This work introduces a rigorous and effective modeling framework for the continuous transverse stub (CTS) array, based on a spectral Green’s function approach. A multi-modal expansion of the equivalent currents over the slots is used to derive an accurate expression for the active impedance of an infinite array. This formula is validated through comparisons with full-wave simulations when the array scans in principal planes. The mathematical formulation highlights the broadband properties of CTS arrays and accurately predicts the impact of the geometrical parameters on the active impedance, as a function of frequency and scan angle. The discussion of the results provides physical insights to outline effective design strategies.