A Resonant Wireless Power Source Consisting of Multiple Coupled Resonators Oscillating in a Single Resonant Eigenmode

A general formula is found for tuning systems of coupled resonators in order to achieve a desired arrangement of RF current magnitudes and directions, and with a coupled resonant eigenfrequency equal to the desired driving frequency. The formula is applied to the case of a magnetic loop antenna with a nested, passive loop, as well as to a metamaterial resonator array. In addition, two self-tuning mechanisms are explored for automatically satisfying the tuning formula for metamaterial arrays constructed from identical resonators.