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Complication of shape of resonant diaphragms in order to change the coulping with a waveguide channel is one of the ways in increasing their quality-factor (Q-factor). Ridged diaphragm in rectangular waveguide has been chosen as a special case of the diaphragm with a complicated cross-section. In accordance with the known decomposition principle, for studying its resonant properties such a diaphragm is decomposed into two consecutive junctions: rectangular-to-ridged waveguide and ridged-to-rectangular waveguide ones. On determining by some technique the basis of eigenmodes of ridged waveguide, the problem of diffraction of waves on the step junction with rectangular waveguide is solved by a known projection technique, providing thus the scattering matrix which describes the junction completely. In its turn the full scattering matrix of the diaphragm is calculated after scattering matrices of key blocks.