An accurate theoretical model for the thin-wire circular half-loop antenna

The conventional Fourier series analysis for the thin-wire circular transmitting loop, or its image equivalent to the half-loop, uses a delta-function generator for excitation. This method of excitation introduces two problems: it does not correspond to any realizable method of feeding the antenna, so an accurate comparison with measurement is not possible, and it produces a divergent series for the input susceptance. To overcome these problems, a new theoretical model is used for the antenna: a half-loop driven through an image plane by a coaxial transmission line, with a transverse electromagnetic mode assumed in the aperture of the coaxial line. This model is solved in a manner that preserves the simplicity of the original Fourier series analysis. All coefficients are obtained as closed-form expressions. Input admittances calculated from this new theoretical model are in excellent agreement with accurate measurements