## 3 Simulations and Experiments
It can be seen that their simulated AR curves overlapped in the entire band once again, with the same 3-dB AR bandwidth 72 MHz (fractional bandwidth 2.95%, 2.402-2.474 GHz), and the minimum AR value of 0.059 dB is observed at frequency 2.438 GHz. For the measured results, the curves are not overlapping due to fabrication error. The 3-dB AR bandwidth for the LHCPA and the RHCPA covers 2.345-2.41 GHz (fractional bandwidth 2.7%) and 2.34-2.405 GHz (fractional bandwidth 2.7%), respectively, with a minimum AR value of 0.05 dB at 2.37 GHz. In the same manner, a frequency shift is observed for both antennas. Nevertheless, all the AR bandwidths are within their impedance bandwidth. The low AR value was obtained with a substantial optimization process, resorting to the inserted short stubs and optimization of their length L\({}_{4}\). Figure 8b shows a set of AR curves with respect to frequency with varied L\({}_{4}\). It is found that the AR has the minimal value at L\({}_{4}\) = 1 mm, which is in the intermediate range of L\({}_{4}\) considered. Otherwise, the 3-dB AR bandwidth can be attained in a proper frequency range. However, with L\({}_{4}\) deviating from the optimum value, the AR deteriorates and the AR bandwidth becomes narrower. Actually, these deteriorations can be alleviated by further tuning other structures of the DSSRs so as to realize good AR performance. Figure 7: (**a**) Simulated and measured reflection coefficients of the optimized EPA, the RHCPA, and the LHCPA; (**b**) effect of inversely offsetting SSRs by equal distance (\(\Delta\)S) on the reflection coefficients of the RHCPA. Simulated and measured two-dimensional radiation patterns of the RHCPA and the LHCPA are shown in Figure 9a-d. The realized gain and the cross-polarization of the RHCPA and the LHCPA are, respectively, 9.25 dBi and lower than \(-10.9\) dBi at 2.438 GHz, as seen from Figure 9a,b. For the measured results, Figure 9c,d show a gain of 8.54 and 8.86 dBi at 2.37 GHz, with the cross-polarization lower than \(-9.71\) and \(-10.52\) dBi for both antennas, respectively. In addition, the measured (simulated) half-power beamwidths for both antennas are approximately \(60^{\circ}\) across their 3-dB AR bandwidth. As indicated from these results, the conversion from the linear polarization to the right-hand or the left-hand circular polarization is verified after adding their respective polarizers. In addition, after reversing only the offset direction of the dual bottom splits of the DSSRs, the corresponding RHCP and LHCP characteristics of the proposed antennas are validated. Simulated and measured gains in the broadside direction of the RHCPA and the LHCPA are plotted in Figure 10. Both simulated curves coincide and have the same peak gain up to 9.26 dBi, which is increased by about 3.9 dB compared to that of the optimized EPA. Regarding the measured results, the peak gains of both antennas are up to 8.7 and 9 dBi, respectively, with a variation of less than 0.7 dB across their 3-dB AR bands. The acceptable discrepancy between simulation and measurement can be ascribed to fabrication and measurement tolerances. In addition, the simulated efficiency of the RHCPA and the LHCPA is higher than 89% over their 3-dB AR bands. Table 2 compares the performance of the proposed circularly polarized microstrip antennas with that of two other antennas reported in the recent literature. It can be observed that the patch antennas proposed in this paper exhibits superiority in CP bandwidth, profile height and gain. In particular, their profile height of \(0.063\lambda_{0}\) is approximately one-half of the contrasted lowest one (\(0.13\lambda_{0}\)) while maintaining a wider CP bandwidth and higher gain, which manifests their low profile characteristics. It should be mentioned that, in our previous work [23] the CP antenna was built in a multi-layer patch structure without air gap, this has a lower profile height (\(0.016\lambda_{0}\)).