directivity
Description
returns the Directivity (dBi) of an array of antenna or microphone elements, D
= directivity(array
,FREQ
,ANGLE
)array
,
at frequencies specified by FREQ
and in angles of direction specified by
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.
directivity(___,
plots the
array pattern with additional options specified by one or more Name,Value
)Name,Value
pair arguments.
Examples
Directivity of Uniform Linear Array
Compute the directivities of two different uniform linear arrays (ULA). One array consists of isotropic antenna elements and the second array consists of cosine antenna elements. In addition, compute the directivity when the first array is steered in a specified direction. For each case, calculate the directivities for a set of seven different azimuth directions all at zero degrees elevation. Set the frequency to 300 MHz.
Array of isotropic antenna elements
First, create a 10-element ULA of isotropic antenna elements spaced 1/2-wavelength apart.
c = physconst('LightSpeed'); fc = 300e6; lambda = c/fc; ang = [-30,-20,-10,0,10,20,30; 0,0,0,0,0,0,0]; myAnt1 = phased.IsotropicAntennaElement; myArray1 = phased.ULA(10,lambda/2,'Element',myAnt1);
Compute the directivity.
d = directivity(myArray1,fc,ang,'PropagationSpeed',c)
d = 7×1
-6.9886
-6.2283
-6.5176
10.0011
-6.5176
-6.2283
-6.9886
Array of cosine antenna elements
Next, create a 10-element ULA of cosine antenna elements spaced 1/2-wavelength apart.
myAnt2 = phased.CosineAntennaElement('CosinePower',[1.8,1.8]); myArray2 = phased.ULA(10,lambda/2,'Element',myAnt2);
Compute the directivity.
d = directivity(myArray2,fc,ang,'PropagationSpeed',c)
d = 7×1
-1.9838
0.0529
0.4968
17.2548
0.4968
0.0529
-1.9838
The directivity of the cosine ULA is greater than the directivity of the isotropic ULA because of the larger directivity of the cosine antenna element.
Steered array of isotropic antenna elements
Finally, steer the isotropic antenna array to 30 degrees in azimuth and compute the directivity.
w = steervec(getElementPosition(myArray1)/lambda,[30;0]); d = directivity(myArray1,fc,ang,'PropagationSpeed',c,... 'Weights',w)
d = 7×1
-297.2705
-13.9783
-9.5713
-6.9897
-4.5787
-2.0536
10.0000
The directivity is greatest in the steered direction.
Input Arguments
array
— Phased array
Phased Array System Toolbox™
System object™
Phased array, 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 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.
Example: CoordinateSystem,'polar',Type,'directivity'
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
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.
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.
Numerical Uncertainty
Grating lobes due to array element spacing greater than ½ wavelength may introduce numerical errors in the computation of array directivity.
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.
Version History
Introduced in R2021a
See Also
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