# Converting From mV/m To Decayed mW (ERP)

I've seen the different conversions for mW, mV, mV/m, dBm, mostly based on 50 ohms. What I'm interested in is converting a given field strength mV/m, at a
given distance for a particular frequency, to the equivalent (decayed) baseline wattage. For instance, in section 73.318, the FCC defines the FM blanket overload boundary as 562 mV/m (115 dBu), having a distance equalling .394 * KW^.5 (ERP), where (I believe) ".394" is supposed to be 50000^.5/562. So, assuming flat terrain with "raw reception" (meaning no antenna and line gain/loss), what would the equivalent ERP wattage be (i.e., if you took a field strength meter and held it next to a transmitter, what would the wattage be to produce 562 mV/m?)? Since wattge can be found from mV/m, what would the equation for decayed wattage (mW_d) be, given an ERP (KW_erp), frequency (MHz) and distance (Km)? Instead of 50, should 2*Pi*60 Hz (~=~ 377) be used for ohms?
~Kaimbridge~
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"Kaimbridge" wrote:

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The radiated power needed to generate a given, free-space field strength of course depends on the length of the propagation path to that value of field strength.
Re-arranging the FCC equation to solve for the radiated power needed to generate 562 mV/m when distance in kilometers is known gives
P = D^2/0.1552
So if there is a need to limit the field strength to 562 mV/m at a location 1 km from the antenna, we see that ERP cannot exceed ~6.44 kW.
Another way of doing it is to massage this "classic" equation.
Field Strength in dB above 1 microvolt/meter 104.77 + ERPi - 20 log (D)
where ERPi = Effective Radiated Power in dB referenced to 1kW from an isotropic radiator D = Distance in kilometers
It gives the same answer as the simpler equation above.
I think this will answer your question, if I understood it right.
RF
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