Design of Wideband Butler Matrix With Equal/Unequal Phase Differences for Flexible Beam-Controllability

Abstract

This brief presents a new generic wideband Butler matrix topology with an expanded range of radiation beam angle. Both Butler matrix with equal phase differences (BM EPD) and Butler matrix with unequal phase differences (BM UEPD) are studied and simulated, and the equations of the array factor are derived. Arbitrary phase differences have been realized when different input ports are excited, referring to flexible beam controllability. To prove the design concept, a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4\times 4$ </tex-math></inline-formula> UEPD BM operating at 3.5 GHz and a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4\times 4$ </tex-math></inline-formula> EPD BM operating at 4.9 GHz are demonstrated and fabricated respectively. A linear antenna array consisting of printed dipoles with integrated balun is integrated with the Butler matrix for verification of its radiation beam steering. The simulation and measurement results agree well with the theoretical analysis.