How to use the Ranatec RI 3101 Butler Matrix 8×8 for antenna beamforming

Butler Matrix topology and port numbering

The Ranatec RI 3101 Butler Matrix 8×8 use the topology and port numbering shown below.

The above table shows the nominal phase progression over the output ports with port 1 as reference. Observe that the phase shift between an input port and port 1 is not specified, i.e., the paths have different lengths.

When the Butler Matrix is used as an antenna beamforming network the ports 4L to 4R are the beam ports and the ports 1 to 8 are the antenna element ports.

All unused ports shall be terminated with a 50ohm load.

The Butler Matrix is a passive network that creates a linear phase progression across the 8 output ports (numbered 1 to 8) when one of the input ports (1R, 1L, 2L etc.) is fed with a radio signal (or received). When the output ports are connected to antenna elements, an antenna beam is radiated in a specific direction depending on the antenna element spacing, which input port is fed and what frequency is used. The Butler Matrix is a passive device and works in the same way for transmitting or receiving.

Butler Matrix beam direction

The beam direction is given by the following expression:

Ɵ is the beam direction from the normal of the line of the elements.

α is the phase progression between two neighboring antenna elements (degrees).

d is the distance between two antenna elements (m).

C0 is the speed of light (m/s).

f is the frequency (Hz).

Example:

Assume we feed port 1L with a signal with the frequency 3 GHz (the other ports need to be terminated in 50 ohms).

Assume a spacing d between the element of 5cm.

From the table we read that the phase progression α is -22.5 degrees.

Inserting this into the expression: we get a beam direction Ɵ=7.2 degrees

If we feed port 4L instead we will have a phase progression of -157.5 degrees which results in a beam direction Ɵ= 61.0 degrees.

If a single transmitter or receiver is used a switch can be connected to select which input port shall be used and hence what beam direction is selected. It is also possible to connect independent transmitter/ receiver to the different ports (1R, 1L, 2L etc.).

The type antenna elements must be selected depending on maximum beam direction, polarisation, frequency etc.