Circuital Analysis of Cylindrical Structures Applied to the Electromagnetic Resolution of Resonant Cavities

The objective of this chapter is first to describe the generalized circuital analysis as a method to solve complex electromagnetic problems and second to apply this specific technique to the determination of the resonant frequency and Q-factor of a cylindrical cavity loaded with a dielectric material when the material is introduced inside the cavity through a hole in the upper wall. The generalized circuital analysis as a method for solving electromagnetic problems consisting of the segmentation of the whole geometry of the microwave circuit into simpler structures which resolution can be solved in a easier way. Once the simpler structures have been solved separately, they can be joined or combined in order to give the complete solution of the complex structure. The resolution of the resonant frequency and Quality factor of a coaxially loaded circular cavity with a dielectric material is very interesting, for instance, for the determination of the dielectric properties (complex permittivity) of materials on this type of cavities. This type of analysis on these cavities can be found in the technical literature but in all cases, the effect of the hole to introduce the dielectric material inside the cavity is neglected and in some cases, such as it will be shown in the second part of the chapter, the effect of the hole can introduce considerable errors in the determination of the resonant frequency and quality factor whose can interfere the precision of the permittivity calculations. In next sections, the effect of the hole for the introduction of dielectric materials inside circular cavities is evaluated by solving the structure by the generalized circuital analysis. Several measurements of circular cavities with dielectric materials will confirm the effect of the hole in the precision of permittivity calculations. 7