System object: phased.ReplicatedSubarray
Directivity of replicated subarray
D = directivity(H,FREQ,ANGLE)
D = directivity(H,FREQ,ANGLE,Name,Value)
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.
H— Replicated subarray
Replicated subarray, specified as a
phased.ReplicatedSubarray System object.
H = phased.ReplicatedSubarray;
comma-separated pairs of
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
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.
To enable this name-value pair, set the
SubarraySteering property of the array to
Complex Number Support: Yes
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
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.