The calculation of the matrix of a scattering wave-guide dielectric resonator of a complex structure

An over-range wave-guide dielectric resonator with flat layers is considered. It consists of three intercepts of a rectangular wave-guide with cross-sections A, B, C, connected in turn with two intercepts of smaller cross-sections a₁, a₂, (a₂ < a₁ < C < B < A) and it is excited by a wave-guide of a greater cross-section. Choosing in a proper way the values of the layers permeability, regions with non-propagating waves over-range layers are created in wave-guides of smaller sizes. The peculiarity of the structure under consideration is the presence of additional wave-guide intercepts with length l₁, l₃ and l₄, l₆ through which a connection of layer l₂ with a regular wave-guide on the input and layer l₅ with a regular wave-guide on the output is realized. The coordinate system is chosen so that axis z coincided with direction of the wave propagation, axis x were perpendicular to z and were in the plane of the structure cross-section the coordinates origin being in the coaxes connection of the supplying and rectangular parts of the cross-section. For the analysis of the wave-guide dielectric structure under consideration we use the method of decomposition according to which the whole electrodynamics object is divided into elementary subregions, which are intercepts of transition regular lines. The planes perpendicular to the direction of the wave propagation (axis z) are boundaries of partial regions. In each of selected subregions the fields are superposition of incident and reflected waves of a particular intercept of the transition line.