Eigenmode analysis of a multiresonant wireless energy transfer system

The eigenmodes of a wireless energy transfer (WET) system consisting of two or more LC resonators, weakly coupled by their magnetic near fields, are investigated by means of a matrix calculus. Generally, such multiresonant systems are known to exhibit a set of specific eigenmodes. In a WET system, these eigenmodes are characterized by eigenfrequencies, the corresponding current distributions, and the resulting magnetic field profiles. A novel approach to the mathematical modeling of a WET system of any order is presented, which is exactly within the limits of the lumped-element approximation. This approach analytically describes an effect that is publicly known as 'modal frequency splitting,' which pertains to challenges for control approaches by means of frequency tracking or power control. From an eigenvalue analysis of the WET system matrix, analytical expressions for the complex eigenfrequencies, current distributions, and spatial magnetic field profiles of the individual eigenmodes are derived for an exemplary system of fourth order. The complex transfer functions from an input port to any of the output ports are calculated and experimentally verified for this system.