The Butler Matrix is a circuit used to implement phased array antennas. It is based on the principle of linear algebra in complex field and realizes the control of phase and amplitude of antenna signal by matrix operation.
The principle of the Butler matrix can be summarized in the following steps:
1. Input signal distribution: First, the Butler matrix receives signals from multiple input ports. The signal on each input port has a different phase and amplitude.
2. Matrix coefficient design: Next, you need to design a matrix coefficient, which describes the phase and amplitude relationship of each input signal on the output port. These matrix coefficients are usually in complex form, where the real part represents amplitude control and the imaginary part represents phase control.
3. Matrix operation: By multiplying the input signal with the matrix coefficient, matrix operation is performed to control the phase and amplitude of each input signal. This results in the formation of a specific signal phase and amplitude distribution on the output port, enabling a phased array of the antenna.
4. Output signal synthesis: Finally, by combining the signals on the output port, a synthetic output signal is formed. The synthesized output signal has a specific beam shape and can be used for antenna beamforming and pointing control.
In general, Butler matrix uses the principle of matrix operation to realize the phased array of the antenna by controlling the phase and amplitude of the input signal. This technology is widely used in the fields of communication, radar and radio spectrum management.
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