General scaling method for electromagnetic fields with application to a matching problem

Abstract

A scaling method that reduces an electromagnetic problem described by a complicated geometry in a complicated medium to one described by a simple Cartesian geometry in a simple medium is explored and developed. This method creates and identifies an equivalent class of problems and their solutions from the Cartesian simple medium problem. We illustrate the usefulness of the method by applying it to the design of a reflectionless, distortionless, loaded matching section connecting a cylindrical and a conical coaxial waveguide, with the TEM fields being explicitly found everywhere.