## 2 Theoretical Analysis of Cavity-Based WPT Systems  
The WPT system under study employs two printed dipole antennas placed in a metal closet. The WPT system was designed to wirelessly power sensors incorporated into a smart suit. The receiving antenna employed in the present study is a classical dipole antenna, except that it has an additional conducting strip along the rear edge intended to suppress the propagation of waves in the opposite direction. The transmitting antenna has a Yagi-like design. As demonstrated in our previous study [8], using a Yagi-like antenna with a single director is more advantageous. Specifically, an additional parasitic element (conducting strip) affects the cavity's field pattern so that high PTE regions may become wider, thereby reducing the PTE's sensitivity to the receiver position. The transmitting antenna is attached to the metallic shelf located in the upper part of the closet. It is intended to place an RF generator and control circuitry used during the measurements of the PTE. An adjustable antenna holder was constructed to keep the Rx antenna in a specific position during measurements of the received power. The holder consists of two vertical U-shaped aluminum profiles running parallel to the closet's side walls and the two horizontal U-shaped PVC profiles to which the antenna is to be attached. The holder's support comprises several aluminum profiles located on the closet's bottom side. The holder is designed so that the antenna position can be changed both in the vertical and horizontal plane during the measurements to assess the effect of the receiving antenna's location on the WPT system's PTE. Notably, the distinct advantage of cavity-based WPT systems is that the conducting walls substantially confine the high-intensity fields needed for WPT to the cavity's interior, thereby eliminating any significant interference from nearby electronic devices. Thus, it is possible to exploit frequency bands outside those intended for unauthorized use (e.g., ISM bands), which increases the WPT system's adaptability. The calculation of the WPT system's PTE and assessment of its behavior are performed using the commercially available full-wave analysis software Ansys HFSS 2023 R1. The full-wave modal analysis of the cavity under study is performed to calculate the S parameters: S\({}_{11}\) (reflection coefficient) and S\({}_{21}\) (transmission coefficient). Figure 2 illustrates a model of the closet containing the receiving and transmitting antenna constructed to estimate the system's PTE. Two lumped ports are defined for field excitation and calculation of the S parameters. Once the scattering parameters are found, the PTE can be calculated as follows:  
\[\text{PTE}=|S_{21}|^{2}\cdot 100\ \%. \tag{1}\]  
The closet is assumed to be empty (filled with air). In the simulation, the losses in the closet walls are considered by imposing impedance boundary conditions on the entire closet surface and the shelf in the upper part of the closet. Note that, in the closet utilized in the experiments, there is a gap between the closet door and shelf edge, which slightly affects the field distribution inside the enclosure. The HFSS model constructed for the full-wave field simulations has the same dimensions and geometry as the carbon closet used the  
Figure 2: The Ansys HFSS model of the steel closet with the Rx antenna holder. real-life measurements of the PTE. The closet's dimensions are as follows: width--477 mm, length--290 mm, height--1420 mm. Both antennas are printed on a rigid FR-4 substrate (standard thickness 1.6 mm) with a dielectric constant and loss tangent of 4.2 and 0.02, respectively. The HFSS model of the receiving antenna is shown in Figure 3, whereas that of the transmitting antenna is illustrated in Figure 4.  
The conducting parts of the antennas are modelled as planar objects on which impedance boundary conditions are imposed.