# patternElevation

**System object: **phased.ReplicatedSubarray

**Package: **phased

Plot replicated subarray directivity or pattern versus elevation

## Syntax

`patternElevation(sArray,FREQ)`

patternElevation(sArray,FREQ,AZ)

patternElevation(sArray,FREQ,AZ,Name,Value)

PAT = patternElevation(___)

## Description

`patternElevation(`

plots
the 2-D array directivity pattern versus elevation (in dBi) for the
array `sArray`

,`FREQ`

)`sArray`

at zero degrees azimuth angle. When `AZ`

is
a vector, multiple overlaid plots are created. The argument `FREQ`

specifies
the operating frequency.

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.

`patternElevation(`

,
in addition, plots the 2-D element directivity pattern versus elevation
(in dBi) at the azimuth angle specified by `sArray`

,`FREQ`

,`AZ`

)`AZ`

.
When `AZ`

is a vector, multiple overlaid plots
are created.

`patternElevation(`

plots the array pattern with additional options specified by one or
more `sArray`

,`FREQ`

,`AZ`

,`Name,Value`

)`Name,Value`

pair arguments.

returns
the array pattern. `PAT`

= patternElevation(___)`PAT`

is a matrix whose entries
represent the pattern at corresponding sampling points specified by
the `'Elevation'`

parameter and the `AZ`

input
argument.

## Input Arguments

`sArray`

— Replicated subarray

System object™

Replicated subarray, specified as a `phased.ReplicatedSubarray`

System object.

**Example: **`sArray= phased.ReplicatedSubarray;`

`FREQ`

— Frequency for computing directivity and pattern

positive scalar

Frequency for computing directivity and pattern, specified as a positive scalar. Frequency units are in hertz.

For an antenna or microphone element,

`FREQ`

must lie within the range of values specified by the`FrequencyRange`

or the`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`

**Data Types: **`double`

`AZ`

— Azimuth angles for computing directivity and pattern

1-by-*N* real-valued row vector

Azimuth angles for computing sensor or array directivities and patterns, specified as a
1-by-*N* real-valued row vector where *N* is the
number of desired azimuth directions. Angle units are in degrees. The azimuth angle must
lie between –180° and 180°.

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.

**Example: **`[0,10,20]`

**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.*

`Type`

— Displayed pattern type

`'directivity'`

(default) | `'efield'`

| `'power'`

| `'powerdb'`

Displayed pattern type, specified as the comma-separated pair
consisting of `'Type'`

and one of

`'directivity'`

— directivity pattern measured in dBi.`'efield'`

— field pattern of the sensor or array. For acoustic sensors, the displayed pattern is for the scalar sound field.`'power'`

— power pattern of the sensor or array defined as the square of the field pattern.`'powerdb'`

— power pattern converted to dB.

**Example: **`'powerdb'`

**Data Types: **`char`

`PropagationSpeed`

— Signal propagation speed

speed of light (default) | positive scalar

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`

`Weights`

— Subarray weights

*M*-by-1 complex-valued column vector

Subarray weights, specified as the comma-separated pair consisting
of `'Weights'`

and an *M*-by-1 complex-valued
column vector. Subarray weights are applied to the subarrays of the
array to produce array steering, tapering, or both. The dimension *M* is
the number of subarrays in the array.

**Example: **`'Weights',ones(10,1)`

**Data Types: **`double`

**Complex Number Support: **Yes

`SteerAngle`

— Subarray steering angle

`[0;0]`

(default) | scalar | 2-element column vector

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`

`ElementWeights`

— Weights applied to elements within subarray

`1`

(default) | complex-valued *N*_{SE}-by-*N*
matrix

_{SE}

Subarray element weights, specified as complex-valued *N _{SE}*-by-

*N*matrix. Weights are applied to the individual elements within a subarray. All subarrays have the same dimensions and sizes.

*N*is the number of elements in each subarray and

_{SE}*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

`Elevation`

— Elevation angles

`[-90:90]`

(default) | 1-by-*P* real-valued row vector

Elevation angles, specified as the comma-separated pair consisting
of `'Elevation'`

and a 1-by-*P* real-valued
row vector. Elevation angles define where the array pattern is calculated.

**Example: **`'Elevation',[-90:2:90]`

**Data Types: **`double`

`Parent`

— Handle to axis

scalar

Handle to the axes along which the array geometry is displayed specified as a scalar.

## Output Arguments

`PAT`

— Array directivity or pattern

*L*-by-*N* real-valued matrix

Array directivity or pattern, returned as an *L*-by-*N* real-valued
matrix. The dimension *L* is the number of elevation
angles determined by the `'Elevation'`

name-value
pair argument. The dimension *N* is the number of
azimuth angles determined by the `AZ`

argument.

## Examples

### Elevation Pattern of Array with Subarrays

Create a 2-by-2-element URA of isotropic antenna elements, and arrange four copies to form a 16-element URA. Plot the elevation directivity pattern within a restricted range of elevation angles from -45 to 45 degrees in 0.1 degree increments. Plot directivity for 0 degrees and 15 degrees azimuth.

**Create the array**

fmin = 1e9; fmax = 6e9; c = physconst('LightSpeed'); lam = c/fmax; sIso = phased.IsotropicAntennaElement(... 'FrequencyRange',[fmin,fmax],... 'BackBaffled',false); sURA = phased.URA('Element',sIso,... 'Size',[2 2],... 'ElementSpacing',lam/2); sRS = phased.ReplicatedSubarray('Subarray',sURA,... 'Layout','Rectangular','GridSize',[2 2],... 'GridSpacing','Auto');

**Plot elevation directivity pattern**

fc = 1e9; wts = [0.862,1.23,1.23,0.862]'; patternElevation(sRS,fc,[0,15],... 'PropagationSpeed',physconst('LightSpeed'),... 'Elevation',[-45:0.1:45],... 'Type','directivity',... 'Weights',wts);

## More About

### Directivity

Directivity describes the directionality of the radiation pattern of a sensor element or array of sensor elements.

Higher directivity is desired when you want to transmit more radiation in a specific direction. Directivity is the ratio of the transmitted radiant intensity in a specified direction to the radiant intensity transmitted by an isotropic radiator with the same total transmitted power

$$D=4\pi \frac{{U}_{\text{rad}}\left(\theta ,\phi \right)}{{P}_{\text{total}}}$$

where
*U*_{rad}*(θ,φ)* is the radiant
intensity of a transmitter in the direction *(θ,φ)* and
*P*_{total} is the total power transmitted by an
isotropic radiator. For a receiving element or array, directivity measures the sensitivity
toward radiation arriving from a specific direction. The principle of reciprocity shows that
the directivity of an element or array used for reception equals the directivity of the same
element or array used for transmission. When converted to decibels, the directivity is
denoted as *dBi*. For information on directivity, read the notes on Element Directivity and Array Directivity.

## Version History

**Introduced in R2015a**

## See Also

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