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., k12, opt forWPT i-Rx systems and k1r, opt forWPT 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 k12, opt is always larger than k1r, 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.