Profit of antenna

Calculation

The profit of an antenna is calculated by taking for reference a isotropic Radiator, i.e. an antenna which radiates uniformly in all the directions. The profit of this antenna is thus 1, or 0dBi (for decibels isotropic). This reference is universal, it exists nevertheless another reference, nearer to reality, the dipolar Antenne. The profit will then be expressed in dBd (decibels dipolar). A profit in dBd is of 2.15 + the profit in dBi.

Concerning the directing antennas, there exists an empirical law to estimate the profit of an antenna according to its directivity:

$G = 10.log \ left (\ frac {41000} {\ theta_a. \ theta_e} \ right)$

G represents the estimated Profit of the antenna in dBi
$\ theta_a$ is the aperture -3dB of the antenna in Azimut (in degrees)
$\ theta_e$ is the aperture -3dB of the antenna in rise (in degrees)
This estimate is valid only for angles lower than 90 degrees and for antennas whose principal lobe is distinguished clearly from the secondary lobes.

The parabola S standards for the Satellite television, around 12,5 GHz, (between bracket profit with 2,4 GHz) and for a usual output of 70%, (45%) bring:

60 cm: 36 dB (20,5 dB)
80 cm: 38,5 dB (22,5 dB)
90 cm: 39,5 dB (23,5 dB)
120 cm: 42 dB (26,5 dB)

Theoretical basic rules:

Each time the diameter is doubled, the profit is of 6 dB
Each time one adds 12,24% to the preceding diameter + 1 dB.

These rules are as well valid for the Wi-Fi and the ISM and them bands Radioamateur S.

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