Analytical Solution for the Scattering by a Cylinder Perpendicular to the Narrow Walls inside a Rectangular Waveguide and Its Application to ε_r and μ_r Measurement

Abstract

In this paper, a new swept-frequency method for the measurement of the complex permittivity and permeability of materials is proposed. The method is based on the S-parameters measurement of a cylindrical material placed inside a rectangular waveguide, where the axis of the cylinder is perpendicular to the narrow waveguide walls. The usage of cylinders in measurement is beneficial because they are easy to fabricate and handle. A novel exact solution of the field scattered by the cylinder is developed. The solution is based on expanding the field in a sum of orthogonal modes in cylindrical coordinates. Excitation coefficients relating the cylindrical scattered field to the waveguide modes are derived, and are used to rigorously formulates the S-parameters. Measurement are performed in the S-band with two dielectric materials (PTFE, nylon), and in the X-band with one magnetic material (ferrite epoxy). The measurement results agree with those from the literature.