Wireless power transmision has been analytically studied in near-field coupling systems based on the small-antenna and near-field approximations, and in microwave power beaming systems based on the far-field approximation. This paper attempts to provide a general solution based on full-wave analysis to wireless power transmission between two circular loops. The solution applies to arbitrary transmit and receive loop radii, transmission range, orientation and alignment of the loops, and dielectric properties in a homogeneous isotropic medium. The power link is modeled as a two-port network and the efficiency based on simultaneous conjugate matching is used as the performance metric. The self and mutual admittances are analytically solved by expressing the current on the loops in Fourier series and the fields in vector spherical wave functions, and by the use of vector addition theorem to relate the coupling between the loops. The general solution is then applied to draw new insights such as the optimal carrier frequency between symmetric loops and impact of higher order modes on the power transfer efficiency between asymmetric loops.
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