Propagation Characteristics of Confocal Elliptical Coaxial Lines Filled with Multilayered Media

Abstract

By using the method of separation of variables in the elliptical coordinate system, a recursive formula for the electromagnetic fields in a confocal elliptical coaxial line filled with multilayered homogeneous isotropic mediums is derived; and the eigenequation is given in this paper. When the confocal elliptical coaxial line becomes circular coaxial line, the fields and the eigenequation for the circular coaxial line can be carried out from the eigenequation of the confocal elliptical coaxial line using the asymptotic formulae of Mathieu and the modified Mathieu functions with a large radial variable in elliptical system. The results show that the eigenequation of a circular coaxial line filled with multilayered media can be treated as a special case of a confocal elliptical coaxial line. In addition, some numerical examples will reveal the influence of the permittivity and the permeability of the media in the confocal elliptical coaxial line on the propagation characteristics.