# Formula for Field Strength

According to this document on page 3, the formula for Field strength is stated as follows: I can't find reference to this formula elsewhere and was wondering if someone can verify this is correct, in particular where the value of 30 comes from. Thanks.

• The $30$ comes from the impedance of free space, $120\pi$, divided by the area of a sphere, $4\pi r^2$ – tomnexus Feb 6 '17 at 6:31

The formula the document states is what is called the far field strength of an antenna. The formula is correct. There are plenty of resources on line to check it.

For example:

http://www.zen22142.zen.co.uk/Theory/antenna.htm

Imagine a sphere radius $$\r\$$.

At its centre is an antenna with gain $$\G\$$ that radiates equally in all directions (isotropic).

Transmitter is fed with $$\P \$$ watts.

At any point on surface of sphere, power density $$\P_d = {{P.G} \over {4 \pi r^2}} \space \bigg[ {W \over m^2} \bigg]\$$

Free space impedance $$\Z_0 = {E \over H} = 120 \pi \space [\Omega]\$$

Therefore $$\H = {E \over {120\pi}}\$$ and $$\E = {120\pi H}\$$

$$\P_d = EH = E({E \over {120\pi}}) = {E^2 \over {120 \pi}} \space \bigg[ {W \over m^2} \bigg]\$$

So, $$\{P.G \over {4 \pi r^2}} = {E^2 \over {120 \pi}}\$$

Hence, $$\P = {{4 \pi r^2}E^2 \over {120 \pi}} = {E^2 r^2 \over {30 G}} \space [W]\$$