Based on the asymptotic method of averaging, an approximate analytical solution of the integral equation concerning a magnetic current in slot-hole coupling apertures of electrodynamic volumes, which differ profitably from the known ones in literature, has been obtained. The formulas for the currents and characteristics scattering of transverse and longitudinal slots in common broad and narrow walls of rectangular waveguides are given. The comparison to results obtained by other methods and experimental data has been done.
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