System object: phased.IsotropicProjector
Directivity of isotropic projector
D = directivity(projector,FREQ,ANGLE)
Compute the directivity of an isotropic projector in different directions. Assume the signal frequency is 3 kHz. First, set the projector parameters.
fc = 3e3; projector = phased.IsotropicProjector('FrequencyRange',[1,10]*1e3, ... 'VoltageResponse',[100,110,120,110,100]); patternElevation(projector,fc,45)
Select the angles of interest to be constant elevation angle at zero degrees. The five azimuth angles are centered around boresight (zero degrees azimuth and zero degrees elevation).
ang = [-20,-10,0,10,20; 0,0,0,0,0];
Compute the directivity along the constant elevation cut.
d = directivity(projector,fc,ang)
d = 5×1 0 0 0 0 0
The directivity of an isotropic projector is zero in every 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.