A centered-inclined waveguide slot coupler has been modeled as a series-series ideal transformer since ever. Actually this equivalent circuit is not exact, but only approximate though, for resonant couplers, the approximation being usually very good. The approximation gets worse as the slot length moves away from resonance, and is completely useless for off-resonant slots, needed in shaped-beam slot arrays. In this paper, an in-depth discussion of the properties of such a slot coupler and of the admissible approximations allows to quantitatively set the limit of the "standard" model, and leads to suitable generalizations to non-resonant slots as well. The resulting equivalent circuits are compared against full-wave simulated data and result to be very accurate in a quite large frequency range.