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Based on the theoretical formulation of the electromagnetic field distributions within a square patch resonator, an equivalent circuit and corresponding coupling model of the patch resonator for dual-mode filter operations are first constructed. Then, a circular hole (called as a perturbation element) etched on the patch itself with symmetric or antisymmetric to the excitation ports is studied. Further, the hole is shifted to the ground plane, and the effect of the revised structure on the electric performance is investigated in this paper. To validate the study, several demonstrator filters are presented and compared. Results show good consistency between the predicated data and the measured performance.