Effect of quality factor on determining the optimal position of a transmitter in wireless power transfer using a relay

In this letter, the optimal placement of a transmitter is investigated under a given arrangement of a relay and a receiver for nonradiative wireless power transfer. Specifically, a closed-form equation is derived for the optimal coupling coefficient between the transmitter and the relay using an equivalent circuit model. Based on this theoretical analysis, it is found that the quality factor of the transmitter has a great effect on determining its optimal placement. In particular, the transmission efficiency can be improved by locating the resonator with a smaller quality factor (e.g., transmitter or receiver) closer to the relay. In order to support the validity of the analysis, the resonators, including the relay, receiver, and three different types of transmitters, are experimentally designed and fabricated. It is shown that our analytical results are well matched with the measured ones in various settings.