Single Layered <inline-formula> <tex-math notation="LaTeX">$4\times4$ </tex-math></inline-formula> Butler Matrix Without Phase-Shifters and Crossovers

Abstract

Traditional design of 4 × 4 Butler matrix (BM) uses couplers, phase shifters (PSs), and crossovers. Due to some troublesome issues related to PS and the crossovers involved in the design of BM, which degrades its performance, this paper presents a planar 4 × 4 BM without PS and crossovers. It is accomplished with the help of a modified coupler. The modified coupler is realized to have a 45° output phase difference, which replaces the function of the 45° PSs. The 45° output phase differences obtained from this type of coupler combined with quadrature coupler give the desired phase differences required at the output of the BM. The BM is meant to operate at 6 GHz. The simulated and measured reflection coefficients and isolations at all ports are below -17 dB at the center frequency. The result also shows an amplitude imbalance within ±3 dB with phase mismatch of about ±3° at the center frequency. The -10-dB reflection coefficient bandwidth is 37.10%, and the transmission bandwidth between -5 and -9 dB is about 31.0%. Both the simulated and experimental radiation patterns obtained by exciting the input ports (P1-P4) of the BM produce four orthogonal beams deposed at +15.3°, -47.6°, +47.6°, and -15.3°. This beam steering depicts a stable beam scanning angle of the BM, which is in good agreement with the theoretical predictions.

Keywords

• Crossovers
• Butler matrix
• modified coupler and phase shifters