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

Abstract

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 of beams. It also describes the associated numerical design method, supported by several design examples. The concept is further validated with a full-wave model of a generic 5 × 5 switching matrix designed at 76 GHz. The proposed matrices are obtained by cascading units consisting of a two-way coupler and a phase shifter in a parallel configuration, providing theoretically lossless operation as a direct consequence of the orthogonal BFN topology and equalized path lengths, expected to benefit the frequency bandwidth. The design method is general, also including the configurations equivalent to Butler matrices when the number of beams is a power of two. The obtained planar matrix designs combine some benefits of the well-known Butler and Nolen matrices, namely the parallel topology and the arbitrary number of beams. The minimum number of cascaded units required by the proposed topology, also corresponding to the number of layers, is found to be <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula> , where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula> is the number of beams, which is less than the number of cascaded units for the corresponding “parallel” Nolen matrix, for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula> larger than three, thus providing a reduction in the number of layers of up to 38% for an 8-beam matrix. This reduction is close to the theoretical upper boundary of 50%, reached for large values of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula> . This significant reduction is expected to have a positive impact on RF performance, and in particular insertion losses, as well as amplitude and phase dispersion over the operating band. Interestingly, the proposed switching matrix configuration reduces to a standard Butler matrix when the number of beams is equal to 4, and demonstrates a reduction in the number of layers of 20% over the corresponding planar Butler matrix for a design with 8 beams. The proposed matrix configuration is a promising solution for the design of low-cost single-layer beam-switching matrices.