Well, let's see. We can start with an isotropic antenna, which
distributes its power equally in all directions. I did that one three
days ago on this newsgroup, in the thread "Theoretical antenna
question". The result is that the power density from an isotropic source
at any distance r is

PD = P / (4 * pi * r^2)

where P is the total power radiated. Power density PD will be in
watts/square meter if P is in watts and r is in meters.

In the far field, the field strength E from any antenna is sqrt(PD *
Z0), where Z0 is the impedance of free space, very nearly 120 * pi ohms.
E is in volts/meter if PD is watts/meter^2 and Z0 is in ohms.
Substituting in the first equation gives

E = sqrt[(P * Z0) / (4 * pi * r^2)] ~ sqrt(30 * P) / r

So that's the field strength from an isotropic source. In free space,
the power density from a dipole in its most favorable direction is 1.64
times the power density from an isotropic source at the same distance.
This is the dipole's directivity which, if it's lossless, is the same as
the gain (2.15 dBi). You can find this derivation in nearly any antenna
text. So the field from a free-space dipole in its best direction is

E = sqrt(1.64 * 30 * P) / r = 7.01 * sqrt(P) / r

Roy Lewallen, W7EL

Dr. Slick wrote:
Hi Folks,

Someone once mentioned the following to me:


"You can calculate field strength from power and distance according to
this formula I found in an old broadcast engineering handbook...

e = 7 * sqrt(P) / d

where e = field strength in volts/meter, d = distance in meters, P =
power in watts. Antenna is assumed to be 1/2 wave dipole."


I'd like to know exactly how this simple formula was derived.

Any info greatly appreciated.


Thanks,

Slick