Theoretical Limit of the Radiation Efficiency for Electrically Small Self-Resonant Spherical Surface Antennas

Abstract

Theoretical maximum radiation efficiency of electrically small spherical surface antennas has been derived in this study. The current on the antenna surface is described in terms of vector spherical harmonics, and the radiated and the dissipated powers are calculated to obtain the radiation efficiency. It has been found that non-resonant TM_1m mode shows the best radiation efficiency, and a proper combination of TM₁₀ and TE₁₀ modes establishes a resonant spherical surface antenna whose radiation efficiency is bounded by those values of non-resonant TM₁₀ and TE₁₀ modes. As a practical example of the spherical surface antennas, the radiation efficiency of the spherical helix antennas has also been computed to check the validity of our formulation.