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# How to calculate Antenna's Gain

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##### Newbie level 5
Antenna Gain Calculation

Hi, I need to calculate the Radiation Pattern of an antenna. I got S21 Mag and Ang data of the antenna from VNA by measuring the AUT with a standard horn.
Now, how do I calculate the gain of Antenna.What are the conversions of S21 Mag and Ang in dB. How to calculate the gain?
Can someone please write the formulas?

Antenna Gain Calculation

Unless you don't know the exact antenna factor of the horn antenna, you have to use a reference antenna (preferably a dipole) in place of the AUT to determmine the gain.

Points: 2
Re: Antenna Gain Calculation

I know the gain of the horn it is 12 dB

Re: Antenna Gain Calculation

ATUgain = S21magn - αf - RecvAntgain

S21magn in dB
αf is the free space attenuation 10*log((4 pi r)²/λ²)
Both antenna gains are isotrope not dipole referenced values

Points: 2
Re: Antenna Gain Calculation

Hello,

The common way to measure antenna gain is by the Gain transfer method:

1. Place a Calibration antenna againts an arbitrary Transmission antenna, direct them both and measure S21(cal).
2. Replace the Calibration antenna with your tested antenna, direct again and measure S21(test).
3. Using the following measurements and the known calibration antenna gain you can easily derive the antenna gain:
Gain(test)=S21(test)-S21(Cal)+G(Cal)

Meaning: The difference of S21 terms gives us the gain difference of the antennas and when added to the know calibration gain yield the wanted result.

*Make sure that the antennas are in Far-Field - meaning that the distance is larger than D^2/lamda, otherwise you will get an error !
* D=antenna longest dimension
* lamda=wave length

If you want to get high precision make sure you conduct this in a suitable antenna range such as an unechoic chamber, use a Calibration antenna that has a gain which is relatively close to your tested antenna (i can elaborate more for better precision).

If all you have is the data that you presented, you can use the equation that was presented in the last reply, but you need the correct distance between the centers of phase of the antennas. Keep in mind that for a horn it's not necessary on the boundary.
*If the range is very large you can neglct this correction and measure from the boundary.

Good luck !

Heylal

Points: 2
Antenna Gain Calculation

You're well illustrating, why I previously asked for the horns's exact antenna factor and also suggested to use a reference antenna.
Seriously, you can't expect much more than 3-6 dB accuracy.

Points: 2
Re: Antenna Gain Calculation

I got the values of S21 Mag in the order of 1E-3 and S21 Ang as say -170 i.e.
S21 Mag: 1E-3 and S21 Ang : -170.
Now do I have to covert the Ang to phase in rad? or how else will I get the dB?

or do I just have to take the S21 Mag raw value 1E-3 in the eqn for gain calculation?

Antenna Gain Calculation

S21db = 20 log (S21mag)

Re: Antenna Gain Calculation

Hi there,

You got the right answer from FvM, there is no need whatsoever for the phase in this case.

Heylal