This paper presents an efficient analysis method for a novel continuous transverse stub (CTS) antenna. As opposed to state-of-the-art CTS antenna designs, the proposed architecture achieves circular polarization using a single CTS array and without any polarization converter. The structure consists of long radiating slots/stubs fed by over-moded parallel-plate waveguides. More precisely, the transverse electromagnetic (TEM) mode and the first transverse electric (TE1) mode of the feeding waveguides are used to generate a circularly-polarized field. The array is analyzed using a spectral mode-matching method. First, the active reflection coefficient of the infinite array is derived in closed form. A windowing approach is then adopted to compute the radiation patterns of finite-size arrays. Numerical results obtained with this method are in excellent agreement with fullwave simulations, carried out with a commercial software. The performance of this class of CTS antennas has been investigated using the developed model. It is theoretically demonstrated that the proposed array can be designed to attain an axial-ratio (AR) lower than 3 dB over a 52.9% relative bandwidth at broadside. Furthermore, the active input reflection coefficient is lower than-10 dB over a 40.8% relative bandwidth when the array steers its main beam at θ0 = 45 •. This solution is an attractive candidate for next generation satellite communication terminals. Index Terms-Continuous transverse stub array, circular polarization, oversized parallel-plate waveguides.