Accurate calculation of the power transfer and efficiency in resonator arrays for inductive power transfer

This paper studies the power transfer characteristics of a resonator array for inductive power transfer by means of the accurate analytical solution of its circuit model. Through the mathematical inversion of a tridiagonal matrix, it is possible to obtain closed-form expressions for the current in each resonator and consequently expressions for the power transfer and efficiency of the system. The method can be applied to a resonator array powering a load at the end of the array or a receiver facing the array at any position. With the expressions obtained, it is possible not only to achieve a better understanding of the power transfer characteristics in resonator arrays but also to obtain the conditions for maximum power transfer or maximum efficiency, for several conditions and parameters of the system. A prototype of a stranded-wire resonator array powered by a resonant inverter, capable of delivering power to a load from 65 W to 90 W with efficiency values between 63% and 88%, was built in order not only to validate the expressions obtained but also to show their practical applicability and demonstrate that these arrays can be used for higher power transfer applications.