# 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 $\scriptstyle EIRP$ and $\scriptstyle P_T$ (output power of transmitter) are in dBm, cable losses ($\scriptstyle L_c$) is in dB, and antenna gain ($\scriptstyle G_a$) 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.

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

and

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

A transmission output of 50 W is the same as 17 dBW or 47 dBm.

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

The EIRP is used to estimate the service area of the transmitter, and to coordinate 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.

The Arecibo Planetary Radar transmits up to 1 MW (60 dBW) of power with an antenna gain of about 73.3 dB at 12.6 cm wavelength, resulting in an EIRP of roughly 133 dBW (20 TW).