## 3 Results and Discussion
### Final Design Overview  
Following the thorough parametric analysis, key antenna parameters, including the dielectric layer and the gaps along the sides, top, and arms (c, g, h, p, r, s), were fine-tuned to mitigate the effects of the manufacturing tolerances. After optimization, additional parametric analyses were conducted to determine the appropriate step spacing by considering  
Figure 6: S\({}_{11}\) values corresponding to parametric analyses: (**a**) arm spacing width (g), (**b**) arm spacing height (h), (**c**) upper gap width (r), (**d**) upper gap height (s). Figure 7: S\({}_{11}\) parametric analysis of the (**a**) arm spacing (g, h) and (**b**) upper gap (r, s). antenna manufacturing sensitivity and the influence of each separation on the S\({}_{11}\) values. For the dielectric layer, which has minimal impact on S\({}_{11}\), a step interval of 0.5 mm was used, while intervals of 0.1 mm and 0.15 mm were applied for the upper gap analyses. Building upon the optimized parameters, further investigations were conducted to analyze the impact of the slot dimensions on the dual-band operation of the proposed antenna. Since slot geometry plays a crucial role in resonance tuning and impedance matching, a detailed parametric study was performed to evaluate the influence of key slot dimensions. Figure 8 presents a comprehensive analysis of key slot dimensions affecting the dual-band operation of the proposed antenna. The parameters analyzed include the side slot width (p), side slot length (o), bottom slot width (l), and bottom slot length (m), detailed in Figure 9. The impact of these notches and slots on resonance frequencies, bandwidth, and return loss was systematically examined, leading to the identification of optimal slot configurations. The side slot width (p) plays a significant role in influencing field distribution, impedance bandwidth, and resonance stability. The side slot length (o) is crucial for shaping the secondary resonance by modifying the effective inductance and capacitance. The bottom slot width (l) governs coupling strength, bandwidth, and radiation efficiency, while the bottom slot length (m) directly impacts the effective electrical path, affecting both impedance matching and resonance characteristics. Figure 8: Parametric analysis of slot dimensions and their effects on dual-band performance: (**a**) side slot width (p), (**b**) side slot length (o), (**c**) bottom slot width (l), and (**d**) bottom slot length (m). To systematically assess these effects, parametric analyses were conducted with a 10% step interval, while the notch structures were examined with a 100% dimensional variation to evaluate their full impact. The results depicted in Figure 8a,b indicate that variations in the side slot width (p) primarily affect the horizontal current distribution, leading to noticeable shifts in the lower resonance frequency. In contrast, the side slot height (o) has a more pronounced effect on impedance matching, as corroborated by both numerical and experimental findings. Furthermore, higher-order modes, which are generally more sensitive to vertical structural modifications, exhibit minimal influence on the secondary resonance frequency. Figure 8c,d further analyze the effects of bottom slots on S\({}_{11}\). While these slots exert limited influence on current distribution, their proximity to the feeding point significantly impacts impedance matching. Consequently, even under substantial dimensional variations, their effect on resonance frequencies and bandwidth remains minimal, whereas their influence on return loss is found to be considerable, as validated through both numerical simulations and experimental measurements. These findings underscore the critical role of slot geometry in achieving effective dual-band operation. The results emphasize the necessity of precise slot dimensioning to optimize impedance matching and radiation characteristics, thereby enhancing the overall antenna performance.