Butler matrix
A Butler matrix is a beamforming network used to feed a phased array of antenna elements.
some power of two) with hybrid couplers and fixed-value phase shifters at the junctions.
[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.
[4] Horns have limited bandwidth and more complex antennae may be used if more than an octave is required.
[6] A Butler matrix can also feed a circular array giving 360° coverage.
[7] A circular antenna array can be made to simultaneously produce an omnidirectional beam and multiple directional beams when fed through two Butler matrices back-to-back.
Since they are passive and reciprocal, the same matrix can do both – in a transceiver for instance.
They have the advantageous property that in transmit mode they deliver the full power of the transmitter to the beam, and in receive mode they collect signals from each of the beam directions with the full gain of the antenna array.
[9] The essential components needed to build a Butler matrix are hybrid couplers and fixed-value phase shifters.
Microwave circuits are often manufactured in the planar format called microstrip.
Lines that need to cross over each other are typically implemented as an air bridge.
This will add an additional 90° phase shift to the lines being crossed, but this can be compensated for by adding an equivalent amount to the phase shifters in lines not being crossed.
[14] In this kind of implementation, the phase shifters are constructed as delay lines of the appropriate length.
The cumulative insertion loss from all these components in microstrip can make it impractical.
The technology usually used to overcome this problem, especially at the higher frequencies, is waveguide which is much less lossy.
[17] Linear antenna arrays driven by Butler matrices, or some other beam-forming network, to produce a scanning beam are used in direction finding applications.
[18] They are especially useful in naval systems because of the wide angular coverage that can be obtained.
[19] Another feature that makes Butler matrices attractive for military applications is their speed over mechanical scanning systems.
To be orthogonal (that is, not interfere with each other) the beam shapes must meet the Nyquist ISI criterion, but with distance as the independent variable rather than time.
