Circuit model of a resonator array for a WPT system by means of a continued fraction

This paper presents the circuit model of an array of magnetically coupled identical resonators, which is represented with an equivalent impedance expressed as a continued fraction. By solving this continued fraction with the theory of linear homogeneous difference equations, it is possible to determine the equivalent impedance of an array of identical resonators terminated in a given load as well as the equivalent impedance in the case of one or more receivers above the resonator line. The equivalent impedance is used afterwards to analyse the behaviour of the input impedance of the resonator array as seen from the voltage source, when series or parallel resonance configurations are considered. Additionally, some numerical examples are made considering an array of resonators with two receivers over the line. Finally, using the software Simulink as circuit simulator, the theoretical results presented in this work are numerically validated for different conditions of the system.