## 4 Experimental Verification and Discussion
### Measurement Results
The second optimal position is when \(d_{\text{TX-to-RX}}=29\) cm, in which case the PTE is slightly lower than the optimal one. Another local PTE peak is at \(d_{\text{TX-to-RX}}=29\) cm. The rest of the positions show unacceptably low PTE in the frequency range between 850 MHz and 870 MHz. Interestingly, at a frequency of about 830 MHz, all the considered  
Figure 15: The calculated and measured PTE against the separation between the receiving and transmitting antennas \(x_{\text{RX}}=0\) mm and \(z_{\text{RX}}=0\) mm. Rx positions give quite a high PTE comparable to the optimal PTE at 865.5 MHz; moreover, the most optimal position at 830 MHz is \(d_{\rm TX-to-RX}=38\) cm. The third pronounced PTE peak is seen in the range from 805 MHz to about 830 MHz. The second set of PTE values is obtained by measuring and calculating the transmission coefficient at different \(d_{\rm TX-to-RX}\), when the receiving antenna holder is shifted by 40 mm towards one the broader closet's side walls (along the \(z\)-axis). Like in the previous case, the PTE is measured at equidistant points with a step size of 30 mm. The relevant results are shown in Figure 17.  
The WPT system's PTE measured at different frequencies when the Rx horizontal position was \(x_{\rm RX}=0\) mm and \(z_{\rm RX}=40\) mm is presented in Figure 18. The highest PTE position in this case was \(d_{\rm TX-to-RX}=29\) cm, like in the first case discussed above. The frequency dependence was obtained only for four Rx antenna positions. Figure 18 shows that the vertical Rx positions other than the optimal one give considerably lower PTE even at 865.5 MHz. This behavior may be attributed to a small distance between the Rx antenna and the side wall of the enclosure, resulting in weaker TEM wave coupling to the TE\({}_{01}\) mode, which has low electric field intensity near the side walls perpendicular to the z-axis. The other Rx antenna positions fail to provide adequate PTE at 865.5 MHz. Only when the Rx antenna is placed 56 cm away from the Rx antenna can  
Figure 16: The measured PTE against the frequency for the Rx antenna located at \(x_{\rm RX}=0\) mm and \(z_{\rm RX}=0\) mm. Figure 17: The calculated and measured PTE against the separation between the receiving and transmitting antennas at \(x_{\rm RX}=0\) mm and \(z_{\rm RX}=40\) mm. a PTE of about 50% be achieved. Another pronounced PTE maximum was achieved for the same Rx position (\(d_{\rm TX-to-RX}=29\) cm), but in a different frequency range, namely 800 MHz-830 MHz, with the system PTE peaking at 810 MHz. Compared to the previous horizontal Rx position, in the present case, there is a noticeable increase in the number of PTE peaks, with the PTE at these peaks being lower than those at 865.5 MHz and 830 MHz. The third set of measurement data was acquired similarly, but this time, the measurement position (point) was shifted by 80 mm along the \(z\)-axis. The calculated and measured results obtained for the 8 cm shift of the receiving antennas are shown in Figure 19. Both the theoretical and experimental curves exhibit two PTE peaks. The PTE value in the vicinity of the first peak is significantly higher than that of the second one. However, the highest PTE value in this case is lower than in the previous two, which the resonant cavity excitation theory can explain. More specifically, placing the receiving or transmitting probe close to the cavity walls (provided the walls are highly conducting) makes the coupling between the probes weaker due to the lower electric field. As can be seen, as the distance between the midpoint of the antenna and the midpoint of the top of the closet increases, the received power level decreases for all considered positions of the Rx antenna along the \(y\)-axis. Such a result agrees well with the classical theory of excitation of cavity resonators--the closer the excitation source is to the wall of  
Figure 19: The calculated and measured PTE against the separation between the receiving and transmitting antennas at \(x_{\rm RX}=0\) mm and \(z_{\rm RX}=80\) mm.