Closed-Form Expression of Radiation Characteristics for Electrically Small Spherical Helix Antennas

To understand the radiation mechanism of an electrically small spherical helix antenna, we develop a theory on the radiation characteristics of the antenna. An analytical model of the antenna presuming a current on the wire to be sinusoidally distributed is proposed and analyzed with the spherical wave expansion. The radiation efficiency, radiation resistance, and radiation patterns are obtained in closed-form expression. The radiation efficiency evidently varies with the surface area of the wire and the radiation resistance depends on the square of the length of the wire. The obtained result for the radiation pattern illustrates the tilt of the pattern caused by the modes asymmetric to the z-axis. The radiation efficiency formula indicates a good agreement between the simulation and measurement result. In addition, the radiation resistance of the theoretical and simulation results exhibits good agreement. Considering the effect of the feeding structure of the fabricated antenna, the radiation resistance of the analytical model can be treated as a reasonable result. The result of radiation pattern also shows good agreement between the simulation and measurement results excluding a small contribution from the feeding cable acting as a scatterer.