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A hard-walled conical horn fed in the TE11-mode from a regular circular waveguide is analyzed. The hard wall is formed by a dielectric layer with cylindrical inner surface loaded with longitudinal conducting strips. The analysis is carried out by using a stepwise representation of the horn with subsequent application of the method of generalized scattering matrices in combination with the method of factorization. The approach used refines values of the limiting aperture efficiency by 5 to 15% for diameters up to 3.2 wavelength in comparison with the underrated data based on the Kirchhoff method, and reveals the effect of the sharp worsening of the hard horn performance at some values of the horn length caused by resonances of the strip-line mode excited in the loaded section. Beyond the resonance points, the aperture efficiency remains relatively high (from 80 to 85%), and the crosspolar level is a few decibels lower than that of a standard smooth-walled horn.