# Documentation

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# step

System object: phased.CosineAntennaElement
Package: phased

Output response of antenna element

## Syntax

`RESP = step(H,FREQ,ANG)`

## Description

 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.

`RESP = step(H,FREQ,ANG)` returns the antenna's voltage response `RESP` at operating frequencies specified in `FREQ` and directions specified in `ANG`.

 Note:   The object performs an initialization the first time the `step` method is executed. This initialization locks nontunable properties and input specifications, such as dimensions, complexity, and data type of the input data. If you change a nontunable property or an input specification, the System object issues an error. To change nontunable properties or inputs, you must first call the `release` method to unlock the object.

## Input Arguments

 `H` Antenna element object. `FREQ` Operating frequencies of antenna in hertz. `FREQ` is a row vector of length L. `ANG` Directions in degrees. `ANG` can be either a 2-by-M matrix or a row vector of length M. If `ANG` is a 2-by-M matrix, each column of the matrix specifies the direction in the form [azimuth; elevation]. The azimuth angle must be between –180 and 180 degrees, inclusive. The elevation angle must be between –90 and 90 degrees, inclusive. If `ANG` is a row vector of length M, each element specifies a direction's azimuth angle. In this case, the corresponding elevation angle is assumed to be 0.

## Output Arguments

 `RESP` Voltage response of antenna element specified as an M-by-L, complex-valued matrix. In this matrix, M represents the number of angles specified in `ANG` while L represents the number of frequencies specified in `FREQ`.

## 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

Construct a cosine antenna element. The cosine response is raised to a power of 1.5. The antenna frequency range is the IEEE® X band from 8 to 12 GHz. The antenna operates at 10 GHz. Obtain the antenna's response for an incident angle of 30 degrees azimuth and 5 degrees elevation.

```hant = phased.CosineAntennaElement(... 'FrequencyRange',[8e9 12e9],... 'CosinePower',1.5); % operating frequency fc = 10e9; % incident angle ang = [30;5]; % use the step method to obtain the antenna's response resp = step(hant,fc,ang);```