Abstract—This paper presents a full-wave analysis of coupling between rectangular waveguides through a cross-aperture. The rigorous mode-matching method is used to derive the generalized scattering matrix of a waveguide T-junction having a crossed waveguide as the side arm. Two three-port T-junctions are then cascaded together to form a number of cross-aperture couplers. The analysis method can handle both broad-wall and narrow-wall, both parallel and crossed coupling structures. Our numerical results for a variety of couplers are in good agreement with those obtained by Ansoft’s HFSS.