## 4 Analysis of Numerical Results
### Glycerin Resonator

Table 5: Patch antenna with a glycerin-made resonator: Key parameters values at the resonant frequency. the patch antenna size, and introduces multiple resonant frequencies. Conversely, the hemisphere geometry increases the resonant frequency, which can be advantageous for applications requiring higher operating frequencies. In terms of BW, as listed in Table 5, the concave hemisphere offers BW value similar to that of the patch antenna without a resonator. In contrast, the hollow concave hemisphere exhibits a reduced BW, indicating limitations in its frequency range. When analyzing the radiation pattern, the concave hemisphere stands out with a notable improvement in terms of MLM, exceeding that of the patch antenna without a resonator. Moreover, it attains a reduction in HPBW and SLL, as listed in Table 5, contributing to enhanced directionality and overall radiation efficiency. Furthermore, the LPA half-cylinder increases the HPBW compared to the patch antenna without a resonator. Finally, the hemisphere geometry alters the MLD value compared to the patch antenna without a resonator. Rectangular prism-based geometries exhibit reductions at the resonant frequency, as illustrated in Figure 8b, underscoring their potential for antenna size reduction. Despite this advantage, their performance at the resonant frequency yields an unacceptable \(|S_{11}|\), Table 5. The radiation pattern analysis in Figure 10b shows contrasting behaviors. For instance, the rectangular prism geometry achieves a notable increase in the MLM value, maintaining a value higher than that of the patch antenna without a resonator, indicating its potential for improving radiation efficiency. In contrast, the hollow rectangular prism substantially decreases the MLM value. Furthermore, as summarized in Table 5, the rectangular prism achieves reductions in both HPBW and SLL and, consequently, enhances the directionality compared to the patch antenna without a resonator. Moreover, the hollow rectangular prism only yields a reduction in terms of HPBW and, unfortunately, with insignificant impact on SLL. For the cone-based geometries, the analysis of \(|S_{11}|\), as shown in Figure 8c and detailed in Table 5, reveals that the inverted cone and cone achieve acceptable values. Furthermore, in terms of BW, the inverted cone outperforms the cone; however, its BW remains lower than that of the patch antenna without a resonator, as listed in Table 5. Regarding the radiation pattern, depicted in Figure 10c and summarized in Table 5, the inverted cone exhibits the highest MLM value, followed by the cone, with both exceeding the performance of the patch antenna. The inverted cone also exhibits reductions in both HPBW and SLL compared to the patch antenna without a resonator, enhancing the directionality of the patch antenna. In contrast, the hollow inverted cone and cone geometries only achieve reductions in terms of HPBW. Analyzing the half-cylinder-based geometries, it is clear that the LPA half-cylinder attains a significant reduction in the value of the resonant frequency, as shown in Figure 9a, highlighting its potential for minimizing patch antenna size. This is followed by the LPA hollow inverted half-cylinder and the WPA inverted and hollow inverted half-cylinders. As detailed in Table 5, the WPA hollow inverted half-cylinder achieves the highest BW value, in contrast to the LPA half-cylinder-based geometries. Observing the radiation pattern in Figure 11a and the values in Table 5, we conclude that the WPA inverted half-cylinder and half-cylinder geometries achieve MLM values higher than the patch antenna without a resonator. Concerning the HPBW parameter, the LPA half-cylinder offers better results than the patch antenna without a resonator, while the others yield lower ones. Taking a look at the SLL, the numerical results show that the LPA half-cylinder and the WPA inverted half-cylinder exhibit reductions compared to the patch antenna without a resonator, enhancing its directionality.