In this paper the characteristic equations of the Eymn and Exmn modes of the dielectric rectangular waveguide have been derived using the mode matching technique. No assumptions have been taken in the derivations which have been straight forwardly done. Two ratios have been introduced in the characteristic equations and the new set of characteristic equations thus obtained are then plotted and graphical solutions are obtained for the propagation parameters assuming certain numerical values for the introduced ratios. The results have then been compared to those obtained by Marcatilli and Goell for rectangular dielectric waveguides. The comparisons depict a good agreement in the three methods at frequencies well above cut-off.
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