The near field of annular antennas

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Abstract
The circular loop antenna has been investigated by many authors beginning as early as 1897 with Pocklington's study of the thin wire loop excited by a plane wave. Later, both Hallen and Storer considered the case of driven antennas. All of these authors used a Fourier series expansion for the loop current, and the latter two found numerical difficulties with the approach. These difficulties, as pointed out by Wu, can be avoided by integration of the free-space Green's function over the toroidal surface of the wire. The theory developed here is an improvement on previous works because it specifically takes into account the finite dimension of the wire. Consequently, the range of validity for our solution extends to fatter wires than previously considered. Furthermore, some detail of the loop current around the cross section of the wire is revealed. The theory, if applied to thin wire loops, gives radiation admittances in excellent agreement with results obtained by previous investigators. The computations of the electromagnetic fields near resonant loops show that the electric field strength is larger by a factor of ten than previously published values. Experimental results validate the theory presented in the following sections.

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