit lower MLM values. Furthermore, among the evaluated geometries, the hollow half-cylinder achieves the highest MLM values when the alignments are considered. This are followed by the inverted half-cylinder geometries, with the half-cylinder geometries exhibiting the lowest MLM values. This trend highlights how relevant the type of alignment of geometries of the resonator over the patch antenna is in terms of radiation. When examining the SLL, only the WPA hollow inverted half-cylinder exhibits a change, showing a reduction in its SLL value. Consequently, it shows a unique behavior among the evaluated geometries, where the WPA hollow inverted half-cylinder enhances antenna directionality because SLL is reduced. Regarding the HPBW, all half-cylinder geometries attain lower values compared to the patch antenna without a resonator. Concerning the trapezoidal prism-based geometries, \(|S_{11}|\) in Figure 13b shows a slight shift in the resonant frequency. This shift is more pronounced for the LPA inverted trapezoidal prism and hollow inverted trapezoidal prism, as well as for the WPA inverted trapezoidal prism. Moreover, the BW is the largest for the WPA trapezoidal prism. The radiation pattern plots in Figure 15b show all trapezoidal prism-based geometries achieve higher MLM values compared to the patch antenna without a resonator, indicating their usefulness for enhancing radiation performance. According to Table 6, the LPA and WPA hollow inverted trapezoidal prisms exhibit the highest MLM values. In terms of HPBW, Table 6, most trapezoidal prism-based geometries show a reduction compared to the patch antenna without a resonator, except the LPA trapezoidal prism. Regarding the SLL, reductions are observed for the LPA inverted trapezoidal and hollow inverted trapezoidal prisms, improving antenna performance. Similar enhancements are also noted for the WPA inverted trapezoidal prism, Table 6. Lastly, these geometries show a reduction in their SLL values, indicating their usefulness for improving antenna directionality. Overall, analyzing various geometry shapes for graphite resonators, several trends emerge across the different geometries. Most are characterized by a slight shift in resonant frequency, with the most significant changes observed in the half-cylinder-based geometries,mainly aligned in the LPA half-cylinder-based geometries, and for the hemisphere within the cap-based geometries. Regarding BW, the highlight is the cylindrical hemisphere, which exhibits a BW value higher than the patch antenna without a resonator. This is followed by the cone, which obtains BW value similar to the patch antenna without a resonator. Regarding the MLM value, the greatest improvement is observed in the hollow inverted cone, which outperforms the other geometries. The hollow inverted cone also shows the highest reduction in HPBW, indicating a more focused radiation pattern and enhanced directionality than the patch antenna without a resonator. Among the geometry shapes that present changes in SLL, the hollow concave hemisphere achieves the greatest reduction in this value and enhances its directionality.