Two-Mode Waveguide for Equal Mode Velocities

A rectangular waveguide, with a T-septum attached to one of its side walls, is capable of supporting two modes with equal-phase velocities. Stationary expressions are developed for the cutoff wavelengths of these two modes as functions of the cross-sectional dimensions. A Rayleigh-Ritz procedure is used to produce families of curves relating each cutoff wavelength to the septum dimensions; intersections of corresponding curves establish theoretically those combinations of dimensions that permit the two modes to propagate at a common velocity. Experimental corroboration of the theory is also presented.