Approximate solutions for localized modes appearing in resonant circuit array with an external shorted coil

Abstract

Localized modes in resonant circuit array consisting of circular coils and capacitors are analytically investigated. First, an appropriate approximation of magnetic couplings between the coils is introduced. Then, analytical solutions are successfully derived by solving simultaneous polynomials for two different positions of the external coil. These solutions are evaluated by comparing with numerically exact solutions in the original problem. It is confirmed that the obtained solutions fit well the exact solutions when the overlapping and the diameter of the external coil are not too large.