Flexible Phase Difference of 4 × 4 Butler Matrix without Phase-Shifters and Crossovers

Abstract

This paper proposes a new Butler matrix topology. The proposed Butler matrix consists of only four couplers without phase shifters and crossovers. The output phase difference is relatively flexible. Compared with the phase differences (±45° and ±135°) generated by the conventional Butler matrix, the proposed design can generate different sets of phase differences, which can be realized from −180° to 180°. The proposed new Butler matrix replaces the traditional 90° coupler with arbitrary phase-difference couplers. In this paper, closed-form design equations are derived and presented. A 4 × 4 Butler matrix with output phase differences of −30°, +150°, −120°, and +60° is designed according to equations. The 4 × 4 Butler is meant to operate at 2 GHz. The simulation results show that the amplitude unbalance is less than 0.1 dB, the phase mismatch is within 1°, the return loss is higher than 29 dB, and the isolation is higher than 32 dB.