Phase Shifter-Relaxed and Control-Relaxed Continuous Tuning 4×4 Butler Matrix

A novel continuous tunable phase progression beamforming feeding network is proposed using 4×4 Butler matrix and tunable phase shifters. To tune the progressive phase difference at the output ports, four phase shifters (i.e. two phase shifters with tuning range 90°, and other two with 180° phase tuning range) are integrated with Butler matrix. Two channel digital voltages control all four phase shifters simultaneously to tune the phase difference in 90° range for each input excitation of Butler matrix, and the 360° full range of phase difference is realized by switching four input ports. The theoretical analysis is carried out to reduce the number of phase shifters as well as their phase tuning ranges, and the closed-form equations are derived to minimize the control complexity. To prove the design concept, a prototype of proposed tunable Butler matrix is designed at 5.8 GHz, and the experimental results agree well with the simulation results to prove the design theory.