Watts are the units used to describe the amount of power generated by a transmitters. Microvolts per meter (uV/m) are the units used to describe the strength of an electric field created by the operation of a transmitter.

A particular transmitter that generates a constant level of power (Watts) can produce electric fields of different strengths (uV/m) depending on, among other things, the type of transmission line and antenna connected to it. Because it is the electric field that causes interference to authorized radio communications, and since a particular electric field strength does not directly correspond to a particular level of transmitter power, the emission limits of e.g. short range devices and broadcasting transmitters are specified in field strength.

Although the precise relation between power and field strength can depend on a number of additional factors, commonly-used equation to approximate their relationship is

((1)PG)/(4d^{2}) = (E^{2})/(120)

where *P* is transmitter power in Watts, *G* is the numerical gain of the transmitting antenna
relative to an isotropic source, *d* is the distance of the measuring point from the
electrical center of the antenna in meters, and *E* is the field strength in Volts/meter.

4*d ^{2}*
is the surface area of the sphere centered at the radiating source whose surface is

120 is the characteristic impedance of free space in Ohms.

Using this equation, and assuming a unity gain antenna (*G* = 1) and a measurement distance
of 3 meters (*d* = 3), a formula for determining power given field strength can be
developed:

(2)P= 0.3E^{2}

where *P* is the transmitter power (EIRP) in Watts and *E* is the field strength in
Volts/meter.

From this explanation the following simple expression relates power flux-density in dB(W/m^{2})
with field strength in dB(uV/m):

=E(3)(S + 145.8)

where *E* is field strength in dB(uV/m) and *S* is power flux-density in dB(W/m^{2})

** Note:** free-space propagation is assumed

Electromagnetic fields can be sub-divided into two components: the electric field E
[measured in V/m] and the magnetic field H [measured in A/m]. The E-field and the H-field are
mathematically interdependent in the far-field, that means only one component has to be measured.

For example, in free space if the H-field is measured in this region, it can be used to calculate
the magnitude of the E-field and power density S [W/m^{2}]:

Consequential, the relation between dB(uV/m) and dB(uA/m) is as follows:

, (4)E=HxZ

(5)S=Hx^{2}Z, knowing Z_{0}_{0}= 377Omega

(6)x dB(uV/m) = (x - 51.5) dB(uA/m)

The field strength emission limits are converted to an e.i.r.p. level in dBm using the following equation:

(7)E.I.R.P. = E_{0}+ 20 log_{10}D – 104.8

taken from section 2 of the NTIA document Assessment of Compatibility between Ultrawideband Devices and selected Federal systems, NTIA Special Publication 01-43, where

*E.I.R.P.* = e.i.r.p. corresponding with the electric field strength E_{0} (in dBm)

*E _{0}* = electric field strength (in dB(uV/m))

** Note:** free-space propagation is assumed

(8)E = P_{t}- 20 log_{10}D + 74.8

** Note:** free-space propagation is assumed

The isotropically received power and the field strength are related with each other as follows:

(9)P_{r}= E - 20 log_{10}f – 167.2

** Note:** free-space propagation is assumed

When the power flux density, *pfd*, is given in dB(W/m^{2}) and the e.i.r.p., *e*, in dBm, the relation between
these can be derived from relations (3) and (7) as

(10)e = S + 20 log_{10}D + 41

where

*e* = e.i.r.p. (dBm)

*S* = power flux density (dB(W/m^{2})

*D* = reference measurement distance (m)

** Note:** free-space propagation is assumed

The free-space basic transmission loss, the isotropically transmitted power and electric field strength are related with each other as follows:

(11)L_{bf}= P_{t}- E + 20 log_{10}f + 167.2

where

*L _{bf}* = free-space basic transmission loss (dB)

** Note:** free-space propagation is assumed

Last modified: September 11, 2006