**System object: **phased.IsotropicProjector

**Package: **phased

Directivity of isotropic projector

`D = directivity(projector,FREQ,ANGLE)`

returns the Directivity of the isotropic projector,
`D`

= directivity(`projector`

,`FREQ`

,`ANGLE`

)`projector`

, at frequencies specified by
`FREQ`

and in the directions specified by
`ANGLE`

.

`projector`

— Isotropic projector`phased.IsotropicProjector`

System
object™Isotropic projector, specified as a `phased.IsotropicProjector`

System
object.

**Example: **`phased.IsotropicProjector`

`FREQ`

— Frequency for computing directivity and patternspositive scalar | 1-by-

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 directivity1-by-

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`

`D`

— DirectivityCompute the directivity of an isotropic projector in different directions. Assume the signal frequency is 3 kHz. First, set the projector parameters.

fc = 3e3; projector = phased.IsotropicProjector('FrequencyRange',[1,10]*1e3, ... 'VoltageResponse',[100,110,120,110,100]); patternElevation(projector,fc,45)

Select the angles of interest to be constant elevation angle at zero degrees. The five azimuth angles are centered around boresight (zero degrees azimuth and zero degrees elevation).

ang = [-20,-10,0,10,20; 0,0,0,0,0];

Compute the directivity along the constant elevation cut.

d = directivity(projector,fc,ang)

`d = `*5×1*
0
0
0
0
0

The directivity of an isotropic projector is zero in every direction.

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.

Computing directivity requires integrating the far-field transmitted radiant intensity over all directions in space to obtain the total transmitted power. There is a difference between how that integration is performed when Antenna Toolbox™ antennas are used in a phased array and when Phased Array System Toolbox™ antennas are used. When an array contains Antenna Toolbox antennas, the directivity computation is performed using a triangular mesh created from 500 regularly spaced points over a sphere. For Phased Array System Toolbox antennas, the integration uses a uniform rectangular mesh of points spaced 1° apart in azimuth and elevation over a sphere. There may be significant differences in computed directivity, especially for large arrays.

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