# patternElevation

Plot array directivity or pattern versus elevation

## Syntax

## Description

`patternElevation(`

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

,`FREQ`

,`AZ`

,`Name,Value`

)`Name,Value`

pair arguments.

## Input Arguments

`array`

— phased array

System object™

Phased array, specified as a System object.

**Example: **`array = phased.UCA;`

`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.*

**Example: **`CoordinateSystem,'polar',Type,'directivity'`

`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`

— Array weights

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

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

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

**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(10,1)`

**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.

## 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.

### Azimuth and Elevation Angles

Define the azimuth and elevation conventions used in the toolbox.

The *azimuth angle* of a vector is the angle between the
*x*-axis and its orthogonal projection onto the
*xy*-plane. The angle is positive when going from the
*x*-axis toward the *y*-axis. Azimuth angles lie between
–180° and 180° degrees, inclusive. The *elevation angle* is the angle
between the vector and its orthogonal projection onto the *xy*-plane. The
angle is positive when going toward the positive *z*-axis from the
*xy*-plane. Elevation angles lie between –90° and 90° degrees, inclusive.

## Version History

**Introduced in R2021a**

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