Butler matrix

A Butler matrix is a beamforming network used to feed a phased array of antenna elements. Its purpose is to control the direction of a beam, or beams, of radio transmission. It consists of an ${\displaystyle n\times n}$ matrix (${\displaystyle n}$ some power of two) with hybrid couplers and fixed-value phase shifters at the junctions. The device has ${\displaystyle n}$ input ports (the beam ports) to which power is applied, and ${\displaystyle n}$ output ports (the element ports) to which ${\displaystyle n}$ antenna elements are connected. The Butler matrix feeds power to the elements with a progressive phase difference between elements such that the beam of radio transmission is in the desired direction. The beam direction is controlled by switching power to the desired beam port. More than one beam, or even all ${\displaystyle n}$ of them can be activated simultaneously.

The concept was first proposed by Butler and Lowe in 1961.^[1] It is a development of the work of Blass in 1960.^[2] Its advantage over other methods of angular beamforming is the simplicity of the hardware. It requires far fewer phase shifters than other methods and can be implemented in microstrip on a low-cost printed circuit board.^[3]