An alternate parameter that measures the same thing is effective (or equivalent) radiated power (ERP). Effective radiated power is the total power that would have to be radiated by a half-wave dipole antenna to give the same signal strength as the actual source in the direction of the antenna's strongest beam. The difference between ERP and EIRP is that ERP is the ratio of actual signal strength to that of a half-wave dipole antenna, while EIRP is the ratio to that of an isotropic antenna. Since a half-wave dipole antenna has a gain of 1.64, or 2.15 decibels compared to an isotropic radiator, if ERP and EIRP are expressed in watts their relation is

${\displaystyle \mathrm {ERP} =\mathrm {EIRP} /1.64}$

If they are expressed in decibels

${\displaystyle \mathrm {ERP} _{\text{dB}}=\mathrm {EIRP} _{\text{dB}}-2.15}$

## Antenna gain and directivity

Antenna gain (or simply gain) is closely related to directivity (the term directive gain is deprecated by IEEE) and often incorrectly used interchangeably. However, antenna gain is always less than directivity by a factor called radiation efficiency, η. Whereas directivity is entirely a function of wavelength and the geometry and type of antenna, gain takes into account the losses that always occur in the real world. Specifically, accelerating charge (time-varying current) causes electromagnetic radiation per Maxwell's equations. Therefore, antennas use a current distribution on radiating elements to generate electromagnetic energy that propagates away from the antenna. This coupling is never 100% efficient (by Laws of Thermodynamics), and therefore gain will always be less than directivity by this efficiency factor.

An ideal isotropic radiator is a theoretical device that cannot actually exist but that provides a mathematical construct for a common baseline of comparison. Isotropic radiation is at identical power in all directions spherically from the isotropic source. In other words, a notional receiver in a given direction from the transmitter would receive the same power if the source were replaced with an isotropic source and with an antenna input power equal to the EIRP. The receiver would not be able to determine a difference.

A Yagi-Uda antenna's maximum directivity is 10.92 dBi. Its gain necessarily must be less than this by the factor η, which must be negative in units of dB. EIRP cannot be calculated without knowledge of the power accepted by the antenna, i.e., it is not correct to use units of dBi with EIRP. Let us assume a 100 Watt (20 dBW) transmitter with losses of 6 dB prior to the antenna. EIRP < 24.92dBW, less than ideal by η in dB. Let us now assume that the receiver is in the first side-lobe of the transmitting antenna, and EIRP is further reduced by 7.2 dB, which is the decrease in directivity from the main to side-lobe of the Yagi-Uda. Therefore, anywhere along the side-lobe direction from this transmitter, a blind receiver could not tell the difference if the Yagi-Uda was replaced with an isotropic radiator with antenna input power increased by 1.57 dB.[1]

## Polarization

EIRP assumes that the radiated power is also of uniformly distributed polarization.[citation needed] If a receiver is capable of dual polarization receive, then it will theoretically capture all of the available energy (less the radiation efficiency factor) impacting its aperture. If, however, the receiver is only single polarization, then it will necessarily lose at least an additional 3 dB. This polarization loss is not accounted for in the calculation of EIRP. Rather, the receiving system designer must account for this loss as appropriate.