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.

A rectangular-to-radial waveguide transformer through a crossed slot is proposed as a feeder of a radial line slot antenna (RLSA) for use in a system of solar power satellite (SPS). The transformer is analyzed and designed by using the MoM with numerical eigenmode basis functions. The measured ripple of the amplitude is 3.0 dB in the φ-direction and a 7.0% frequency bandwidth for rotating mode with the ripple below 6 dB is obtained. This bandwidth is wider than that of conventional ring slot or cavity resonator with a coaxial feeder. The antenna measurements at 5.8 GHz show reasonable rotational symmetry both in the near-field distribution and the far field radiation patterns. The reflection is -27.7 dB at the design frequency and below -15 dB in the 7.0% bandwidth. The gain of the antenna with the diameter of 300 mm is 22.7 dBi and the efficiency is 56%.