# directivity

System object: phased.HeterogeneousConformalArray
Package: phased

Directivity of heterogeneous conformal array

## Syntax

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

## Description

`D = directivity(H,FREQ,ANGLE)` computes the Directivity of a heterogeneous conformal array of antenna or microphone elements, `H`, at frequencies specified by the `FREQ` and in angles of direction specified by the `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)` computes the directivity with additional options specified by one or more `Name,Value` pair arguments.

## Input Arguments

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Heterogeneous conformal array specified as a `phased.HeterogeneousConformalArray` System object.

Example: `H = phased.HeterogeneousConformalArray;`

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 comma-separated pairs of `Name,Value` arguments. `Name` is the argument name and `Value` is the corresponding value. `Name` must appear inside quotes. You can specify several name and value pair arguments in any order as `Name1,Value1,...,NameN,ValueN`.

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`

Array weights, specified as the comma-separated pair consisting of `'Weights`' and an N-by-1 complex-valued column vector or N-by-L complex-valued matrix. Array weights are applied to the elements of the array to produce array steering, tapering, or both. The dimension N is the number of elements in the array. The dimension L is the number of frequencies specified by `FREQ`.

Weights DimensionFREQ 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 `FREQ`.

Note

Use complex weights to steer the array response toward different directions. You can create weights using the `phased.SteeringVector` System object or you can compute your own weights. In general, you apply Hermitian conjugation before using weights in any Phased Array System Toolbox™ function or System object such as `phased.Radiator` or `phased.Collector`. However, for the `directivity`, `pattern`, `patternAzimuth`, and `patternElevation` methods of any array System object use the steering vector without conjugation.

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

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 a steered heterogeneous conformal array. Construct a 24-element heterogeneous disk array using elements having different antenna patterns and then show how to compute the array's directivity.

Set the signal speed to the speed of light and the signal frequency to 2GHz.

```c = physconst('LightSpeed'); freq = 2e9;```

Choose two different types of elements - both are cosine antenna elements with different powers.

```myElement1 = phased.CosineAntennaElement('CosinePower',1.5); myElement2 = phased.CosineAntennaElement('CosinePower',1.8);```

Set up a three-ring disk array with 8 elements per ring. The inner ring has different elements from the outer rings.

```N = 8; azang = (0:N-1)*360/N-180; p0 = [zeros(1,N);cosd(azang);sind(azang)]; posn = [0.6*p0, 0.4*p0, 0.2*p0]; myArray = phased.HeterogeneousConformalArray; myArray.ElementPosition = posn; myArray.ElementNormal = zeros(2,3*N); myArray.ElementSet = {myElement1,myElement2}; myArray.ElementIndices = [1 1 1 1 1 1 1 1,... 1 1 1 1 1 1 1 1,... 2 2 2 2 2 2 2 2];```

Set up the steering vector to point at 30 degrees azimuth and compute the directivity in that direction.

```lambda = c/freq; ang = [30;0]; w = steervec(getElementPosition(myArray)/lambda,ang); d = directivity(myArray,freq,ang,'PropagationSpeed',c,... 'Weights',w)```
```d = 20.9519 ```