# directivity

System object: phased.ReplicatedSubarray
Package: phased

Directivity of replicated subarray

## Syntax

```D = directivity(H,FREQ,ANGLE) D = directivity(H,FREQ,ANGLE,Name,Value) ```

## Description

`D = directivity(H,FREQ,ANGLE)` returns the Directivity (dBi) of a replicated array of antenna or microphone element, `H`, at frequencies specified by `FREQ` and in angles of direction specified by `ANGLE`.

The integration used when computing array directivity has a minimum sampling grid of 0.1 degrees. If an array pattern has a beamwidth smaller than this, the directivity value will be inaccurate.

`D = directivity(H,FREQ,ANGLE,Name,Value)` returns the directivity with additional options specified by one or more `Name,Value` pair arguments.

## Input Arguments

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Replicated subarray, specified as a `phased.ReplicatedSubarray` System object.

Example: `H = phased.ReplicatedSubarray;`

Frequencies for computing directivity and patterns, specified as a positive scalar or 1-by-L real-valued row vector. Frequency units are in hertz.

• For an antenna, microphone, or sonar hydrophone or projector element, `FREQ` must lie within the range of values specified by the `FrequencyRange` or `FrequencyVector` property of the element. Otherwise, the element produces no response and the directivity is returned as `–Inf`. Most elements use the `FrequencyRange` property except for `phased.CustomAntennaElement` and `phased.CustomMicrophoneElement`, which use the `FrequencyVector` property.

• For an array of elements, `FREQ` must lie within the frequency range of the elements that make up the array. Otherwise, the array produces no response and the directivity is returned as `–Inf`.

Example: `[1e8 2e6]`

Data Types: `double`

Angles for computing directivity, specified as a 1-by-M real-valued row vector or a 2-by-M real-valued matrix, where M is the number of angular directions. Angle units are in degrees. If `ANGLE` is a 2-by-M matrix, then each column specifies a direction in azimuth and elevation, `[az;el]`. The azimuth angle must lie between –180° and 180°. The elevation angle must lie between –90° and 90°.

If `ANGLE` is a 1-by-M vector, then each entry represents an azimuth angle, with the elevation angle assumed to be zero.

The azimuth angle is the angle between the x-axis and the projection of the direction vector onto the xy plane. This angle is positive when measured from the x-axis toward the y-axis. The elevation angle is the angle between the direction vector and xy plane. This angle is positive when measured towards the z-axis. See Azimuth and Elevation Angles.

Example: `[45 60; 0 10]`

Data Types: `double`

### Name-Value Arguments

Specify optional pairs of arguments as `Name1=Value1,...,NameN=ValueN`, where `Name` is the argument name and `Value` is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose `Name` in quotes.

Signal propagation speed, specified as the comma-separated pair consisting of `'PropagationSpeed'` and a positive scalar in meters per second.

Example: `'PropagationSpeed',physconst('LightSpeed')`

Data Types: `double`

Subarray weights, specified as the comma-separated pair consisting of `'Weights`' and an N-by-1 complex-valued column vector or N-by-M complex-valued matrix. The dimension N is the number of subarrays in the array. The dimension L is the number of frequencies specified by the `FREQ` argument.

`Weights` dimension`FREQ` dimensionPurpose
N-by-1 complex-valued column vectorScalar or 1-by-L row vectorApplies a set of weights for the single frequency or for all L frequencies.
N-by-L complex-valued matrix1-by-L row vectorApplies each of the L columns of `‘Weights’` for the corresponding frequency in the `FREQ` argument.

Example: `'Weights',ones(N,M)`

Data Types: `double`

Subarray steering angle, specified as the comma-separated pair consisting of `'SteerAngle'` and a scalar or a 2-by-1 column vector.

If `'SteerAngle'` is a 2-by-1 column vector, it has the form `[azimuth; elevation]`. The azimuth angle must be between –180° and 180°, inclusive. The elevation angle must be between –90° and 90°, inclusive.

If `'SteerAngle'` is a scalar, it specifies the azimuth angle only. In this case, the elevation angle is assumed to be 0.

This option applies only when the `'SubarraySteering'` property of the System object is set to `'Phase'` or `'Time'`.

Example: `'SteerAngle',[20;30]`

Data Types: `double`

Subarray element weights, specified as complex-valued NSE-by-N matrix. Weights are applied to the individual elements within a subarray. All subarrays have the same dimensions and sizes. NSE is the number of elements in each subarray and N is the number of subarrays. Each column of the matrix specifies the weights for the corresponding subarray.

#### Dependencies

To enable this name-value pair, set the `SubarraySteering` property of the array to `'Custom'`.

Data Types: `double`
Complex Number Support: Yes

## Output Arguments

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Directivity, returned as an M-by-L matrix. Each row corresponds to one of the M angles specified by `ANGLE`. Each column corresponds to one of the L frequency values specified in `FREQ`. Directivity units are in dBi where dBi is defined as the gain of an element relative to an isotropic radiator.

## Examples

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Compute the directivity of an array built up from ULA subarrays. Determine the directivity of the replicated subarray when the array is steered to towards 30 degrees azimuth.

Set the signal propagation speed to the speed of light. Set the signal frequency to 300 MHz.

```c = physconst('LightSpeed'); fc = 3e8; lambda = c/fc;```

Create a 4-element ULA of isotropic antenna elements spaced 0.4-wavelength apart.

```myArray = phased.ULA; myArray.NumElements = 4; myArray.ElementSpacing = 0.4*lambda;```

Construct a 2-by-1 replicated subarray.

```myRepArray = phased.ReplicatedSubarray; myRepArray.Subarray = myArray; myRepArray.Layout = 'Rectangular'; myRepArray.GridSize = [2 1]; myRepArray.GridSpacing = 'Auto'; myRepArray.SubarraySteering = 'Time';```

Steer the array to 30 degrees azimuth and zero degrees elevation.

```ang = [30;0]; mySV = phased.SteeringVector; mySV.SensorArray = myRepArray; mySV.PropagationSpeed = c;```

Find the directivity at 30 degrees azimuth.

```d = directivity(myRepArray,fc,ang,... 'PropagationSpeed',c,... 'Weights',step(mySV,fc,ang),... 'SteerAngle',ang)```
```d = 7.4776 ```