A Miniaturized $4\times 4$ Butler Matrix Using Distributed Capacitors in the Quasi-Arbitrary Phase-Difference Hybrid Coupler

Abstract

This communication describes a miniaturized <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$4\times 4$</tex> Butler Matrix Using Distributed capacitors in the Quasi-Arbitrary Phase-Difference Hybrid Coupler. First, A traditional branch-line coupler with any phase difference can be calculated by the impedance and phase of each short side. next, a transmission line can be replaced by a high impedance transmission line and parallel capacitors. To miniaturize the circuit, all distributed capacitances are placed inside the branch coupler. On the basis of the compact branch coupler configuration, the compact Butler matrix needs to eliminate the independent phase shifter and frequency divider. A distributed capacitive branch coupler with arbitrary phase difference is proposed to replace the traditional branch coupler. Through the miniaturized design of branch couplers and the elimination of phase shifters and crossover junctions, the design of the butler matrix is 66% smaller than the traditional butler matrix design proceedings.