Two-port network compact representation of resonator arrays for wireless power transfer with variable receiver position

This paper presents an equivalent circuit characterization of an array of resonators for wireless power transfer (WPT) applications. These apparatuses are composed of magnetically coupled resonant coils acting as a transmitter which feeds a receiver coil that can be placed over them at any position, allowing the tolerance of the system to the receiver misalignment to be dramatically enhanced. This advantage makes resonator arrays a suitable solution for both low- and high-power applications. The latter usually involve battery charging, with the resonator array acting as a transformer stage, ensuring galvanic isolation. An equivalent two-port network can be defined for any receiver position, allowing the array to be treated as a traditional transformer. Thereby, the simulation of the system can be simplified, as it is required in the design steps of a converter and control strategy. Analytical expressions of the two-port network parameters are proposed for arrays of any size and length. The formulas have been numerically and experimentally validated.