Phase progression in conical waveguides

Abstract

We studied the phase progression properties of normal modes in a conical waveguide in order to develop techniques for analysis of multimode microwave antennas. We found that the large-order asymptotic expansions of Bessel functions developed by F. W. J. Olver are most appropriate for such calculations by virtue of their simplicity and uniformity with respect to argument. These expansions are applied to analysis of the conical TE 11 and conical TM 11 modes and, in addition, to an examination of the “quasi-cylindrical approximation” in which the conical waveguide is regarded as a cylindrical waveguide with gradually changing cross section.