System object: phased.ULA
Directivity of uniform linear array
D = directivity(H,FREQ,ANGLE)
D = directivity(H,FREQ,ANGLE,Name,Value)
D = directivity( computes
the Directivity (dBi) of a uniform linear
array (ULA) of antenna or microphone elements,
at frequencies specified by
FREQ and in angles
of direction specified by
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 linear array
Uniform linear array specified as a
H = phased.ULA;
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 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, calculated the directivities for a set of seven different azimuth directions all at zero degrees elevation. Set the frequency to 800 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 = 3e8; 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 -297.5224 -13.9783 -9.5713 -6.9897 -4.5787 -2.0536 10.0000
The directivity is greatest in the steered direction.
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.