Complex permittivity extraction of dielectric samples in waveguide

This paper describes a method to determine the relative permittivity of a dielectric material in printed circuit board. The dielectric sample in a PCB is placed to form a finline discontinuity of finite length in a waveguide. S-parameter of a discontinuity from an empty waveguide to finline and back to empty waveguide is measured. An error function that compares the measured and calculated S-parameters of the discontinuity is minimized to extract the permittivity of the sample. The optimization is based on a practical quasi-Newton algorithm. The calculated value of the S-parameter used in the error function is obtained from the modal expansion of the fields in the empty waveguide and the finline structure. Field matching is done at the discontinuity to yield the theoretically calculated S-paramters.