directivity
System object: phased.ReplicatedSubarray
Namespace: phased
Directivity of replicated subarray
Syntax
D = directivity(H,FREQ,ANGLE)
D = directivity(H,FREQ,ANGLE,Name,Value)
Description
D = directivity(
returns
the Directivity (dBi) of a replicated
array of antenna or microphone element, H
,FREQ
,ANGLE
)H
, 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.
D = directivity(
returns
the directivity with additional options specified by one or more H
,FREQ
,ANGLE
,Name,Value
)Name,Value
pair
arguments.
Input Arguments
H
— Replicated subarray
System object™
Replicated subarray, specified as a phased.ReplicatedSubarray
System object.
Example: H = phased.ReplicatedSubarray;
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
— Subarray weights
1 (default) | N-by-1 complex-valued column vector | N-by-L complex-valued
matrix
Subarray weights, specified as the comma-separated pair consisting
of 'Weights
' and an N-by-1 complex-valued
column vector or N-by-M complex-valued
matrix. The dimension N is the number of subarrays
in the array. The dimension L is the number of
frequencies specified by the FREQ
argument.
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 the FREQ argument. |
Example: 'Weights',ones(N,M)
Data Types: double
SteerAngle
— Subarray steering angle
[0;0]
(default) | scalar | 2-element column vector
Subarray steering angle, specified as the comma-separated pair
consisting of 'SteerAngle'
and a scalar or a 2-by-1
column vector.
If 'SteerAngle'
is a 2-by-1 column vector,
it has the form [azimuth; elevation]
. The azimuth
angle must be between –180° and 180°, inclusive.
The elevation angle must be between –90° and 90°,
inclusive.
If 'SteerAngle'
is a scalar, it specifies
the azimuth angle only. In this case, the elevation angle is assumed
to be 0.
This option applies only when the 'SubarraySteering'
property
of the System object is set to 'Phase'
or 'Time'
.
Example: 'SteerAngle',[20;30]
Data Types: double
ElementWeights
— Weights applied to elements within subarray
1
(default) | complex-valued NSE-by-N
matrix
Subarray element weights, specified as complex-valued NSE-by-N matrix. Weights are applied to the individual elements within a subarray. All subarrays have the same dimensions and sizes. NSE is the number of elements in each subarray and N is the number of subarrays. Each column of the matrix specifies the weights for the corresponding subarray.
Dependencies
To enable this name-value pair, set the SubarraySteering
property of the array to 'Custom'
.
Data Types: double
Complex Number Support: Yes
Output Arguments
D
— Directivity
M-by-L matrix
Examples
Directivity of Replicated Subarray
Compute the directivity of an array built up from ULA subarrays. Determine the directivity of the replicated subarray when the array is steered to towards 30 degrees azimuth.
Set the signal propagation speed to the speed of light. Set the signal frequency to 300 MHz.
c = physconst('LightSpeed');
fc = 3e8;
lambda = c/fc;
Create a 4-element ULA of isotropic antenna elements spaced 0.4-wavelength apart.
myArray = phased.ULA; myArray.NumElements = 4; myArray.ElementSpacing = 0.4*lambda;
Construct a 2-by-1 replicated subarray.
myRepArray = phased.ReplicatedSubarray; myRepArray.Subarray = myArray; myRepArray.Layout = 'Rectangular'; myRepArray.GridSize = [2 1]; myRepArray.GridSpacing = 'Auto'; myRepArray.SubarraySteering = 'Time';
Steer the array to 30 degrees azimuth and zero degrees elevation.
ang = [30;0]; mySV = phased.SteeringVector; mySV.SensorArray = myRepArray; mySV.PropagationSpeed = c;
Find the directivity at 30 degrees azimuth.
d = directivity(myRepArray,fc,ang,... 'PropagationSpeed',c,... 'Weights',step(mySV,fc,ang),... 'SteerAngle',ang)
d = 7.4776
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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