Phase Retrieval-Based Z Parameter Estimation Method for Multiple-Input Multiple-Output Wireless Power Transfer Systems

Multiple-input multiple-output (MIMO) wireless power transfer (WPT) systems present various advantages to users, including improved power transfer efficiency, adjustable transmission power, and reduced magnetic field leakage. An essential aspect of controlling MIMO WPT systems is the estimation of
$Z$
parameters, which characterize the behavior of the linear electrical network in these systems. In this study, we propose a method to estimate all elements of the
$Z$
parameters without requiring synchronization between the transmitters and receivers. Instead, the elements are estimated based on the measured complex amplitudes of voltage and current at the transmitters, as well as the direct current (DC) at the output of the full-bridge rectifiers on the receivers. Importantly, all these measurements can be obtained at a minimal cost. Further, circuit simulations and experiments are also conducted to evaluate the performance of the proposed method. Specifically, a
$2 \times 2$
MIMO WPT system is employed for the circuit simulations and experiments, and the
$Z$
parameters are estimated under various receiver position conditions. The evaluation of the simulation and experimental results is based on the power transmission efficiency of the system, considering the estimated
$Z$
parameters. The simulation and experimental results demonstrate that the difference between the power transfer efficiency based on the estimated
$Z$
parameters and the theoretical maximum efficiency based on the true
$Z$
parameters is found to fall within the range of 0.06 % and 0.4 %, respectively.