#  Radar Basics Sisotrop
SAntenna

Figure 1: Illustration of the definition of the computed quantity EIRP. Sisotrop
SAntenna

Figure 1: Illustration of the definition of the computed quantity EIRP.

Effective radiated power (or equivalent radiated power) is a computational quantity defined by IEEE that is used to describe a directional high-frequency power. The equivalent radiated power is the combination of the power generated by the transmitter and the ability of the antenna to concentrate that power in a particular direction.

It is the total power in watts that would have to be radiated by a reference antenna radiating uniformly all around to achieve the same radiation intensity S (signal strength or power flux density in watts per square meter) as the actual, practical antenna at a remote receiver located in the direction of the main lobe of that antenna. It is equal to the input power to the antenna multiplied by the gain of the antenna. An equivalent radiated power is not directly measurable. It must be calculated from the measurable quantity of power generated in the transmitter using known (or separately measured) quantities.

If an omnidirectional isotropic radiator is used as a reference for antenna gain GA, the equivalent isotropic radiated power is abbreviated and referred to as EIRP. When a dipole is used as a reference, the letter “i” is omitted from the abbreviation and becomes ERP (EIRP = 1.64·ERP). When measuring the transmit power at the transmitter PT, the losses L in the feed line to the antenna must also be taken into account.

 EIRP = PT + GA - L where PT = transmitter's power in [dBm] or [dBW] GA = antenna gain in [dBi] L = Losses in [dB] (1)

The equivalent radiated power is used in electronics and telecommunications to quantify the apparent power of a transmitter that is perceived in the receiving area as either a useful signal or interference. It is most often used to specify in a frequency usage plan by regulatory authorities a maximum allowable transmit power that may be used in a frequency range to minimize mutual interference.

##### Representation as integral

The EIRP can be represented as an integral of the power radiated in different directions in the entire radiation range:  (2)

where P(θ,φ) is the power radiated by an antenna at the azimuth (θ) and elevation (φ) angles of the main lobe. Here, this power is P(θ,φ) = PTxGi(θ,φ) with PTx as the conducted power (in watts) at the base of the antenna and Gi(θ,φ) the gain of the antenna in this main (θ,φ) direction. The integrals distribute this power value over the entire half-space above the antenna.