[BC] RF field intensity at a transmitter site

[RichardBJohnson at comcast.net]

For those so inclined...

The equation used in my response to the 10 kW transmitter site's near field RF magnitude is the standard used worldwide for assessment of environmental hazards.

http://www.besjournal.com/freeArticles/pastIssues/2006/No5/200704/P02007042670115238580119200619514495.pdf

the equation, repeated here is:
E  =  300 / r * sqrt(P * G * A)

P is the transmitter power in kW
G is the antenna gain (relative to a Hertz dipole (a dipole with no physical size).
A is the attenuation due to ground decay factor.
r is the distance to the source.

This is an ideal equation for dealing with transmitter sites because it relates to a small radiator over a perfectly-reflecting ground, quite adequate for a radiating tower over a ground-system.

There was a response from one reader that it was not correct and that it seemed to be derived from some incidental field intensity measured somewhere.

This is not correct. It is in fact exact because it is a definition. It is derived from elemental electrostatic theory.

A thumb-nail derivation follows:

A force at a distance varies inversely with the distance and directly with the velocity of the thing producing that force. In this case, the velocity is the speed of a radio wave (nearly the speed of light) and the force is the electromotive force (EMF) produced by its passage through a plane called the Poynting vector).

http://en.wikipedia.org/wiki/Poynting_vector

For MW frequencies the actual frequency has little effect as long as the wavelengths are long enough so the radiator seems "small." Larger radiators need to use trigonometry to sum the multiple voltages and their phases from different vectors. That is why some of the published equations are so complicated.

By proper selection of numerical values, the electromotive force may have the dimension of volts per meter and the power in kilowatts. That is what the 300 in the equation means. It is probably really 299.792458,  rounded up, because 'c' is 299,792,458 meters per second, however I leave its exact meaning for research to those so inclined (something professor Don Howe used to say).

By adjusting the values of G and A, one can calculate the expected field intensity from a single radiator at a distance. Leaving them at 1, gives a good approximation of the field at short distances, i.e., the transmitter site.

Cheers,
Richard B. Johnson
Book: http://www.AbominableFirebug.com/