Analytical Calculation of the Resonant Frequencies for a Corner Cut Square SIW Cavity

In this paper, the resonant frequencies of a dual mode square SIW cavity with a corner cut perturbation are calculated, analytically. Since introducing the perturbation makes small changes in the field pattern of this cavity, the perturbation theory can be used to calculate the resonant frequencies. Using this theory, the first degenerate modes of the dual mode cavity are calculated, approximately. Also, the mode matching technique is used to calculate these resonant frequencies as the eigenvalues of the structure. The analytically obtained results are verified by comparison with full wave simulation results. For the perturbation size less than the third of diameter of the square cavity, the error between resonant frequencies obtained by perturbation theory and HFSS is less than 1%. The mode matching results are also in a good agreement with full wave simulation results.