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 TM1m 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.

To characterize an antenna, the acquisition of its three-dimensional radiation pattern is the fundamental requirement. Spherical antenna measurement is a practical approach to measuring antenna patterns in spherical geometry. However, due to the limitations of measurement range and measurement time, the measured samples may either be incomplete on scanning sphere, or be inadequate in terms of the sampling interval. Therefore there is a need to extrapolate and interpolate the measured samples. Spherical wave expansion, whose band-limited property is derived from the sampling theorem, provides a good tool for reconstructing antenna patterns. This research identifies the limitation of the conventional algorithm when reconstructing the pattern of an antenna which is not located at the coordinate origin of the measurement set-up. A novel algorithm is proposed to overcome the limitation by resampling between the unprimed and primed (where the antenna is centred) coordinate systems. The resampling of measured samples from the unprimed coordinate to the primed coordinate can be conducted by translational phase shift, and the resampling of reconstructed pattern from the primed coordinate back to the unprimed coordinate can be accomplished by rotation and translation of spherical waves. The proposed algorithm enables the analytical and continuous pattern reconstruction, even under the severe sampling condition for deviated AUT. Numerical investigations are conducted to validate the proposed algorithm.