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In this paper, the exact solution for the electromagnetic field diffracted by a perfectly conducting elliptic cone is determined. The solution is presented in the form of a dyadic Green's function which is the most general form of solution. It is used the spheroconal coordinate system where the elliptic cone is one of the coordinate surfaces.

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.

The discontinuity problem of a metallic post coated by a dielectric tube in a rectangular waveguide has been solved numerically.—From the solution parametric curves have been derived displaying the parameters of the T-equivalent circuit in dependence of the post geometrie. Several cases of the dielectric tube permittivity are considered. For some special relations between the frequency, the dielectric constant and the radius of the post the reflection or the transmission coefficient becomes equal to zero. These relations give narrow-band filters. Experimental results have shown the utility of the method as a filter design tool.