## 1 Introduction
The closet contains the transmitting and receiving antenna, the RF signal generator, and the digital multimeter employed to measure the voltage at an RF-DC converter output. The Tx antenna is driven by a sine wave delivered from the generator's output to the Tx antenna input by a 50 \(\Omega\) coaxial cable. The RF signal the receiving antenna receives is converted into a DC voltage using a voltage doubler-based RF-DC converter. A twisted pair of wires connects the RF-DC converter output and the multimeter. The fields in the closet are excited by a Yagi-like antenna, which, along with the reflector, also has an additional conducting strip (director). The Tx antenna design of this antenna resembles that of the Yagi-Uda antennas widely employed in practice, hence the name. Additionally, the closet-based WPT system under study is optimized to maximally extend the volume inside the closet where a PTE higher than 50% is observed. The optimal WPT system's model parameters are found using an exhaustive search algorithm applied to a decomposed model, which results in substantial reduction in the computational burden. Specifically, the original closet-based WPT system's model is decomposed into several sub-models. Two of the three sub-models contain the Rx and the Tx antenna without  
Figure 1: A schematic diagram of the cavity-based (closet-based) WPT system under study. the director. The director of the transmitting Yagi-like antenna is included in the third sub-model to reduce the number of parameter combinations for which the scattering data are to be calculated. The operating frequency is 865.5 MHz, which is the central frequency of the sub-GHz ISM band. At this frequency, the closet acts as a resonant cavity in a multimode regime--seven modes can propagate in the closet at the same time. However, only three of them, TE01, TM21, and TE21, can transfer power from the generator to the receiver due to their strong interaction with the dipole antennas. The decomposition method is validated by comparing the WPT system's S parameters with those obtained for the original system using Ansys HFSS 2023 R1. In addition, a sub-optimal model exhibiting an even wider higher PTE region than the optimal one is constructed at the expense of a narrow dip in the PTE curve in the middle of the region. Also, the sub-optimal model is experimentally validated by measuring the received power. Two PTE measurement scenarios are examined: with and without an RF-DC converter. The Tx antenna is driven by an RF signal generator during the experiments. Depending on the measurement scenario, the received power is measured using an RF power meter or the voltage at the output of the RF-DC converter connected to the Rx antenna is measured using a digital multimeter. Then, the received power is calculated based on the voltage value and the power conversion efficiency of the RF-DC converter. To summarize, the primary objectives of the present study are as follows:  
1. Ascertain the mechanisms responsible for the increase in the size of the high PTE region, by performing an in-depth analysis based on the structure decomposition method. Specifically, this question is answered by examining the interaction of sub-models involving a dipole antenna and director with power-carrying waveguide modes (ensuring the energy transfer from the Tx end to the Rx end). As will be shown in the remainder of this paper, the observed elongation of the high PTE region is due to changes in the power-carrying modes' phase resulting from the modes' interaction with the director strip, which essentially acts as a primitive phase shifter. 2. Apply the model decomposition method to the WPT system at hand, validate it, and assess its accuracy by comparing the results obtained using this method with those retrieved by performing the full-wave analysis of the original WPT systems model (without decomposing it) for a large number of different parameter values. 3.