# Documentation

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# phased.CosineAntennaElement System object

Package: phased

Cosine antenna element

## Description

The `CosineAntennaElement` object models an antenna with a cosine response in both azimuth and elevation. The main response axis (MRA) points to 0° azimuth and 0° elevation in the antenna coordinate system. When placed in a linear array, the MRA is normal to the array axis (see, for example, `phased.ULA`). When placed in a planar array, the MRA points along the array normal (see, for example, `phased.URA`).

To compute the response of the antenna element for specified directions:

1. Define and set up your cosine antenna element. See Construction.

2. Call `step` to compute the antenna response according to the properties of `phased.CosineAntennaElement`. The behavior of `step` is specific to each object in the toolbox.

This antenna element is not capable of supporting polarization.

 Note:   Starting in R2016b, instead of using the `step` method to perform the operation defined by the System object™, you can call the object with arguments, as if it were a function. For example, ```y = step(obj,x)``` and `y = obj(x)` perform equivalent operations.

## Construction

`H = phased.CosineAntennaElement` creates a cosine antenna system object, `H`, that models an antenna element whose response is cosine raised to a specified power greater than or equal to one in both the azimuth and elevation directions.

`H = phased.CosineAntennaElement(Name,Value)` creates a cosine antenna object, `H`, with each specified property set to the specified value. You can specify additional name-value pair arguments in any order as (`Name1`,`Value1`,...,`NameN`,`ValueN`).

## Properties

 `FrequencyRange` Operating frequency range Specify the operating frequency range (in Hz) of the antenna element as a 1-by-2 row vector in the form `[LowerBound HigherBound]`. The antenna element has no response outside the specified frequency range. Default: `[0 1e20]` `CosinePower` Exponent of cosine pattern Specify the exponents of the cosine pattern as a scalar or a 1-by-2 vector. Exponent values must be real numbers greater than zero. When you set `CosinePower` to a scalar, both the azimuth direction cosine pattern and the elevation direction cosine pattern are raised to the specified value. When you set `CosinePower` to a 1-by-2 vector, the first element is the exponent for the azimuth direction cosine pattern and the second element is the exponent for the elevation direction cosine pattern. Default: `[1.5 1.5]`

## Methods

 clone Create cosine antenna object with same property values directivity Directivity of cosine antenna element getNumInputs Number of expected inputs to step method getNumOutputs Number of outputs from step method isLocked Locked status for input attributes and nontunable properties isPolarizationCapable Polarization capability pattern Plot cosine antenna element directivity and patterns patternAzimuth Plot cosine antenna element directivity or pattern versus azimuth patternElevation Plot cosine antenna element directivity or pattern versus elevation plotResponse Plot response pattern of antenna release Allow property value and input characteristics changes step Output response of antenna element

## Definitions

### Cosine Response

The `step` method returns the field response (or field pattern)

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

of the cosine antenna element.

In this expression

• az is the azimuth angle.

• el is the elevation angle.

• The exponents m and n are real numbers greater than zero.

The response is defined for azimuth and elevation angles between –90° and 90°, inclusive, and is always positive. There is no response at the backside of a cosine antenna. The cosine response pattern achieves a maximum value of 1 at 0° azimuth and 0° elevation. Larger exponent values narrow the response pattern of the element and increase the directivity.

The power response (or power pattern) is the squared value of the field response.

`$P\left(az,el\right)={\mathrm{cos}}^{2m}\left(az\right){\mathrm{cos}}^{2n}\left(el\right)$`

## Examples

expand all

Construct a cosine pattern antenna and calculate its response at boresight (0 degrees azimuth and 0 degrees elevation). Then, plot the antenna pattern. Assume the antenna works between 800 MHz and 1.2 GHz and its operating frequency is 1 GHz.

Note: This example runs only in R2016b or later. If you are using an earlier release, replace each call to the function with the equivalent `step` syntax. For example, replace `myObject(x)` with `step(myObject,x)`.

Set the azimuth exponent to 1.5 and elevation exponent to 2.5.

```antenna = phased.CosineAntennaElement('FrequencyRange',[800e6 1.2e9],... 'CosinePower',[1.5 2.5]); fc = 1e9; resp = antenna(fc,[0;0]); pattern(antenna,fc,0,[-90:90],'Type','powerdb','CoordinateSystem','polar') ```

```pattern(antenna,fc,[-180:180],0,'Type','powerdb','CoordinateSystem','polar') ```