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

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 TM10 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.