# Antenna Factor unit and calculation

The antenna factor equation in a 50-ohm system is expressed as:

$$AF={9.73 \over \lambda*\sqrt(Gain)}$$

Where Gain is in dB, the wavelength in meter and the calculated AF is in dB/m.  First, How the unit of the calculated AF is in dB/m? 

Second, there is also another shape of the antenna factor formula where:

$$AF={20*log({9.73 \over \lambda*\sqrt(Gain)})}$$

Where Gain is in numeric form and the AF is in dB/m.

May I ask for some help about deriving this equation? 

In case of a negative gain (in dB), I converted it to a numeric form knowing:

$$Gain (dB)={10*log(Gain(num))}$$



and then used the second formula. Is it ok to do so?



Last, How it is possible to convert dB/m to 1/m.

Is it Ok to use this general formula?

$$AF(db/m)={10*logAF(1/m)}?$$

Thanks.

• Is there a reference for where the expressions come from? The context would probably be helpful in crafting an explanation. Commented Jan 7 at 1:11

Wikipedia has an article on "Antenna Factor"

defined as the ratio of Efield to Impressed voltage (on the antenna feed).

The derivation is shown there.

• Thanks. but what I'm looking for the derivation of the second formula where the Gain is in numeric form. Commented Aug 5, 2020 at 15:30