Optimal Adjacent Output Phase Difference Assignments in Generalized One-Dimensional Five-Beam Switching Matrices

This paper discusses the optimal assignment of phase differences between adjacent output ports in a recently proposed generalized one-dimensional orthogonal switching matrix with five beams by considering the RF performance of the compared matrices, including bandwidth of reflection coefficients, frequency dependence of adjacent output phase differences, etc. To demonstrate the advantages of the optimal assignment, the worst assignment is used for comparison. Both assignments use the same couplers but have different values of phase shift, so the beam directions determined by adjacent output phase differences are decided by the phase shifters. The best and worst assignments are identified using the absolute sum of phase differences with reference to a straight waveguide, defined as the difference between the transmission phase of a one-layer-length straight waveguide and the actual required values of one-layer-length phase shifters. The optimal assignment has the smallest absolute sum of phase differences, while the worst assignment has the largest value. This proposed assignment selection technique is general and suitable for matrices with a large component count, which prevents using full-wave analyses to identify preferred configurations. The two assignments are realized using post-wall waveguide technology and designed to operate over the frequency band from 20 GHz to 24 GHz, using PTFE substrates having a thickness of 3.2 mm and a dielectric constant of 2.17. Both matrices are simulated, manufactured and measured by adding transitions to input ports and output ports and connecting with standard waveguide WR42. Both simulated and measured results confirm that the assignment resulting in the smaller absolute sum of phase differences has better performance than the one with the largest sum in terms of transmission and reflection coefficients, phase differences between adjacent output ports, and array factor, confirming the selected metric as a good indicator of the performance of the generalized orthogonal switching matrix.