# Documentation

## Cosine Antenna Element

### Support for Cosine Antenna Elements

The `phased.CosineAntennaElement` object models an antenna element whose response is cosine raised to a specified power in the azimuth and elevation directions.

The cosine response, or cosine pattern, is given by:

$P\left(az,el\right)={\mathrm{cos}}^{m}\left(az\right){\mathrm{cos}}^{n}\left(el\right)$

In this expression:

• az is the azimuth angle.

• el is the elevation angle.

• The exponents m and n are real numbers greater than or equal to 1.

The response is defined for azimuth and elevation angles between –90 and 90 degrees, inclusive. There is no response at the back of a cosine antenna. The cosine response pattern achieves a maximum value of 1 at 0 degrees azimuth and elevation. Raising the response pattern to powers greater than one concentrates the response in azimuth or elevation.

When you use the cosine antenna element, you specify the exponent of the cosine pattern and the operating frequency range of the antenna.

### Concentration of Cosine Response

This example shows how to visualize the effect of concentrating the response. The example computes and plots the cosine response with powers equal to 1 and 2 for a single angle between –90 and 90 degrees.

```theta = -90:.01:90; Cos1 = cosd(theta); Cos2 = Cos1.^2; plot(theta,Cos1); hold on; plot(theta,Cos2,'r'); legend('Exponent = 1','Exponent = 2','location','northeast'); xlabel('Degrees'); ylabel('Response');```

### Cosine Antenna Element Operating from 1 to 10 GHz

This example shows how to construct an antenna with a cosine squared response in both azimuth and elevation and plot the antenna response. The operating frequency range of the antenna is from 1 to 10 GHz.

```hcos = phased.CosineAntennaElement(... 'FrequencyRange',[1e9 1e10],'CosinePower',[2 2]) plotResponse(hcos,5e9,'RespCut','3D','Format','Polar');```

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