Broadband Butler Matrices with the Use of High-Pass LC Sections as Left-Handed Transmission Lines

Abstract

An application of left-handed transmission line sections in Butler matrices has been investigated. It has been shown, for the first time, that the utilization of both left-handed and right-handed transmission lines allows for broadband differential phase shifters’ realization, required in the Butler matrices. A complete theoretical analysis is given, for Butler matrices incorporating ideal transmission lines of both right- and left handed types and expressions for the achievable bandwidth and differential phase deviation are derived. The presented idea has been verified by the design of a 4 x 4 Butler matrix operating in a frequency range of 2.5 – 3.5 GHz. As an artificial left-handed transmission line, an equivalent high-pass LC circuit realized in a quasi-lumped element technique, has been considered, and the resulting phase shift of such a circuit is given analytically. The obtained measurement results fully confirm the validity of the proposed idea of broadband Butler matrices’ realization.