Resonant coupling efficiency limits for multiple receivers in a wireless power transfer system

Power transfer between two resonators - a transmitter and a receiver- can occur through sympathetic resonance of their near EM fields. Remarkably, the power transfer efficiency is limited by the product of the quality factors Q, of the transmitter and receiver and the coupling coefficient k. In this work, we evaluate the efficiency limit first, for an inductively coupled system consisting of a single transmitter and receiver, based on their equivalent circuit model. This limit is identical to that derived previously using the coupled mode theory. We observe that in order to achieve maximum efficiency, the ratio of the load-to-loss impedances at both the source (R_S/R_L1) and load (R_L/R_L2) should be equal to a prescribed value. This is the same condition that yields simultaneous impedance matching at source and load. Efficiency limits are then calculated for single transmitter and two uncoupled receivers. In that case, maximum efficiency is obtained when the load-to-loss impedance ratio is equal to the same prescribed value for all devices simultaneously. However, this condition does not provide for simultaneous matching at the source and loads, which turns out to be impossible. The analysis can be generalized for a single transmitter and N uncoupled receivers.