System object: phased.ReplicatedSubarray
Package: phased
Directivity of replicated subarray
D = directivity(H,FREQ,ANGLE)
D = directivity(H,FREQ,ANGLE,Name,Value)
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.
H — Replicated subarrayReplicated subarray, specified as a phased.ReplicatedSubarray System object.
Example: H = phased.ReplicatedSubarray;
FREQ — Frequency for computing directivity and patternsFrequencies 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 directivityAngles 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
Specify optional
comma-separated pairs of Name,Value arguments. Name is
the argument name and Value is the corresponding value.
Name must appear inside quotes. You can specify several name and value
pair arguments in any order as
Name1,Value1,...,NameN,ValueN.
'PropagationSpeed' — Signal propagation speedSignal 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 weightsSubarray 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 vectorSubarray 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 subarray1 (default) | complex-valued NSE-by-N
matrixSubarray 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.
To enable this name-value pair, set the SubarraySteering property of the array to 'Custom'.
Data Types: double
Complex Number Support: Yes
D — DirectivityCompute 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
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.
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