Wireless power transfer between one transmitter and two receivers: optimal analytical solution

This paper focuses on non-radiative wireless power transfer implemented by means of a resonant magnetic coupling. The case of one transmitter and two receivers is considered and a rigorous analytical procedure is developed demonstrating that maximum power transfer or maximum efficiency can be achieved by appropriately selecting the load values. Both cases of coupled and uncoupled receivers are solved; closed formulas are derived for the optimal loads, which maximize either power or efficiency. It is shown that the resistances that realize maximum power transfer are always greater than the resistances that realize maximum efficiency. According to this observation, an optimal range of operation for the load resistances is also determined. Furthermore, it is demonstrated that in the case where the receivers are coupled the introduction of appropriate compensating reactances allows retrieving the same results corresponding to the uncoupled case both for powers and efficiency. Theoretical data are validated by comparisons with numerical results.