## 4 Experimental Verification and Discussion
### Measurement Results
Additionally, the Rx antenna vertical position of \(d_{\rm TX-to-RX}=26\) cm proves to give a higher PTE of about 78% at 823 MHz and ensures sufficiently high PTE values in a relatively wide band around this frequency. Interestingly, when the Rx antenna is placed so that \(d_{\rm TX-to-RX}=74\) cm, the PTE of the WPT system in the frequency range about the desired operating frequency of 865.5 MHz, namely, from 850 MHz to 875 MHz, is unacceptably low; in comparison, in a narrow frequency range in the vicinity of 900 MHz, the PTE achieved by the WPT system is just slightly lower than in the optimal case at 865.5 MHz. Also, a few less pronounced PTE maxima occur at 915 MHz, 930 MHz, and 940 MHz for the Rx antenna vertical positions of 56 cm, 68 cm, and 56 cm, respectively. The PTE attains a local peak value at about 860 MHz. Figure 15.6 The measured PTE against the frequency for the Rx antenna located at \(x_{\rm RX}=40\) mm and \(z_{\rm RX}=0\) mm. During the last set of measurements, the antenna was placed so that the receiving antenna was shifted 40 mm away from the closet door and 80 mm towards the same side wall as in the previous two measurements. The measured and calculated PTE for this antenna placement is presented in Figure 15.7 Similar to the case where the receiving antenna was shifted toward a side wall, the agreement between the theoretical and experimental results is very close, except that the experimental PTE is lower than the calculated one. Overall, the PTE curves obtained via measurements with and without the RF-DC converter and the one obtained via direct full-wave analysis (no decomposition method was employed) using Ansys HFSS 2023 R1 are mostly in close agreement, except for the range of Tx-to-Rx distance values from about 0 to 10 cm. In this range, the curve for the PTE measured with the RF-DC converter connected to the receiving antenna differs substantially from the other two curves. The discrepancy may be attributed to variations in the field distribution inside the enclosure caused by wires connecting the multimeter to the RF-DC converter's output. Figure 25 evidences that the most optimal Rx antenna vertical position in terms of the measured system's PTE for this particular horizontal plane location is when the separation distance between the antennas is 26 cm. However, Figure 26 also reveals that this is only the case over the two frequency ranges: 815 MHz to about 835 MHz and 850 MHz to 875 MHz, including the operating frequency of 865.5 MHz. Remarkably, the highest PTE achieved by the WPT system under study is about 75%, which occurs at 822 MHz. However, this frequency is outside the main band, with the desired frequency of 865.5 MHz. Instead, it is  
Figure 15.8 The calculated and measured PTE against the separation between the receiving and transmitting antennas at \(x_{\rm RX}=40\) mm and \(z_{\rm RX}=40\) mm. Figure 15.9 The measured PTE against the frequency for the Rx antenna located at \(x_{\rm RX}=40\) mm and \(z_{\rm RX}=40\) mm. in the first of the above-mentioned optimal frequency ranges. The WPT system PTE in the case when the Rx antenna is placed so that \(d_{\rm TX-to-RX}=38\) cm shows a similar behavior, with two peaks occurring over the same two frequency ranges. Nevertheless, the PTE values are lower than in the optimal case (\(d_{\rm TX-to-RX}=26\) cm), except for a relatively narrow frequency range from 875 MHz to 887 MHz, where for \(d_{\rm TX-to-RX}=38\) cm the PTE provided by the WPT system at hand is seen to be approximately twice as high as that for \(d_{\rm TX-to-RX}=26\) cm. While the other two Rx antenna vertical positions indicated in Figure 26 fail to ensure adequate PTE at the desired frequency, they give slightly lower efficiency peaks at higher frequencies. To summarize, the above data presented in graphical form show that both measured curves are consistent with those calculated, as in the previous measurements.