directivity
System object: phased.HeterogeneousURA
Namespace: phased
Directivity of heterogeneous uniform rectangular array
Syntax
D = directivity(H,FREQ,ANGLE)
D = directivity(H,FREQ,ANGLE,Name,Value)
Description
D = directivity(
computes
the Directivity (dBi) of a heterogeneous
uniform rectangular array of antenna or microphone elements, H
,FREQ
,ANGLE
)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(
computes
the directivity with additional options specified by one or more H
,FREQ
,ANGLE
,Name,Value
)Name,Value
pair
arguments.
Input Arguments
H
— Heterogeneous uniform rectangular array
System object™
Uniform rectangular array specified as a phased.HeterogeneousURA
System object.
Example: H = phased.HeterogeneousURA
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 theFrequencyRange
orFrequencyVector
property of the element. Otherwise, the element produces no response and the directivity is returned as–Inf
. Most elements use theFrequencyRange
property except forphased.CustomAntennaElement
andphased.CustomMicrophoneElement
, which use theFrequencyVector
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
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.
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
1 (default) | N-by-1 complex-valued column vector | N-by-L complex-valued
matrix
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 Dimension | FREQ Dimension | Purpose |
---|---|---|
N-by-1 complex-valued column vector | Scalar or 1-by-L row vector | Applies a set of weights for the single frequency or for all L frequencies. |
N-by-L complex-valued matrix | 1-by-L row vector | Applies 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
D
— Directivity
M-by-L matrix
Examples
Directivity of Heterogeneous Uniform Rectangular Array
Compute the directivity of a 9-element 3-by-3 heterogeneous URA consisting of short-dipole antenna elements. The three elements on the middle row are Y-directed while all the remaining elements are Z-directed.
Set the signal frequency to 1 GHz.
c = physconst('LightSpeed');
freq = 1e9;
lambda = c/freq;
Create the array of short-dipole antenna elements. The elements have frequency ranges from 0 to 10 GHz.
myElement1 = phased.ShortDipoleAntennaElement(... 'FrequencyRange',[0 10e9],... 'AxisDirection','Z'); myElement2 = phased.ShortDipoleAntennaElement(... 'FrequencyRange',[0 10e9],... 'AxisDirection','Y'); myArray = phased.HeterogeneousURA(... 'ElementSet',{myElement1,myElement2},... 'ElementIndices',[1 1 1; 2 2 2; 1 1 1]);
Create the steering vector to point to 30 degrees azimuth and compute the directivity in the same direction as the steering vector.
ang = [30;0]; w = steervec(getElementPosition(myArray)/lambda,ang); d = directivity(myArray,freq,ang,'PropagationSpeed',c,... 'Weights',w)
d = 11.1405
More About
Directivity (dBi)
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
where Urad(θ,φ) is the radiant intensity of a transmitter in the direction (θ,φ) and Ptotal 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.
See Also
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