In this work, a novel synthesis method for optimal efficiency multibeam networks is introduced. The proposed design method can be used to create passive beamforming networks that generate any arbitrary set of non-orthogonal beams, achieving optimal power efficiency as dictated by Stein's limit. This is achieved by decomposing the desired non-orthogonal excitation matrices to two orthogonal and one diagonal excitation matrices with the use of Singular Value Decomposition (SVD). Subsequently, the resulting orthogonal excitation matrices are implemented as Nolen matrices and the diagonal matrix as a set of attenuated transmission lines. As a proof of concept, a 4- beam 2 × 2 planar array network is fabricated and measured using Ridge Gap Waveguide (RGW) technology at 30 GHz. Measured results show a 30% average power efficiency across the operating band compared to the maximum theoretical power efficiency of 55.5% calculated according to Stein's limit.
