On the bi-elliptical toroidal helical antenna problem

摘要

By eliminating the fundamental apriori assumption typical of previously reported formulations of bi-elliptical toroidal helical antenna (THA) problem, that the antenna will operate only at one or more of its three characteristic resonance frequencies, this paper describes a formulation of the problem in a vector potential approach, with basis in the derivation of a Green's function appropriate to the antenna geometry as starting point. Exact closed form expressions are derived for the radiation fields of the THA, and these expressions are shown to represent a general case of certain results reported in the open literature, as special cases. An important contribution of the derivation is that for the first time to the best of our knowledge, analysis is able to identify distinct contributions to the far-zone fields attributable to the main loop and the poloidal loops of the THA. Computational results for the THA operated in the dipole mode are presented in graphical formats displaying separate contributions of the main and poloidal loops, as well as their resultants, to the radiations fields. In the polar direction, radiation fields from these loops have similar shapes; though that due to the main loop is some 20 times larger in magnitude than that due to the poloidal loops. The resultant radiation field in the polar direction has the omnidirectional pattern characteristic of the dipole antenna. On the other hand, the phi-component of the radiation field is characterized by contributions from the main loop that are some 800 times greater in magnitude than those from the poloidal loops. And indeed, the computational results suggest that for the THA operated in the dipole mode, the phi-component in the far-zone dominates, with the net effect that that the THA's radiation field is directional, with the cardioid shape due to the dominant phi-component of the main loop.