Measuring the permittivity and permeability of a sample at K-a band using a partially filled waveguide

A novel method of measuring the relative complex permittivity (epsilon = epsilon' - j epsilon '') and relative complex permeability (mu = mu' j mu '') of material at K-a Band (26.5-40 GHz) using a partially filled waveguide (PFW) (rectangular) and a vector network analyzer (VNA) is presented. The method is based on 1) placing a material sample of length (L) over tilde, width (a) over tilde (waveguide width), and height (d) over tilde less than or equal to (b) over tilde ((b) over tilde is the waveguide height) in a rectangular waveguide, 2) measuring the S-parameters of the sample using the VNA, and 3) inferring the epsilon', epsilon '', mu', and mu '' parameters by comparing the experimental S-parameters with numerically generated S-parameters. The paper presents a method of moments analysis and also a variational formulation of the scattering that occurs from a finite length sample that partially fills a waveguide. Formulas to calculate the complex Poynting power and energy in the waveguide are derived to check the degree to which the numerical solutions obey the conservation of complex power. Numerical methods to extract the material parameters from the S-parameter data are proposed. The experimental PFW S-parameters of a radar absorbing material are measured and its dielectric material parameters are inferred.