A Low Complexity $16\times16$ Butler Matrix Design Using Eight-Port Hybrids

Beamforming networks such as Butler Matrices are important for multibeam array antenna applications. The challenge for Butler Matrix design is that their complexity increases with the number of ports. In this paper, a novel approach of designing a $16\times 16$ Butler Matrix with significant structure simplification is presented. The eight-port hybrids with no crossovers are used to simplify the network. To ensure the network has the same magnitude and phase responses as the standard one, the location and phase shifting value of each fixed phase shifter are derived from the $S$ -matrix of each hybrid. A $16\times 16$ Butler Matrix network operating from 9 GHz–11 GHz is designed to validate this concept. The compensated microstrip 3-dB/90° directional coupler, the phase shifter with a shunt open-and-short stub and the crossover with a resonating patch are used to reduce the transmission loss and enable broadband operation.