Spherical Mode-Based Analysis of Wireless Power Transfer Between Two Antennas

A method is presented to analyze the maximum power transfer efficiency of a wireless power transfer system and its electromagnetic fields via spherical modes. The Z-parameter and Y-parameter for two coupled antennas are derived using the antenna scattering matrix and an addition theorem. In addition, formulas for calculating the maximum power transfer efficiency and optimum load impedance are presented. A formula is derived to calculate the electromagnetic field generated by a wireless power transfer system from the antenna scattering matrix.