This paper develops exact expressions for the radiation field integrals of a single-wound bi-elliptical toroidal helical antenna, based on the vector magnetic potential approach. Using the conventional thin-wire approximation in which current flow is constrained along the wire's axis, a vector-potential integral is developed for the problem in terms of the unknown current distribution and physical attributes of the wire antenna, with the integrals' integrands expressed in matrix format. Entries into these integrand matrices lend themselves into certain physical interpretations, which facilitate a number of conclusions concerning the physics of the problem. For example, it becomes readily discernible that the antenna's radiation field admits description as a sum of two expressions; one deriving from the main loop, and the other associated with the poloidal loops of the antenna. These same conclusions were arrived at from the results of the empirical investigations reported in the open literature by Wanamassa et al. [1], and Corum [2]. Analytical results obtained in the paper also clearly indicate that the radiation fields may also be attributed to contributions associated with electric and magnetic currents excited in the antenna's main loop and poloidal loops, respectively. It is shown in the paper that the field expressions developed by the analytical approach reported, also serve as corresponding expressions for certain other configurations of the toroidal antenna as special cases.
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