Effective Q factor formula for small spherical surface antennas

Abstract

This letter presents an effective Q factor formula for self-resonant spherical surface antennas. The self-resonant lossless Q factor and radiation efficiency calculated using spherical wave expansion provide an approximated expression for the effective Q factor. The resultant effective Q factor is larger than that of the infinitesimal loop antenna and smaller than that of the infinitesimal dipole antenna. Comparison of the result with the Q factor of spherical helix antennas has shown good agreement. A simple estimation formula can help design a small spherical helix antenna.