Equivalent isotropically radiated power

In radio communication systems, Equivalent isotropically radiated power (EIRP) or, alternatively, Effective isotropically radiated power[1] is the amount of power that a theoretical isotropic antenna (which evenly distributes power in all directions) would emit to produce the peak power density observed in the direction of maximum antenna gain. EIRP can take into account the losses in transmission line and connectors and includes the gain of the antenna. The EIRP is often stated in terms of decibels over a reference power emitted by an isotropic radiator with an equivalent signal strength. The EIRP allows comparisons between different emitters regardless of type, size or form. From the EIRP, and with knowledge of a real antenna's gain, it is possible to calculate real power and field strength values.

EIRP = P_T - \ L_c + G_a

where EIRP and PT (power of transmitter) are in dBm, cable losses (Lc) is in dB, and antenna gain (Ga) is expressed in dBi, relative to a (theoretical) isotropic reference antenna.

This example uses dBm, although it is also common to see dBW.

Decibels are a convenient way to express the ratio between two quantities. dBm uses a reference of 1 mW and dBW uses a reference of 1 W.

\text{dBm} = 10 \log \left(power \ out / 1\,\mathrm{mW} \right )

and

\text{dBW} = 10 \log \left( power \ out / 1\,\mathrm{W} \right)

A transmitter with a 50W output can be expressed as a 17dBW output or 47dBm.

16.9897\,\mathrm{dBW} = 10 \log \left( 50\,\mathrm{W} / 1\,\mathrm{W} \right)

The EIRP is used to estimate the service area of the transmitter, and to co-ordinate transmitters on the same frequency so that their coverage areas do not overlap.

In built-up areas, regulations may restrict the EIRP of a transmitter to prevent exposure of personnel to high power electromagnetic fields however EIRP is normally restricted to minimise interference to services on similar frequencies

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