What is a Butler Matrix?

What is a Butler Matrix? Where is it used?

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- everything RF

Aug 28, 2022

A Butler Matrix is an analog beamforming network that is used to feed the phased array antenna elements and control the directions of beams. Many modern wireless technologies used phased array antennas to provide directional beams resulting in higher spectrum efficiency. The direction of the beams in phased array antennas can be controlled by adjusting the relative phase of the signals to each antenna element rather than physically moving the antenna. A Butler matrix is used to feed the required phase difference to the antenna elements of a phased array antenna in order to produce beams in the desired direction. Click here to see Butler Matrix products from the leading manufacturers.

A Butler matrix has an equal number of input and output ports. Example configurations can be 4 x 4, 8 x 8 or N x N, where N is the number of input and output ports. It can transfer the signal from any of the input ports to any of the output ports with progressive phase shifts. The output ports are usually connected directly to each antenna element of the phased array system. Depending on the activated input port, the signals on the output ports are phase-shifted such that the beam turns in the desired direction.

Figure 1

A block diagram of a Butler Matrix can be seen above. It consists of hybrid couplers, fixed value and variable phase shifters, and crossovers. Variable phase shifters help the system to fine-tune the phase and thus the direction of the beam. The crossover allows the crossing of the transmission lines without overlapping them while providing high isolation.

Figure 2Figure 1 is an example of a 4 x 4 Butler matrix where one of the inputs of the matrix is activated to distribute power equally and introduce a progressive phase shift between each of the outputs. The input port selection for activation determines the angle of phase progression at the outputs. The diffraction pattern created by the antennas at the output steers the beam, where the angle of the beam’s direction is dependent on the phase progression observed at the outputs.

Butler matrices are widely used in cellular infrastructure i.e., in base stations to keep pointing the beams towards users. They are also used when testing MIMO antenna array applications. Butler matrices are also used in direction-finding systems such as target finding and warning systems for military applications. They have also proved useful in naval navigation because of their wide angular coverage. 

The Butler matrix can be used in both transmitting and receiving modes. They deliver maximum power in the transmitting mode and in Rx mode can collect signals from each of the beam directions with the full gain of the antenna array.

Butler matrices are available in modules or can also be developed on the printed circuit board it self using microstrip. Most phased array antenna elements are built into the board these days and thus even the feed to it i.e. the Butler matrix is designed using microstrips on the PCB. These microstrips are easy to fabricate and have a compact size.

Figure 3 - Example of a 4x4 Butler Matrix made using microstrips

Click here to see Butler Matrix products from the leading manufacturers.