## 3 Simulations and Experiments  
The proposed circularly polarized antennas were constructed and simulated with high-frequency simulation software (HFSS). According to the EPA, RHCPA, and LHCPA discussed previously, the parameters of these antennas, such as reflection coefficient (\(\ket{S_{11}}\)), axial ratio, and radiation pattern, were calculated and analyzed. Furthermore, the measured reflection coefficient was obtained by a vector network analyzer (VNA), and the radiation performance was measured in a multi-probe spherical near-field test anechoic chamber. Simulated and measured \(\ket{S_{11}}\) of the optimized EPA (without the polarizer), the LHCPA, and the RHCPA are shown in Figure 7, in which the simulated \(\ket{S_{11}}\) of the optimized EPA was obtained by optimizing the feed position of the EPA. It can be observed that the impedance bandwidth (where \(\ket{S_{11}}\leq-10\) dB) of the optimized EPA is 26 MHz (fractional bandwidth 1.1%, 2.338-2.364 GHz) with respect to the center frequency 2.352 GHz. One can observe that the \(\ket{S_{11}}\) curves of the RHCPA and the LHCPA are overlapped over the whole considered frequency band, with an identical impedance bandwidth of 244 MHz (fractional bandwidth 10.2%, 2.258-2.502 GHz), even though their bottom splits are in opposite offsetting, which validates the identical performance predicted previously. While the polarizer is stacked above the EPA, the impedance bandwidth is widened nearly 9-fold due to the overlapping of the lower and upper resonant dips, which are attributed to the polarizer and the EPA, respectively. The measured impedance bandwidth of the RHCPA and the LHCPA are 240 MHz (fractional bandwidth 10.3%, 2.19-2.43 GHz). However, their curves are not completely overlapping over the frequency band as with the simulation case, though they are very close to each other. This is \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Parameters** & L\({}_{1}\) & L\({}_{2}\) & L\({}_{3}\) & L\({}_{4}\) & L\({}_{5}\) & W\({}_{1}\) & W\({}_{2}\) & H\({}_{1}\) & H\({}_{2}\) & H\({}_{3}\) \\ \hline
**Value** & 132 & 39.6 & 3.5 & 1 & 4 & 28 & 2 & 5.5 & 1 & 1.5 \\
**Parameters** & R\({}_{1}\) & R\({}_{2}\) & R\({}_{3}\) & R\({}_{4}\) & R\({}_{5}\) & R\({}_{6}\) & R\({}_{7}\) & R\({}_{8}\) & D\({}_{1}\) & G\({}_{1}\) \\
**Value** & 29 & 15 & 11 & 9 & 28 & 16 & 12 & 10 & 9.6 & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The dimensions of the proposed antennas shown in Figure 6 (unit: mm). Figure 6: Configuration of the proposed circularly polarized antennas: (**a**) Three-dimensional view; (**b**) elliptical radiator; (**c,d**) are, respectively, the front view of fabrication prototype corresponding to the RHCPA and the LHCPA. mainly due to the fabrication difference between the RHCPA and the LHCPA. It can be seen that there is about a 70 MHz downward frequency shift in the measured results compared to the simulated ones. This can be attributed to the practical dielectric loss, which makes the effective dielectric constant increase [30; 31]. It is worth mentioning that one can select a large dielectric board/plane size for the proposed antennas to obtain a higher gain. Figure 7b shows \(\mid\)S\({}_{11}\mid\) varying with the inverse offsetting of two SSRs of the RHCPA: the small SSR shifts to the right while the large one shifts to the left by the same offsetting distance (\(\Delta\)S). This indicates that the covered frequency band can be slightly adjusted under a nearly unaltered bandwidth. Otherwise, the fixed longitudinal spacing between SSRs brings an appropriate coupling to maintain the resonance. In addition, when putting the prototypes of the RHCPA and the LHCPA side by side, the transmission coefficient \(\mid\)S\({}_{21}\mid\) between the two ports of both antennas was less than \(-\)33 dB, which indicates that the coupling between the two antennas is very small [13]. Simulated and measured AR in the broadside (along +z axis) of the RHCPA and the LHCPA are shown in Figure 8a.