## 4 Experimental Verification and Discussion
### Measurement Results
Figure 18: The measured PTE against the frequency for the Rx antenna located at \(x_{\rm RX}=0\) mm and \(z_{\rm RX}=40\) mm. the resonator (in this case, the closet), the weaker the coupling between the resonator and the generator or any other source of electromagnetic fields. The dependence of the WPT system's PTE on the frequency measured at different vertical positions of the Rx antenna is exposed in Figure 15.0  
It is apparent that from the five different antenna separations, the highest PTE is achieved for \(d_{\text{TX-to-RX}}=32\) cm, which corresponds to the peak efficiency at 865.5 MHz seen in Figure 15.1 Nevertheless, there are more optimal PTE values over the 800 to 960 MHz frequency range. Namely, a higher PTE than that at 865.5 MHz can be achieved by slightly adjusting (increasing) the operating frequency since, according to the data of Figure 19, the PTE attains a local peak value at approximately 874 MHz. Furthermore, there is another distinct PTE maximum over a sub-range from 800 to about 840 MHz, with a peak value of about 72% achieved at 812 MHz. This peak value is the highest PTE achievable by the WPT system over the entire frequency range under study. The fourth set of measured data was acquired for the case where both antennas lie in the same plane, but the receiving antenna is shifted a distance of 40 mm away from the closet door. The relevant measurement data are shown in Figure 21, where the simulated and measured PTE are plotted against the distance between the Tx and Rx antennas. Although the calculated and measured data are still in good accord, noticeable discrepancies are observed in the Tx-to-Rx separation range from 35 to about 55 cm. Specifically, a  
Figure 15.2 The calculated and measured PTE against the separation between the receiving and transmitting antennas at \(x_{\text{RX}}=40\) mm and \(z_{\text{RX}}=0\) mm. Figure 15.3 The measured PTE against the frequency for the Rx antenna located at \(x_{\text{RX}}=0\) mm and \(z_{\text{RX}}=80\) mm. shallow, sharp dip is present in the calculated data (solid blue line). At the same time, the measured PTE, both with and without the RF-Dc converter, shows continuous dependence on the distance between the antennas. Furthermore, the measured PTE maximum, occurring at about \(d_{\rm TX-to-RX}=58\) cm, is shifted by 2 cm from the calculated one attained by the WPT system at \(d_{\rm TX-to-RX}=60\) cm. The measured PTE against the frequency for this Rx antenna position is presented in Figure 15.4 It is observed that the PTE reaches the highest value at vertical Rx antenna positions such that the separation distance between the antennas is \(d_{\rm TX-to-RX}=29\) cm. The WPT system's behavior resembles that of the previous case; namely, there is a more optimal PTE value over the frequency range from 800 MHz to 960 MHz, which can be achieved by slightly changing the operating frequency. The PTE attains a local peak value at approximately 860 MHz. Furthermore, there is another distinct efficiency maximum over a sub-range from 800 MHz to about 840 MHz, with a peak value at 818 MHz. Another set of measurements was made for the same horizontal location of the transmitting antenna along the \(z\)-axis but a different positional along the \(x\)-axis (\(x_{\rm RX}=40\) mm). The received power was again measured at a set of points on a vertical line along the largest closet dimension. The measurement and simulation results obtained for this horizontal Rx antenna position are presented in Figure 15.5 In contrast, Figure 24 presents several curves revealing how the PTE varies with frequency in the 800-960 MHz range when the antenna is shifted 40 mm along both the \(x\)- and \(z\)-axes. In this case, the measured PTE is seen to reach the highest value at the vertical Rx antenna position corresponding to the Tx-to-Rx antenna separation distance of \(d_{\rm TX-to-RX}=26\) cm. Again, more than one PTE peak is observed over the frequency range under consideration.