## 3 Results and Discussion  
### Antenna Design Overview  
In this study, a rectangular microstrip patch antenna was selected due to its straightforward design and the ease with which its resonant frequency can be fine-tuned by adjusting the patch length (L). The patch dimensions were determined using standard microstrip antenna equations. Initially, a dual-band antenna for 28/38 GHz was designed, and its S\({}_{11}\) parameters were analyzed by modifying the geometry of the antenna. The investigation involved generating multiple models and varying critical parameters, including the patch length, width, cavity dimensions, and the positioning of the patch arm. A seven-step sizing procedure was employed, where the patch length was incremented by 0.5 steps and the patch width was incremented by 1 mm, up to 20 mm. Based on the evaluation of the S\({}_{11}\) parameters, the optimal configurations were selected based on the gain, directivity, impedance matching, and voltage standing wave ratio (VSWR). Additional customizations included repositioning the patch arm, modifying the gaps on the patch, and adjusting the dielectric and base materials. In some designs, the lower inserts on the patch arm were redesigned with alternative dimensions. Following these modifications, a parametric analysis was conducted to select four optimal designs based on S\({}_{11}\), gain, and VSWR. The antenna design involved a comprehensive parametric analysis of the dielectric layer and patch dimensions. This analysis focused on key geometric factors, such as the gap dimensions (bw, bl), bottom gap dimensions (c, d), inner gap dimensions (e, f), and top gap dimensions (g, h). For all the designs, the patch width (yw) and length (yl) were fixed at 15 and 14 mm, respectively. The insulator layer size was optimized to improve the antenna performance. After analyzing all the dimensions, the final antenna structure was developed, as illustrated in Figure 1.  
The rectangular microstrip patch antenna underwent a detailed parametric analysis of the dielectric layer and patch dimensions to optimize performance. The key geometric aspects were systematically varied, such as gap widths, bottom gap lengths, and inner and top gap dimensions. These adjustments were essential for optimizing S\({}_{11}\) antenna operation and ensuring efficient antenna operation. The final antenna dimensions derived from this analysis are summarized in Table 1.  
Figure 2 shows the simulation results of the S\({}_{11}\) parameters for the designed rectangular microstrip patch antenna across the specified frequency range. The simulation result presented in Figure 2 was generated using CST Studio Suite. Specifically, we utilized the Time Domain Solver, which employs the finite integration technique (FIT) to simulate the time evolution of electromagnetic fields. The FIT was selected for its high accuracy, efficiency, and proven numerical stability, as well as its flexibility in modeling complex geometries. Furthermore, the meshing process was conducted using CST's automatic mesh generation algorithm, which produces a hexahedral mesh. The S\({}_{11}\) value, or return loss, is a critical parameter for assessing how well the antenna matches the transmission line, with lower values (below \(-10\) dB) indicating better impedance matching and minimal power reflection. The figure shows two prominent dips corresponding to the resonant frequencies at 26.6 GHz and 38.6 GHz, where the S\({}_{11}\) values drop well below \(-10\) dB, reaching approximately \(-50\) dB. These deep nulls indicate highly efficient energy transfer at these frequencies, which is consistent with the target dual-band operation of the antenna.