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# Antenna Gain Calculator

Top
Antenna gain online physics calculator used to determine the gain of an antenna if the efficiency of the same is provided. The gain is directly proportional to the efficiency. So the formula is given as,
$G_{dbi}$ = 10$\log _{10}$$(\frac{\eta 4\pi A}{\lambda ^{2}}) Where, G_{dbi} = antenna gain, \eta = efficiency, A = area of the aperture, \lambda = wavelength. ## Steps Back to Top Step 1 : Write down the parameters which is given in the question. Step 2 : Substitute these values in the given formula G_{dbi} = 10\log _{10}$$(\frac{\eta 4\pi A}{\lambda ^{2}})$

and find out the value of unknown parameter.

## Problems

Some problems related to antenna gain is discussed below.

### Solved Examples

Question 1: Find out the antenna gain if the efficiency of the antenna is 60% and the area of the aperture is 15m2 and the wavelength of the signal is 400nm.

Solution:

From the question it is given that,
$\eta$ = 60%,
A = 15m2,
$\lambda$ = 400nm = 400$\times10^{-9}$m

Gain of an antenna is,

$G_{dbi}$ = 10$\log _{10}$$(\frac{\eta 4\pi A}{\lambda ^{2}}) G_{dbi} = 10\log _{10}$$(\frac{60\times 4\times3.14\times15}{(400\times10^{-9}) ^{2}})$

$G_{dbi}$ = 10$\log _{10}(7065\times10^{13})$ = 168.4911db

Question 2: Determine the gain of the antenna if the efficiency of the antenna is 50% and area of the aperture is 30m2 and the wavelength of the signal is 640nm.

Solution:

From the question it is given that,
$\eta$ = 50%,
A = 30m2,
$\lambda$ = 640nm = 640$\times10^{-9}$m

Gain of an antenna is,

$G_{dbi}$ = 10$\log _{10}$$(\frac{\eta 4\pi A}{\lambda ^{2}}) G_{dbi} = 10\log _{10}$$(\frac{50\times 4\times3.14\times30}{(640\times10^{-9}) ^{2}})$

$G_{dbi}$ = 10$\log _{10}(4599.609375\times10^{13})$ = 166.627db