# A Dual-Polarized Omnidirectional Rectenna Array for RF Energy Harvesting Harvesting
## 4 Discussion of the Proposed Rectenna Array
When the polarization direction angle is 0\({}^{\circ}\), the simulated and measured PCEs of the proposed rectenna array versus the input power density for EM wave incomes at angles \(\theta\) of 0\({}^{\circ}\) and 45\({}^{\circ}\) are shown in Figure 17a. Under the incidence angles of 0\({}^{\circ}\) and 45\({}^{\circ}\), the simulated and measured results are basically the same when the input power density is less than 200 \(\mu\)W/cm\({}^{2}\). The maximum PCE is about 60%. Figure 17b plots the simulated and measured PCEs of the rectenna array versus the incident angle under input power densities of 100.3 and 251.9 \(\mu\)W/cm\({}^{2}\). It is not difficult to find that the PCEs of the rectenna array at different power densities are relatively constant with only slight fluctuations when the incidence angle of the electromagnetic wave varies. The main reason why the measured PCEs at higher power densities are better than the simulated ones is that the rectifiers have a wider operating input power range in the measurement. When the polarization direction angle is 90\({}^{\circ}\), the simulated and measured PCEs of the proposed rectenna array versus the input power density for EM wave incomes at angles \(\theta\) of 0\({}^{\circ}\) and 45\({}^{\circ}\) are shown in Figure 18a. It can be clearly seen that the PCEs of the rectenna array at the incidence angles of 0\({}^{\circ}\) and 45\({}^{\circ}\) of the EM waves decrease significantly, and the input power densities corresponding to the peak PCEs are increased. However, the rectenna array is still able to obtain PCEs of more than 40% at input power densities of less than 400 \(\mu\)W/cm\({}^{2}\). Figure 18b plots the simulated and measured PCEs of the rectenna array  
Figure 16: Simulation and test environments of the proposed rectenna array: (**a**) Simulation environment; (**b**) Test environment. versus the incident angle under input power densities of 287.2 uW/cm\({}^{2}\) and 555.1 uW/cm\({}^{2}\). It can be found that the fluctuations of PCEs at different power densities increase when the incidence angle of EM waves changes. However, generally, the fluctuations remain within a tolerable range. This could be attributed to the imperfect omnidirectional radiation performance of the antenna array in the vertically polarized state and the fact that the phase superposition may be non-ideal during RF power combining. When the polarization direction angle is 45\({}^{\circ}\), the simulated and measured PCEs of the proposed rectenna array versus the input power density for EM wave incomes at angles \(\theta\) of 0\({}^{\circ}\) and 45\({}^{\circ}\) are shown in Figure 19a. Similar to the case where the polarization direction angle is 0\({}^{\circ}\), the rectenna array is also capable of achieving maximum PCEs of about 60% at power densities of less than 200 uW/cm\({}^{2}\), when the incidence angles of the EM wave are 0\({}^{\circ}\) and 45\({}^{\circ}\). However, the input power densities under which the peak PCEs are obtained increase slightly. Figure 19b plots the simulated and measured PCEs of the rectenna array versus the incident angle under input power densities of 133.5 uW/cm\({}^{2}\) and 305.7 uW/cm\({}^{2}\). Similarly, the PCEs of the rectenna fluctuate slightly at different power densities when the incidence angle of the EM wave varies, demonstrating the stability of the rectenna array for omnidirectional RF energy harvesting. Figure 18: Simulated and measured results of the rectenna array when the polarization direction angle is 90\({}^{\circ}\): (**a**) PCEs versus input power density; (**b**) PCEs versus incident angle. Figure 17: Simulated and measured results of the rectenna array when the polarization direction angle is 0\({}^{\circ}\): (**a**) PCEs versus input power density; (**b**) PCEs versus incident angle.