Magnetic Resonator Design for Wireless Power Transfer Using a Mathematical Design Approach

In this study, we propose an unprecedented structure of a metallic magnetic resonator to harvest the magnetic energy for the wireless communication in a very high frequency range using the phase field design method. For the finite element analysis of electromagnetic wave propagation in the very high frequency range, the skin effect is a critical factor to determine the performance of the device so that the highly refined mesh generation is required to deal with the skin effect. In this study, we propose an artificial conductive material and a modified interpolation scheme based on the sigmoid function to deal with the skin effect. The proposed conductive material is derived from the complex permittivity and it is approximately regarded as a perfect electric conductor condition. The reaction diffusion equation combined with double well potential functions is applied as the update scheme for the phase field parameter. For the electromagnetic wave analysis in a transverse magnetic mode, the Helmholtz equation derived by Maxwell’s equations is solved as the governing equation. The derived optimal structure is reformed by employing a post processing scheme that determines the clear boundary to improve the performance and manufacturing feasibility of the final result. Finally, we propose a symmetry model based on the derived optimal model and its performance is verified by numerical simulations.