An Approach to Permittivity Determination at Microwave Frequencies Through the Eigenvalue Problem

Abstract

A simple method of solving the inverse medium problem in order to determine the complex dielectric constant of a lossy dielectric material at microwave frequencies is presented. The arbitrarily shaped dielectric sample placed in a rectangular waveguide is considered. Electromagnetic fields in the waveguide are expanded in series of harmonic functions. A set of linear equations is obtained using the finite–difference technique. An additional empirical condition, which is related to the measured reflection and/or transmission coefficients and results in an overdetermined system, is added and then the system is defined by the addition of a trivial extra parameter. The sample's dielectric properties are obtained by solving the resulting eigenvalue problem. An algorithm to extract proper results from the set of eigenvalues is defined by considering the properties of numerical solution. The system is tested by using an alternative method.