Analysis of elliptical waveguides in cylindrical reference basis
Abstract
Analysis of elliptical waveguides and determination of their eigenfunctions by the classical method of coordinate surfaces and angularly periodic Mathieu functions in an elliptical system of coordinates is cumbersome. A simpler method of solving the problem of electrodynamics is generalized separation of variables in a cylindrical system of coordinates, which yields series of circular cylindrical waves which satisfy the corresponding homogeneous Helmholtz equation and are periodic with respect to the angular coordinate. This method is applied here to an ideal elliptical waveguide with a homogeneous filler occupying the entire cavity and to a coaxial elliptical waveguide with a tubular filler. In an elliptical reference basis the eigenfunctions of both waveguides would appear in closed form. Determination of eigenfunctions for the corresponding simply connected region reduces to solving a homogeneous system of linear algebraic equations.
 Publication:

USSR Rept Electron Elec Eng JPRS UEE
 Pub Date:
 April 1985
 Bibcode:
 1985RpEEE....R..61V
 Keywords:

 Cartesian Coordinates;
 Eigenvectors;
 Electrodynamics;
 Ellipses;
 Mathieu Function;
 Spherical Coordinates;
 Wave Equations;
 Waveguides;
 Euclidean Geometry;
 Functions (Mathematics);
 Helmholtz Vorticity Equation;
 Waveforms;
 Communications and Radar