Circuit Analysis of Achievable Transmission Efficiency in an Overcoupled Region for Wireless Power Transfer Systems

On nonradiative wireless power transfer (WPT) using a pair of magnetically coupled resonators, we investigate the achievable transmission efficiency for a different set of resonators. Using a simplified equivalent circuit model, we analyze the phenomenon of frequency splitting mathematically in the overcoupled region ( $k > k_{\rm {ref}}$ ). Even though the transmission efficiency tends to gradually decrease as the distance between the two resonators gets closer and closer in the overcoupled region, the transmission efficiency can be improved by tracking one of two separated frequency modes. Based on this observation, we prove mathematically that the achievable transmission efficiency at $k_{\rm {ref}}$ is maintained almost constantly even when $k > k_{\rm {ref}}$ if the identical resonators are used. In order to validate the accuracy of the analysis, we design and fabricate two types of magnetically coupled resonators: one is the set of identical resonators and the other is the set of nonidentical resonators. Through experiments in various environments, we show that the analytical results are in good agreement with the measured ones. Our work can provide an insight into design resonators for short-range WPT systems, in order to ensure better and stable performance.