## 5 Parametric Study  
Parametric study holds a pivotal position in the process of antenna design and optimization. It not only enables us to gain an in-depth understanding of the intrinsic relationships between antenna performance and various structural parameters but also provides a scientific basis for the final antenna design, ensuring that the antenna can achieve the desired performance metrics. In this study, we utilized HFSS to conduct extensive parameter sweeping and optimization. Through meticulous adjustment and analysis of different parameters, we ultimately achieved excellent broadband performance for the antenna. This chapter will elaborate on the learning and optimization processes of several key parameters involved in the antenna design. (1) Patch number optimization  
The number of patches is an important parameter affecting antenna performance. In this study, we conducted simulation analyses on antenna structures with 3 \(\times\) 3, 4 \(\times\) 4, and 5 \(\times\) 5 patch numbers, respectively, and compared them with the final proposed structure, as shown in Figure 7.  
The 3 \(\times\) 3 unit structure clearly exhibits the narrowest IBW and ARBW, indicating that an insufficient number of patches makes it difficult for the antenna to generate additional resonances. The 4 \(\times\) 4 unit structure displays three resonance points on the S11 curve, located at 4.95 GHz, 5.4 GHz, and 6.03 GHz, respectively, and two resonance points on  
Figure 6: Surface current density on MTS after excitation by the feeding network at different phases at 6.9 GHz. (a) 0\({}^{o}\); (b) 90\({}^{o}\). Figure 7: Comparison of antennas with different patch numbers. (a) S\({}_{11}\); (b) AR. the axial ratio curve, located at 5.1 GHz and 7.25 GHz. However, the axial ratio in the frequency band between these two resonance points is greater than 3 dB. The 5 \(\times\) 5 unit structure achieves an IBW of 5-7.25 GHz and an axial ratio within approximately 3 dB in the frequency range of 5.3-7.45 GHz, demonstrating the potential for realizing broadband circular polarization. Therefore, in this paper, based on the 5 \(\times\) 5 unit structure, we removed corner patches and placed parasitic patches and mode-suppression patches. The specific effects will be presented in the next section. (2) Influence of parasitic patches and mode-suppression patches  
As previously discussed in the preceding sections, adding parasitic patches and mode-suppression patches can effectively enhance the desired modes and suppress the undesired ones. To verify the effectiveness of CMA, the same feeding network was used to excite three antennas with different MTS structures, respectively, as shown in Figure 8. The comparison results of the S11 parameters and axial ratios of these three antennas, which are simulated using HFSS, are presented in Figure 9.  
The impedance bandwidth of an antenna is mainly determined by its resonant characteristics and the matching condition between the antenna and the feed source. Therefore, in Figure 9a, the impedance bandwidths obtained for these three antenna structures remain basically unchanged. As shown in Figure 9b, the axial ratio values decrease with the improvement of the antenna structures, ultimately achieving an axial ratio below 3 dB across the entire operating frequency band (5.25-7.33 GHz). Although the reduction in the AR value is relatively limited, it must be noted that ensuring that the axial ratio stays below 3 dB throughout the desired operating frequency band is an essential requirement for a  
Figure 8: Schematic diagrams of antennas with different MTS. (**a**) Antenna1; (**b**) Antenna2; (**c**) Proposed. Figure 9: Comparison of antennas with different MTS. (**a**) S\({}_{11}\); (**b**) AR. satisfactory CP antenna. We carefully adjusted the number and positional distribution of the patches and combined extensive software simulations and parameter scanning analyses to bring the axial ratio of Antenna 1 close to the critical threshold of 3 dB.