A waveguide crossed-slot linear array with a matching element is accurately analyzed and designed by the method of moments using numerical-eigenmode basis functions developed by the authors. The rounded ends of crossed-slots are accurately modeled in the analysis. The initial values of the slot parameters determined by a model with assumption of periodicity of field are modified and refined by the full-wave finite-array analysis for uniform excitation and small axial ratio. As an example, an 8-element linear array is designed at 11.85 GHz, which radiates a circularly polarized wave at a beam-tilting angle of 50 degrees. The radiation pattern, the frequency characteristics of the reflection and the axial ratio are compared between the analysis and the measurement and they agree very well. The calculated and measured axial ratio at the beam direction are 0.1 dB and 1.7 dB, respectively. This method provides a basic and powerful design tool for slotted waveguide arrays.

A round-ended wide straight slot cut in the broad wall of a rectangular waveguide is analyzed by the Method of Moments (MoM) using numerical eigenmode basis functions derived by the edge-based finite element method (FEM), referred to as MoM/FEM. The frequency characteristics of the calculated transmission coefficients are compared with the measured ones, and good agreement is observed for a wide variety of antenna parameters. For simpler analysis that does not use MoM/FEM, an equivalent rectangular slot approximation for a round-ended slot is discussed. The resonant frequencies of empirically introduced "equal-area" and "equal-perimeter" slots are compared with those of round-ended slots for a wide variety of parameters such as slot width, wall thickness and dielectric constant inside the waveguide. Based upon MoM/FEM, which can be a reliable reference, it is found that the equal-area slot always gives a better approximation of the order of 1% over that of the equal-perimeter one which is of the order of 5%. For higher accuracy, a new rectangular slot approximation of a round-ended slot is proposed to be a linear combination of equal-area and equal perimeter approximation. The error is around 0.25% for a wide variety of parameters such as slot width-to-length ratio, wall thickness and dielectric constant of the filling material inside the waveguide.