# directivity

## Description

returns the Directivity of the antenna or transducer element,
`D`

= directivity(`element`

,`FREQ`

,`ANGLE`

)`element`

, at frequencies specified by FREQ in direction
angles specified by `ANGLE`

.

## Input Arguments

`element`

— Antenna or transducer element

Phased Array System Toolbox™
System object™

Antenna or transducer element, specified as a Phased Array System Toolbox System object.

`FREQ`

— Frequency for computing directivity and patterns

positive scalar | 1-by-*L* real-valued row vector

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`

`ANGLE`

— Angles for computing directivity

1-by-*M* real-valued row vector | 2-by-*M* real-valued matrix

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`

## Output Arguments

`D`

— Directivity

*M*-by-*L* matrix

## 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

The *azimuth angle* of a vector is the angle between
the *x*-axis and the orthogonal projection of the vector onto the
*xy*-plane. The angle is positive from the *x*-axis
toward the *y*-axis. Azimuth angles lie between –180 and 180 degrees. The
*elevation angle* is the angle between the vector and its
orthogonal projection onto the *xy*-plane. The angle is positive toward the
positive *z*-axis from the *xy*-plane. By default, the
boresight direction of an element or array is aligned with the positive
*x*-axis. The boresight direction is the direction of the main lobe of an
element or array.

**Note**

The elevation angle is sometimes defined as the angle a vector makes with the positive
*z*-axis. The MATLAB^{®} and Phased Array System Toolbox products do not use this definition.

This figure illustrates the azimuth and elevation angles of a direction vector.

## Version History

**Introduced in R2019a**

## See Also

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