Power Transfer Efficiency Analysis of Intermediate-Resonator for Wireless Power Transfer

We investigate the effect of intermediate resonators (i.e., intermediate receiver (i-Rx) or relay) on the power transfer efficiency (PTE) for nonradiative wireless power transfer (WPT) with transmitter (Tx), intermediate-resonators, and end receiver (e-Rx). Specifically, we consider WPT systems with two different types of an intermediate resonator: 1) WPT relay systems, where the relay has no load resistor and just forwards the power from the Tx to the e-Rx, and 2) WPT i-Rx systems, where both i-Rx and e-Rx have a load resistor each and the power transmitted by the Tx is consumed at each Rx. Using an equivalent circuit model, we derive a closed-form solution for representing the optimal coupling coefficients between the Tx and the intermediate resonator for a given placement of the intermediate resonator and the e-Rx, i.e., k_12,opt for WPT i-Rx systems and k_1r,opt for WPT relay systems, respectively. The analytical result indicates that the quality factors of resonators have a great effect on determining their optimal positions. We also provide performance comparisons between the considered WPT systems. From the result, it is observed that k_12,opt is always larger than k_1r,opt, which indicates that the optimal position of the Tx is closer to the i-Rx rather than the relay. Moreover, in this case, WPT i-Rx systems can attain a higher PTE than WPT relay systems. Performing experiments under a variety of scenarios, we verify that the analytical results are in concordance with the measured ones.