A Compact Broadband 4×4 Butler Matrix With 360° Continuous Progressive Phase Shift
Xi-Zhu Wang, Fu‐Chang Chen, Qing‐Xin Chu
Abstract
This article presents a novel compact broadband <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> Butler matrix with 360° continuous progressive phase shift. The tunable Butler matrix is composed of a typical <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> Butler matrix and four wideband continuously tunable phase shifters (PSs). To realize the size miniaturization, the right-handed transmission line (RHTL) is employed to construct the compact branch-line couplers and crossovers, which performs well over the operating bandwidth. The size of the proposed Butler matrix utilizing the compact coupler and crossover is reduced about 50% compared with the traditional design. A novel coupled-resonant PS is proposed to realize <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$135^{\circ }\pm 10^{\circ }$ </tex-math></inline-formula> continuous phase shift over a wide fractional bandwidth (FBW) of 33.3% (2.0–2.8 GHz). By cascading the miniaturized <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> Butler matrix and the 135° continuously tunable PSs, 360° continuous progressive phase shift between four outputs can be obtained. The measured results verify the feasibility of the design.