MATLAB Examples

# Switched Beam Array With Butler Matrix

This example shows a switched beam array of 4 resonant dipoles. The beam switching is accomplished by using a 4 X 4 Butler matrix. The effect of the beam switching is shown by observing the outputs of 4 reciving antennas that are placed in the far-field of the array at the approximate azimuthal angles corresponding to the beam peaks. The effect of mutual coupling between the array elements on the transmit side is accounted for using S-parameters.

This example requires the following products:

• RF Blockset

## System Description

The system comprises of the following subsystems

• A Signal source and port switch
• A 4 X 4 Butler matrix implemented using directional couplers and phase shifters
• Array coupling model to capture the mutual coupling between the dipole linear array
• Channel transfer function model between linear array and the receiving antennas in the far-field
```model = 'AtxSwitchedBeamArrayWithButlerMatrixModel'; open_system(model); ```

## Butler Matrix

The Butler matrix is a type of analog beamforming network that can be constructed from purely passive devices like directional couplers and phase shifters. The number of input and output ports in a Butler matrix are equal. The output ports are connnected directly to each antenna element. Depending on the input port which is excited, the signals on the output ports are phase-shifted such that the beam switches in direction.

```open_system([model '/Butler Matrix'], 'force'); ```

## Array Mutual Coupling Model

The transmit side comprises of a 4 element linear array of resonant dipoles. The mutual coupling between array elements is calculated by using the scattering parameters.

```open_system([model '/Array Coupling Model'], 'force'); ```

## Channel and Receiving Antenna Output

There are 4 receiving antennas, resonant dipoles, placed in the far-field of this array. These 4 dipoles are placed in the azimuthal plane at 15 degree , 45 degree, 315 degree and 345 degree. The locations correspond to the expected beam peaks from the switched beam array output. The response at each of these far-field receiving antenna elements is computed as a superposition of the contributions from each antenna element in the 4-element transmit array.

```open_system([model '/Channel & Receivers/Channel-Rx1'], 'force'); ```

## Run the Simulation

In the simulation, switch the input port that gets driven with the signal by using the repeating staircase sequence generator. Each port is excited for 0.1 ms. Depending on the port that gets excited, the array main beams switch in direction. This can be seen in the output signal levels at each receving antenna. Within a 0.1 ms block of time, 1 out of the 4 received signals dominates the remaining three indicating the effect of the beamforming.

```sim(model) ```
```bdclose(model); clear model; ```