The discontinuity problem of a cylindrical dielectric post in a waveguide and its application on the dielectric constant measurements of liquids

An exact solution of the discontinuity problem of a circular cylindrical dielectric post centered in a rectangular waveguide is presented. The waveguide is divided in three regions where the field is expressed in cylindrical waves or in waveguide modes. By point matching, a system of linear equations determining the reflection and transmission coefficients is found. - The structure of our interest includes a liquid column surrounded by a cylindrical glass tube. For this case, curves have been made showing the relationship between the coefficients of reflection and transmission and the permittivity of the rod. Such curves are used for measuring the dielectric properties of liquids.