Scattering Analysis for Layered Cylindrical Object Perpendicularly Piercing the Wider Walls of a Rectangular Waveguide and Its Application to ${\varepsilon _{r}}$ and ${\mu _{r}}$ Measurement

This paper describes a novel analysis for the scattering problem of a layered cylindrical object that pierces a rectangular waveguide through a pair of holes made at the center of the wider walls. In this analysis, the
S
-parameters are rigorously formulated in terms of the modal scattering coefficients of the cylindrical object. Here, the modal scattering coefficients are expressed as solutions to a set of linear equations of infinite extent. The layered object is represented by the admittance function, which can readily be calculated for an arbitrary number of layers, using a recurrence formula. To show the applicability of the presented formulas, two types of dielectric samples (polytetrafluoroethylene and polyacetar) and a ferrite sample were measured, and reasonable values were obtained. In addition, the complex permittivity of water was determined by using a glass capillary tube as a liquid container, and an excellent agreement was shown with the value predicted by Debye's formula.