{"id":23309,"date":"2025-09-12T11:55:08","date_gmt":"2025-09-12T09:55:08","guid":{"rendered":"https:\/\/ranatec.com\/how-to-use-the-ranatec-ri-3101-butler-matrix-8x8-for-antenna-beamforming\/"},"modified":"2025-09-12T11:55:08","modified_gmt":"2025-09-12T09:55:08","slug":"how-to-use-the-ranatec-ri-3101-butler-matrix-8x8-for-antenna-beamforming","status":"publish","type":"post","link":"https:\/\/ranatec.com\/en-ca\/how-to-use-the-ranatec-ri-3101-butler-matrix-8x8-for-antenna-beamforming\/","title":{"rendered":"How to use the Ranatec RI 3101 Butler Matrix 8×8 for antenna beamforming"},"content":{"rendered":"

Butler Matrix topology and port numbering<\/h2>\n

The Ranatec RI 3101 Butler Matrix 8×8<\/a> use the topology and port numbering shown below.<\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

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.<\/span><\/p>\n

When the Butler Matrix<\/a> 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.<\/span><\/p>\n

All unused ports shall be terminated with a 50ohm load.<\/span><\/p>\n

The Butler Matrix<\/a> 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.<\/span><\/p>\n

Butler Matrix beam direction<\/h2>\n

The beam direction is given by the following expression:<\/b><\/p>\n

\u019f<\/b> is the beam direction from the normal of the line of the elements.<\/span><\/p>\n

\u03b1<\/b> is the phase progression between two neighboring antenna elements (degrees).<\/span><\/p>\n

d<\/b> is the distance between two antenna elements (m).<\/span><\/p>\n

C0<\/b> is the speed of light (m\/s).<\/span><\/p>\n

f<\/b> is the frequency (Hz).<\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

Example:<\/b><\/p>\n

Assume we feed port <\/span>1L <\/b>with a signal with the frequency <\/span>3 GHz<\/b> (the other ports need to be terminated in 50 ohms).<\/span><\/p>\n

Assume a spacing <\/span>d<\/b> between the element of <\/span>5cm<\/b>.<\/span><\/p>\n

From the table we read that the phase progression <\/span>\u03b1<\/b> is -22.5 degrees.<\/span><\/p>\n

Inserting this into the expression: \"\"<\/span> we get a beam direction <\/span>\u019f<\/b>=7.2 degrees<\/span><\/p>\n

If we feed port <\/span>4L instead<\/b> we will have a phase progression of -157.5 degrees which results in a beam direction <\/span>\u019f<\/b>= 61.0 degrees.<\/span><\/p>\n

\"\"<\/p>\n

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.).<\/span><\/p>\n

The type antenna elements must be selected depending on maximum beam direction, polarisation, frequency etc.<\/span><\/p>\n<\/div><\/div><\/div>