Phase Shifter-Relaxed and Control-Relaxed Continuous Steering Multiple Beamforming 4 × 4 Butler Matrix Phased Array

A novel continuous tunable phase progression beamforming feeding network is proposed using $4\times 4$ Butler matrix and tunable phase shifters. To tune the progressive phase difference at the output ports of matrix network, four phase shifters (i.e. two phase shifters with 90° tuning range, and other two with 180° phase tuning range) are integrated within the 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 the Butler matrix, and the 360° full range of the progressive phase difference is realized by switching four input ports. The theoretical analysis is carried out to reduce the number of the 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 the 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. Integrating with four patch antenna elements, the measured radiation beam is steered from −51° to 52° by tuning two control voltages.