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In this paper, we have designed rectangular waveguides with discontinuities to analyze and improve their performance by using finite element solution method. Mathematical formulation is shown for the transverse electric mode for analyzing the waveguides. The analyses of some other wave properties (both electric and magnetic) of the designed rectangular waveguides are discussed in this paper. The S-parameters of the waveguides as a function of frequency are also calculated to find the cavity resonance frequency windows for minimizing the losses.