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Several methods have been used for the study of a ridged waveguide. In this paper, we propose the use of Gegenbauer polynomials in the decomposition of the electromagnetic field near the edges of the septum, for the computation of cut-off frequencies and electromagnetic TE and TM fields in the ridged waveguide sections. This study is applied to analyse a waveguide septum polarizer that was experimentally studied by M.H. CHEN and G.N. TSANDOULAS en 1972. The useful performances of the polarizer (ellipticity ratio, circular polarization ratio) are computed from the geometrical dimensions of the waveguide and the septum. The method is based on the computation of discontinuities between waveguides with different ridge height by mode matching and the cascading of scattering parameter matrices representing the discontinuities and the waveguide lengths, resulting in the global S matrix of the polarizer. The computed results are compared with those obtained by other methods and shown to be in good agreement which verify the theory. Plots of field distributions prove also the accuracy of the results. Copyright © 2003 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]