# A Miniaturized RHCP Slot Antenna for Wideband Applications Including Sub-6 GHz 5G
## 5 Parametric Study  
In this section, the effects of some key parameters on the \(S_{11}\) and the AR in the broadside direction are studied. These parameters include the width of the rectangular strip in the ground plane (\(W_{s1}\)), the length of a vertical strip (\(L_{p}\)), the cutting depth of the tuning stub (t), the width of the parasitic strip (\(W_{s2}\)), and the width of a thin horizontal strip (S). As mentioned previously, every parameter participates in generating CP withwide frequency coverage. Figure 7a,b reveal the \(S_{11}\) and AR, respectively, at different values of \(W_{s1}\) while keeping other parameters at their optimum values. This parameter improves the coupling between the stub and the radiating element at the first resonant frequency. Since this rectangular strip controls the length of the current path around the radiating slot, the impedance matching is shifted toward a lower frequency band. It is evident that it significantly introduces a wide range of CP because it provides a path perpendicular to the original path of the conventional rectangular slot. \(W_{s1}\) equal to 11 mm gives the best results for the ARBW and impedance BW. The effect of the length \(L_{p}\) of the vertical strip is exhibited in Figure 8. As can be seen from Figure 8a, the different values of \(L_{p}\) slightly impact the coupling in the impedance matching at 4.2 GHz, while they have no effect in the lower band. The reason for this is that the tuning stub does not contribute in the radiation of the antenna, and it does not control the radiating current path. For the same reason, the mismatching at the upper frequency band of the ARs can be decreased by tuning \(L_{p}\) as in Figure 8b. It extends the CP bandwidth to the highest frequency band when its optimum value of 6 mm is attained. Figure 9a,b display the \(S_{11}\) and AR at different depths of the truncated corner t. It has a minor impact on the reflection coefficient because it does not affect the line-slot coupling of the antenna. This truncation exhibits a significant effect to make AR less than 3 dB at 2.9 GHz when t is equal to 8.14 mm. This means that it controls the phase orthogonality between the current modes of the antenna, but it has a minor effect on their amplitudes. The \(S_{11}\) and AR of the parameter \(W_{s2}\) are shown in Figures 10a,b, respectively. The parasitic strip (\(W_{s2}\)) plays an essential role in achieving both phase orthogonality and improved impedance matching. A parametric study on the width of this strip, as shown in Figure 10, demonstrates its significant influence on the antenna's performance. Specifically, when \(W_{s2}=13\) mm, the design achieves optimal matching across the three resonance frequencies, along with the lowest axial ratio within the desired band. This is because \(W_{s2}\) enhances the excitation of the orthogonal modes by modifying the horizontal surface current distribution  
Figure 7: Simulation results of the proposed antenna with \(L_{p}=6\) mm, t = 8.14 mm, \(W_{s2}=13\) mm, S = 1 mm, and different values of \(W_{s1}\): (**a**) reflection coefficient and (**b**) AR. Figure 11 illustrates the effect of changing the width of the horizontal strip (S) attached to the tuning stub on the \(S_{11}\) and AR. Since it is a part of the tuning stub, the impedance matching is extended to the upper side of the frequency as S decreases. Meanwhile, it contributes to obtaining a wide ARBW at the higher frequency band by reducing the mismatching at 3.7 GHz to reach its optimum value of 1 mm. The effect of the width of the horizontal strip (S) appears for values larger than 1 mm because it generates a vertical current component that distorts the orthogonality of the orthogonal current paths. It is known that FR4 introduces higher dielectric losses at frequencies above 3 GHz, which can impact the radiation efficiency and bandwidth. This effect was considered during the design, and the antenna dimensions were optimized accordingly to achieve acceptable performance within the target frequency band.