Generalized One-Dimensional Parallel Switching Matrices With an Arbitrary Number of Beams

This paper introduces a novel family of one-dimensional switching matrices, also known as beamforming networks (BFNs), which can be sized for an arbitrary number beams. It describes the associated numerical design method, supported by several examples. The concept is further validated with full-wave model generic 5 × matrix designed at 76 GHz. proposed matrices are obtained cascading units consisting two-way coupler and phase shifter in parallel configuration, providing theoretically lossless operation direct consequence orthogonal BFN topology equalized path lengths, expected to benefit frequency bandwidth. method general, including configurations equivalent Butler when beams power two. planar designs combine some benefits well-known Nolen namely minimum cascaded required topology, corresponding layers, found $N$ , where beams, less than “parallel” matrix, larger three, thus reduction layers up 38% 8-beam matrix. close theoretical upper boundary 50%, reached large values . significant have positive impact on RF performance, particular insertion losses, well amplitude dispersion over operating band. Interestingly, configuration reduces standard equal 4, demonstrates 20% 8 promising solution low-cost single-layer beam-switching matrices.