Gain expressions for resonant inductive wireless power transfer links with one relay element

In this paper, a resonant inductive wireless power transfer link using a relay element is analyzed. Different problems of practical interest are considered and solved by modeling the link as a lossy two-port network. According to the two-port network formalism, the standard gain definition (i.e. the power, the available, and the transducer gains) are used for describing the network behavior. Firstly, the case of a link with given parameters is considered and the analytical expressions of the optimal terminating impedances for maximizing the link gains are derived. Later on, the case of a link with given source and load is analyzed and the possibility of maximizing the performance by acting either on the transmitting or on the receiving side is investigated. It is shown that by using a single relay element, it is not always possible to maximize all the figures of merit that could be of interest in the WPT context. Theoretical data are validated by comparisons with circuital simulation results.