Analytical Methods in Theory of Slot-Hole Coupling of Electrodynamic Volumes

Abstract

Abstract-The approximate analytical solution of the integral equation concerning the equivalent magnetic current in the narrow slot, coupling two electrodynamic volumes, has been obtained by the averaging method. The formulas and the plots for currents and the coupling coefficients of longitudinal and transverse slots in the common walls of rectangular waveguides are represented. By means of the induced magnetomotive forces method using basis functions of current distribution, obtained by the averaging method, the following electrodynamic structures have been considered: the electrically long longitudinal slot in the common broad wall of rectangular waveguides; two symmetrical transverse slots in the common broad wall of rectangular waveguides; the transverse slots system in the common broad wall of rectangular waveguides. The problem about the resonant iris with the arbitrary oriented slot in the plane of cross-section of a rectangular waveguide has been solved by the averaging method. The problem about stepped junction of two semi-infinite rectangular waveguides with the impedance slotted iris has been solved by the induced magnetomotive forces method. The analytical formulas for the distributed surface impedance of homogeneous and inhomogeneous magnetodielectric coatings of iris surface have been obtained. For a greater number of the considered electrodynamic structures the calculated values are compared with the results, obtained by numerical methods (also using commercial programs) and the experimental data.

Diffraction of a Plane Electromagnetic Wave by a Slot in a Conducting Screen of Finite Thickness Placed in Front of a Half-Infinite Dielectric

“…The form of the corresponding equations for E polarization is distinguished from (12) by the presence of the factor 1/k instead of the constant factor α 0 . Besides, in the matrix element (13), the coefficient α will go from the numerator to the denominator.…”

“…At first, the slot amplitudes are determined as the solutions of two systems (12), then the mode amplitudes outside of a screen are calculated by means of expressions (11), and afterwards one can determine the scalar field functions in each of the field existence regions using expressions (3), (5), (7) and (8). The components of the electric and magnetic vectors in these regions are computed with the help of Equations (1), into which the given expressions should be substituted.…”

“…That is why the problem of simulation of a plane wave diffraction by slots in conducting screens, as well the like problem of diffraction by a complementary screen in the form of a strip, is of great interest [2,3,[8][9][10][11][12][13][14]. The classic statement of these problems proceeds from the premise of a conducting screen having infinitesimal thickness [1,2,8,9].…”

“…This approach is based on the mode-matching method [2], which looks like the method used in the rigorous diffraction theory [1,8,9]. It provided the possibility to obtain the solutions [3][4][5][6][10][11][12][13], which may be unwieldy, but is greatly simple than the rigorous solution for a screen of infinitesimal thickness [15] and is convenient for computer programming. However, the solutions obtained by the mode-matching method, are applicable only in the cases when thickness of a screen with a slot is in the order of the wavelength of diffracted radiation or more.…”

Combined Vibrator-Slot Structures in Electrodynamic Volumes

“…During last decades, researchers have published results which make it possible to create a modern theory of thin vibrator and narrow slot radiators. This theory combines the fundamental asymptotic methods for determining the single radiator characteristics [5][6][7], hybrid analytic-numerical approaches [8][9][10], and direct numerical techniques for electrodynamic analysis of such radiators [11]. However, the electrodynamics of single linear electric and magnetic radiators is far from being completed.…”