Antenna gain calculation formula

Antenna gain refers to the ratio of the power density of the signal generated by the actual antenna and the ideal radiating unit at the same point in space under the condition of equal input power. It quantitatively describes the degree to which an antenna radiates the input power. The gain is obviously closely related to the antenna pattern. The narrower the main lobe of the pattern and the smaller the side lobe, the higher the gain.

The physical meaning of gain can be understood in this way: to generate a signal of a certain size at a certain point at a certain distance, if an ideal non-directional point source is used as the transmitting antenna, an input power of 100W is required, while when a directional antenna with a gain of G = 13 dB = 20 is used as the transmitting antenna, the input power is only 100 / 20 = 5W. In other words, the gain of an antenna, in terms of its radiation effect in the maximum radiation direction, is the multiple by which the input power is amplified compared to an ideal non-directional point source.

The gain of a half-wave symmetrical oscillator is G = 2.15dBi. Four half-wave symmetrical oscillators are arranged vertically to form a vertical quaternary array, and its gain is about G = 8.15dBi (dBi means that the comparison object is an ideal point source with uniform radiation in all directions).

If a half-wave symmetrical oscillator is used as the comparison object, the unit of gain is dBd.

The gain of a half-wave symmetrical oscillator is G=0dBd (because it is comparing itself with itself, the ratio is 1, and the logarithm is zero.) The gain of a vertical quaternion array is approximately G=8.15 – 2.15=6dBd.

Several calculation formulas for antenna gain

1) The narrower the antenna main lobe width, the higher the gain. For general antennas, the following formula can be used to estimate their gain:
G (dBi) = 10Lg {32000 / (2θ3dB, E × 2θ3dB, H)}
In the formula, 2θ3dB, E and 2θ3dB, H are the antenna lobe widths on the two main planes respectively;
32000 is the empirical data obtained by statistics.

2) For parabolic antennas, the gain can be approximately calculated using the following formula:
G (dBi) = 10Lg {4.5 × (D/λ0) 2}
where D is the diameter of the parabola;
λ0 is the central operating wavelength;
and 4.5 is statistically derived empirical data.

3) For upright omnidirectional antennas, there is an approximate calculation formula
G (dBi) = 10Lg{2L/λ0}
, where L is the antenna length;
λ0 is the central operating wavelength;