Equivalent isotropically radiated power

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Equivalent isotropically radiated power (EIRP), or synonymous Effective Isotropically Radiated Power, is an IEEE standardized definition of directional radio frequency (RF) power, in terms of the power that would be required to transmit a signal equally in all directions, from a strictly theoretical spherically radiating source. It is the total power that a distant receiver in the beam of the antenna's strongest signal would conclude was being radiated in all directions, knowing the distance to the transmitting antenna but not that the signal was directional.

EIRP is differentiated from effective (or equivalent) radiated power (ERP) by use of absolute antenna gain in the calculation instead of relative antenna gain. The term "gain" is assumed to mean "antenna gain" and also "absolute" (referenced to isotropic) unless specifically stated to be relative. The gain is then multiplied by the power actually accepted by the antenna to result in the actual EIRP. Power losses which occur prior to the antenna, e.g., in the transmission line or from inefficiency in the generator itself are therefore not included in the calculation.[1]

Antenna gain and directivity[edit]

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.

Isotropic radiator[edit]

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.[2]


EIRP assumes that the radiated power is also of uniformly distributed polarization. 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.

See also[edit]


  1. ^ "IEEE Std 145-2013". IEEE. 11 December 2013. 
  2. ^ Cheng, David K. (1992). Field and Wave Electromagnetics, 2nd Ed. Addison-Wesley. pp. 648–650. 
  • Recommendation ITU-R BS.561-2, Definitions of radiation in LF, MF and HF broadcasting bands