System object: phased.URA
Directivity of uniform rectangular array
D = directivity(H,FREQ,ANGLE)
D = directivity(H,FREQ,ANGLE,Name,Value)
D = directivity( computes
the Directivity of a uniform rectangular
array (URA) of antenna or microphone elements,
at frequencies specified by the
FREQ and in angles
of direction specified by the
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— Uniform rectangular array
Uniform rectangular array specified as a
H = phased.URA
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
Compute the directivity of two uniform rectangular arrays (URA). The first array consists of isotropic antenna elements. The second array consists of cosine antenna elements. In addition, compute the directivity of the first array steered to a specific direction.
Array of isotropic antenna elements
First, create a 10-by-10-element URA of isotropic antenna elements spaced one-quarter wavelength apart. Set the signal frequency to 800 MHz.
c = physconst('LightSpeed'); fc = 3e8; lambda = c/fc; myAntIso = phased.IsotropicAntennaElement; myArray1 = phased.URA; myArray1.Element = myAntIso; myArray1.Size = [10,10]; myArray1.ElementSpacing = [lambda*0.25,lambda*0.25]; ang = [0;0]; d = directivity(myArray1,fc,ang,'PropagationSpeed',c)
d = 15.7753
Array of cosine antenna elements
Next, create a 10-by-10-element URA of cosine antenna elements also spaced one-quarter wavelength apart.
myAntCos = phased.CosineAntennaElement('CosinePower',[1.8,1.8]); myArray2 = phased.URA; myArray2.Element = myAntCos; myArray2.Size = [10,10]; myArray2.ElementSpacing = [lambda*0.25,lambda*0.25]; ang = [0;0]; d = directivity(myArray2,fc,ang,'PropagationSpeed',c)
d = 19.7295
The directivity is increased due to the directivity of the cosine antenna elements.
Steered array of isotropic antenna elements
Finally, steer the isotropic antenna array to 30 degrees in azimuth and examine the directivity at the steered angle.
ang = [30;0]; w = steervec(getElementPosition(myArray1)/lambda,ang); d = directivity(myArray1,fc,ang,'PropagationSpeed',c,... 'Weights',w)
d = 15.3309
The directivity is maximum in the steered direction and equals the directivity of the unsteered array at boresight.
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.
Computing directivity requires integrating the far-field transmitted radiant intensity over all directions in space to obtain the total transmitted power. There is a difference between how that integration is performed when Antenna Toolbox™ antennas are used in a phased array and when Phased Array System Toolbox antennas are used. When an array contains Antenna Toolbox antennas, the directivity computation is performed using a triangular mesh created from 500 regularly spaced points over a sphere. For Phased Array System Toolbox antennas, the integration uses a uniform rectangular mesh of points spaced 1° apart in azimuth and elevation over a sphere. There may be significant differences in computed directivity, especially for large arrays.