Transmitter power from field strength calculations.

[dspxscott]

Hi Guys.

I'm looking for the formula to work out a required transmitter RF output power (into a dipole - or other known gain antenna) to achieve a certain field strength at a given distance.

For example, what would the power in watts be if a recieved signal of 1mV/M at 10 metres was required.

Thanks in advance.

Regards
Scott

 

[Play Freebird]

Scott,

The following should work if you convert the units. The FCC accepts this equation for free-space FM contour exhibits.

E = 106.92 - 20 LOG(D) + ERP

Where
E = FREE-SPACE FIELD IN (DBU)
D = DISTANCE (KM)
ERP = ERP IN (DBK)

 

[rfry]

In the case of the power needed at the feedpoint of a matched, center-fed, linear, 1/2-wave dipole, a simpler equation is:

P = (E*D)^2 / 49.2

where

E = Maximum Free-Space Field Intensity, V/m
P = Power, watts
D = Distance, meters

The answer applying to the example question is about 2 microwatts (0.000 002 watts).

Note this is the maximum value of field intensity from the dipole at a given path distance in free space. The "received signal" at the terminals of the receiving antenna will depend on its gain and physical orientation.

RF

 

[dspxscott]

Thanks Guys.

 

[rfry]

RE: P = (E*D)^2 / 49.2

Just to note that this equation is accurate only for the radiated far-field of the transmit antenna, which becomes dominant at a radius of 1/(2*pi) wavelengths from the radiation center. The electric field intensity nearer to the radiator than that is higher than calculated by this equation.

So in this case where the distance to the field intensity of interest is only 10 meters, the applied frequency would need to be higher than about 4.78 MHz in order for the equation to be approximately accurate.

For practical purposes the equation gives an accurate solution for distances >1 wavelength from the radiation center.
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