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.battery charging, circuit modeling, inductive power transfer, resonator array, transformer, wireless power transfer
| INTRODUCTIONIn the last decade, wireless power transfer (WPT) systems have become a convenient and reliable solution in many applications, ranging from powering portable electronic devices to automatic machines and electric vehicle (EV) charging. [1][2][3] These apparatuses offer many advantages, as the ability of operating in difficult environments or the possibility to transfer power to moving loads. The size and weight of high-power batteries can be reduced by more frequent charging, which can be dramatically eased by wireless chargers. Several different technologies have been proposed in literature for both stationary and dynamic charging. [4][5][6] For high-power transfer, among near-field WPT technologies, inductive power transfer (IPT) is largely employed. One of its major limits is the misalignment between the transmitter and receiver apparatuses, which dramatically affects the efficiency and the transferred power. In order to improve the tolerance to the misalignment, arrays of magnetically coupled resonating L-C circuits (also referred as relay coils) can be used, which represent a very cheap solution since only few passive electronic components are required. [7][8][9][10][11] In these systems, the power travels from the source to the load through the relay coils at the expense of an increased sensitivity to the mismatch between the input and output side impedances, 12,13 which reflects also on the magnetic near-field distribution. 14 Solutions to this problem have been proposed in Sandoval et al, 15,16 making arrays of