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The method of moments in the spectral domain is employed to analyse coupling between a cylindrical cavity resonator and micro-strip transmission line. By extracting the dyadic Green's function of the structure and matching the tangential magnetic fields on the slot surface, fields in the structure and its scattering parameters are obtained. Parasitic elements are added to the equivalent circuit as a result of coupling which causes an additional anti-resonance in the frequency response. The significant property of the structure is that it exhibits both bandpass and bandstop responses depending on the slot dimensions. Numerical results have been validated by direct comparison to high frequency structure simulator (HFSS) results. As an example, a second-order band-pass filter is designed using the described resonator.