Ultra‐compact 3 × 3 Nolen matrix beamforming network

Abstract

A novel compact 3 × 3 Nolen matrix beamforming network is proposed in this study. Unlike the Butler matrix and Blass matrix, in this design, the proposed feeding network only requires couplers and phase shifters and removes crossovers and load terminations. To minimise the size, the authors’ proposed novel Nolen matrix is realised by lumped-element couplers. First, the design theory for 3 × 3 Nolen matrix is derived, and the associated pyramidal layout consisting of three couplers with two coupling ratios and three-phase shifters is proposed. Based on the determined topology, the S-parameters of the proposed feeding network and desired coupling ratios are derived, and it is found that the phase differences among the output ports are dependent on the characteristics of the couplers. Then, each coupler is realised by using lumped-elements (including inductors and capacitors) in the proposed topologies, where the values of the elements are obtained by analysing the ABCD-matrix of the branch lines in the couplers. To verify the proposed concept, an experimental prototype working at 1 GHz is fabricated and tested. The simulation and measurement results agree well with each other, and an ultra-compact size 0.17λ × 0.06λ is implemented to achieve more than 90% size reduction comparing with the previous designs.