Optimal Adjacent Output Phase Difference Assignments in One-Dimensional Parallel Switching Matrices With Four Beams

This article provides for the first time a detailed discussion of the optimal assignment of adjacent output phase differences in terms of matrix performance out of all possible combinations in generalized one-dimensional parallel switching matrices with four beams. In this specific case, the topology of the proposed matrix reduces to that of a single-layer Butler matrix, connecting hybrid couplers and crossovers with adequate phase shifters. The values of the phase shift required are dependent on the assignment of the output phase differences, which in turn is shown to have an impact on the radiation characteristics of the linear array fed by such networks when imposing constraints on the matrix layout for a more generic implementation. The configuration having the smallest phase difference with reference to the transmission phase of a straight waveguide with the same length as the coupled region of the crossover is chosen and compared with the conventional well-known Butler matrix. The two matrix configurations are implemented using post-wall waveguides designed to operate over the band 20 GHz – 24 GHz. The prototypes are manufactured and tested, using transitions to standard waveguide WR42. The measured results confirm the benefits of the identified optimal adjacent phase difference assignment in terms of transmission coefficients, reflection coefficients, phase differences between adjacent output ports, and frequency dependence of the array factor. These results will also benefit the design of larger generalized one-dimensional parallel switching matrices.