This paper presents the mode matching (MM)/finite element method (FEM) hybrid analysis for a short-slot 2-plane coupler, and an optimization process for a wideband design based on a genetic algorithm (GA). The method of the analysis combines a fast modal analysis of the MM which reduces the computation time, with the flexibility of an FEM which can be used with an arbitrary cross-section. In the analysis, the model is reduced into the one-eighth model by using the three-dimensional structural symmetry. The computed results agree well with those by the simulation and the computation time is reduced. The bandwidth is improved by the optimization based on the GA from 2.4% to 6.9% for the 2-plane hybrid coupler and from 5.4% to 7.5% for the 2-plane cross coupler. The measured results confirm the wideband design.

A wideband design of the waveguide short-slot 2-plane coupler with 2×2 input/output ports is designed, fabricated, and evaluated. Using coupling coefficients of complementary propagating modes which are TE11, TE21, and TE30 modes, the flatness of the output amplitudes of 2-plane coupler is improved. The coupler operates from 4.96GHz to 5.27GHz (bandwidth 6.1%) which is wider than the former coupler without considering the complementary propagating mode from 5.04GHz to 5.17GHz (bandwidth 2.5%).

A 42×42-way one-body 2-D beam-switching Butler matrix with waveguide short-slot 2-plane couplers is designed and fabricated in the 22GHz band. The one-body configuration using the commutativity and the overlapping of units allows reducing the size and loss in comparison with a cascade of matrices beam-switching for the horizontal and the vertical planes. It is achieved by replacing 2×2-way 1-plane couplers in the conventional block configuration for a Butler matrix with 22×22-way 2-plane couplers. The measured bandwidth is approximately 2% restricted by the frequency characteristics of the 2-plane couplers. In the radiation from the aperture array antenna of the 42 output ports, the 3.9dB-down coverage of 3-D solid angle by the sixteen beams is around 1.72 steradian which is same as 27.4% of hemisphere at the design frequency for the aperture spacing of 0.73×0.73 wavelength.