The rectangular waveguide is attached to a hole in a wall of rectangular resonator and the corresponding to the hole part of the waveguide boundary is cross-section of the waveguide. The problem of...

A rectangular resonator with holes embedded in two plane-transverse resonant diaphragms is built in a plane infinite waveguide. The problem of diffraction of the intrinsic wave of a waveguide incident on the diaphragm (hole in the wall of the resonator) is solved. The paired series functional equations of the diffraction problem, by the method of integral-adder identities, are reduced to an infinite set of linear algebraic equations, which is solved by the truncation method. The initial diffraction problem is studied from the point of view of the resonant passage of the wave through the resonator region. A computational experiment has shown that partial or complete passage of a wave through a resonator with holes is observed only at frequencies close to the eigen frequencies of the resonator without holes, while the holes in the resonator walls (diaphragm parameters) significantly affect the scattering matrix of this waveguide structure.

The two-dimensional problem of the diffraction of an electromagnetic wave by a metal diaphragm of finite thickness in an infinite rectangular waveguide is solved and investigated. Using the method of the integral-series identity, the problem is reduced to an infinite system of linear algebraic equations. Through computational experiments, it was shown that the expansion coefficients of the vectors of the diffracted electromagnetic field from the spectral parameter are of a resonant nature. Based on this, it was concluded that the waveguide region corresponding to the hole in the diaphragm is resonant. Moreover, the resonant frequencies of this region are close to the natural frequencies of the corresponding resonator without holes.

Resonant properties of semi-infinite place and rectangular waveguides in the presence of a thin conductive diaphragm placed near the cross-wall are investigated. The diffraction problems of electromagnetic waves by diaphragms are reduced by the method of integral-series identities to the infinite sets of linear algebraic equations. It is found that at some values of the frequency of the excitatory wave there is a sharp resonant increase of the amplitude of standing waves in the area between the diaphragm and the flange.

In this work, the boundary value problem for the Helmholtz equation in a half-band, corresponding to the physical problem of diffraction of TE-polarized electromagnetic wave on the wall of a resonator with a hole in a semi-infinite waveguide, is solved by the finite element method. The obtained solution is compared with the solution obtained earlier by the method of partial domains. Good correspondence between the solutions obtained by two different methods is shown. The absolute difference between the solutions was calculated. The dependence of the absolute difference on the triangulation parameter in the finite element method is given for a fixed ISLAE truncation parameter in the partial domain method.