A closed-form solution for reconstruction of permittivity of dielectric slabs placed at the center of a rectangular waveguide

A simple analytical approach for determining the complex relative permittivity of dielectric and composite materials "partially" filling a rectangular waveguide is presented. The procedure requires the measurement of the reflection and transmission coefficient data of the test specimen by placing a thin slab of the material-under-test (MUT) at the center of a rectangular waveguide cross section. The dielectric constant and the loss tangent of the MUT are reconstructed from the measured reflection and transmission coefficient data-using the newly proposed closed-form expressions, which represent the approximated form of the transcendental equation normally used to describe partially filled waveguides. A technique is also presented here to resolve the ambiguity problem generally associated with samples of electrical length greater than a wavelength. The applicability and range of validity of the proposed approach is tested by reconstructing a I number of samples of varying dielectric properties.