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Abstract
In this paper, improved analytic formulas for the radiation pattern of a plain conical horn are given in terms of the sum and difference of certain members of a conveniently defined family of functions. These formulas provide an increased level of physical insight into the operation of the antenna. In particular it is shown that the most significant portion of the radiation field wavefront necessarily will be astigmatic, a matter that has ramifications for the use of plain conical horns in radio-optical applications.