A Practical $Z$-Parameter Two-Port Modeling Method to Evaluate Long-Distance and High-Efficiency Wireless Power-Relay Systems

In a wireless power transfer system, applying power-relay coils is an effective method to achieve both long distance and high efficiency. However, the wireless power-relay system (WPRS) has many variables, which will perplex the system design. In this article, an evaluation method based on the black-box $Z$ -parameter two-port model is introduced for the WPRS. This method can easily obtain the theoretical optimal efficiency and the corresponding load from black-box measurement instead of acquiring all the parameters of the resonant coils. This feature can be used to compare potential performance of different WPRSs. WPRSs based on printed circuit board coils are built to verify black-box $Z$ -parameter two-port modeling. Experiments are also carried out on WPRS ac resonant tanks and WPRS dc–dc converters.