OPERATOR METHOD IN DIFFRACTION PROBLEM OF WAVES OF CIRCULAR WAVEGUIDE BY THE ANNULAR DISCONTINUITIES

Abstract

Purpose. Diff raction problem of the H11 and E11 waves of circular waveguide by the fi nite and semi-infi nite system of similar discontinuities is considered. Four types of discontinuities are considered: iris, disk, ring, annular slot. Th e distance between irregularities is the same. Th e waveguide is fi lled by the dielectric with losses. Design/methodology/approach. To solve the problem we chose the operator method. While so-called key problem, the diff raction problem by a single discontinuity, is solved by the method of moments. The field in the domain of the obstacle is represented as a series in terms of eigenwaves of infi nite waveguide which cross section coincides with the cross section of discontinuity, with unknown amplitudes. To fi nd the amplitudes we obtain the infi nite system of equations, which is solved by the reduction. As a result, the transmission and refl ection operators of a key-problem are obtained. The properties of fi nite sequence are determined from the operator equations relatively amplitudes of the scattered field. To write these equations the iterative procedure is used. The properties of the structure, which consists of N discontinuities are obtained under assumption that the properties of the structure, which consists of N – 1 discontinuity are known. The reflection operator of the semi-infi nite system is obtained from known non-linear operator equation of the second kind. Findings. The systems of equations for every single discontinuity are obtained. The operator equations relatively amplitudes of the scattered fields for fi nite system are presented. With the help of the created model the dependences of the transmission, refl ection coeffi cients of the H11 wave as well as transformation coeffi cients of the H11 to E11 wave of the circular waveguide on the wavenumber, geometrical and material parameters for fi nite and semi-infi nite structures are studied. The comparison of the results obtained by presented method with the results obtained in HFSS is made. Conclusions. With the use of the operator method the scattering model of the H1n and E1n eigenwaves by the system of annular discontinuities of zero thickness in a circular waveguide is built. Th e study of the scattering characteristics on the parameters is made. The coincidence of the behavior of the curves obtained by the presented method with those obtained in HFSS allows us to draw a conclusion about the correctness of the results. Th e results can be used during creation of a series of the microwaves and optic devices.