## 4 Experimental Verification and Discussion
### Measurement Results  
The values of the conductivity (\(\sigma\)) and relative magnetic permeability (\(\mu_{\mathrm{r}}\)) needed for theoretical analysis were initially chosen based on the data provided in handbooks on metal properties, including the electromagnetic ones and the available information on the metal the closet walls are made of. The initial values of \(\sigma\) and \(\mu_{\mathrm{r}}\) were assumed equal to \(7\cdot 10^{7}\) S/m and 100, respectively. However, these values caused unacceptably large discrepancies between the measured and calculated WPT system's responses. This problem was overcome by estimating the values of both quantities based on the agreement between the theoretical and experimental curves. Following this approach, the conductivity and permeability were estimated to be about \(10^{5}\) S/m and 100, respectively. These values were used in all the simulations, the results of which are presented below. Figure 14: The measured PCE of the BAT6804 Schottky diode-based voltage doubler RF-DC converter as a function of the input RF power level in dBm (**a**) and as function of the frequency at different fixed-input RF power levels (**b**). The measured PTE is plotted on the same graph as the calculated one at different vertical positions in the closet for convenience. Six measurement series were made, each corresponding to a different horizontal position (positions along the \(x\)- and \(z\)-axes) that was kept fixed during the series. The first set of PTE values was obtained at points along the vertical line with \(x_{\text{RX}}=0\) mm and \(z_{\text{RX}}=0\) mm, where \(x_{\text{RX}}\) and \(z_{\text{RX}}\) denote the \(x\) and \(z\) coordinates of the central point of the receiving antenna, respectively. For this horizontal position, the centers of both antennas were located on the same imaginary vertical line. For each set of measurements, the PTE was measured at equidistant points with a step size (distance between adjacent points) of 30 mm. The experimental results obtained for the first set of positions are shown in Figure 15. The very first vertical position corresponds to the case where the front ends of both antennas come in contact with each other. The figure reveals that the shape of the curve obtained experimentally is close to that obtained by employing the simulator. The maximum value of the measured PTE is slightly above 60%, whereas the highest theoretical PTE value is about 70%. This discrepancy arises because the closet wall conductivity and magnetic permeability values used in the simulations differ from the actual ones. The field within the cavity is, in fact, a superposition of multiple waveguide modes, three of which ensure the energy transfer between the Rx and Tx. Thus, it is natural that such a field distribution is likely to be highly sensitive to changes in the operating frequency, as each of the propagation constants of the modes is frequency-dependent. Furthermore, the coupling between the modes and the feed line TEM wave is also dispersive. To ascertain the effect of the frequency on the WPT system's performance as for each set of measurements described above, a frequency sweep over a range from 800 MHz to 960 MHz was performed to experimentally obtain the frequency dependence of the PTE for a relatively wide frequency range. Several measurements were performed at different fixed vertical positions of the Rx antenna. For each horizontal position, one of the frequency sweeps was made for the vertical position of the Rx antenna, giving the highest PTE at 865.5 MHz. The other sweeps were performed for either the worst or locally optimal Rx antenna positions or for an arbitrary position. In the first case, such an optimal position corresponds to the distance between the antennas equal to 26 cm. Figure 16 presents the measured data, with each curve corresponding to one of six different Rx antenna positions. As can be seen in the immediate vicinity of 865.5 MHz, the Rx position of 26 cm yields the highest PTE.