Effective radiated power

Effective radiated power (ERP), synonymous with equivalent radiated power, is an IEEE standardized definition of directional radio frequency (RF) power, such as that emitted by a radio transmitter. It is the total power in watts that would have to be radiated by a half-wave dipole antenna to give the same radiation intensity (signal strength or power flux density in watts per square meter) as the actual source antenna at a distant receiver located in the direction of the antenna's strongest beam (main lobe). ERP measures the combination of the power emitted by the transmitter and the ability of the antenna to direct that power in a given direction. It is equal to the input power to the antenna multiplied by the gain of the antenna. It is used in electronics and telecommunications, particularly in broadcasting to quantify the apparent power of a broadcasting station experienced by listeners in its reception area.

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

Isotropic gain is the ratio of the power density $S_{\text{max}}$ (signal strength in watts per square meter) received at a point far from the antenna (in the ) in the direction of its maximum radiation (main lobe), to the power $S_{\text{max,iso}}$ received at the same point from a hypothetical lossless isotropic antenna, which radiates equal power in all directions
$\mathrm {G} _{\text{i}}={S_{\text{max}} \over S_{\text{max,iso}}}$ Gain is often expressed in logarithmic units of decibels (dB). The decibel gain relative to an isotropic antenna (dBi) is given by $\mathrm {G} {\text{(dBi)}}=10\log {S_{\text{max}} \over S_{\text{max,iso}}}$

far field

Dipole gain is the ratio of the power density received from the antenna in the direction of its maximum radiation to the power density $S_{\text{max,dipole}}$ received from a lossless antenna in the direction of its maximum radiation
$\mathrm {G} _{\text{d}}={S_{\text{max}} \over S_{\text{max,dipole}}}$ The decibel gain relative to a dipole (dBd) is given by $\mathrm {G} {\text{(dBd)}}=10\log {S_{\text{max}} \over S_{\text{max,dipole}}}$

half-wave dipole

Effective radiated power and effective isotropic radiated power both measure the power density a radio transmitter and antenna (or other source of electromagnetic waves) radiate in a specific direction: in the direction of maximum signal strength (the "main lobe") of its radiation pattern.^[1]^[2]^[3]^[4] This apparent power is dependent on two factors: the total power output and the radiation pattern of the antenna – how much of that power is radiated in the direction of maximal intensity. The latter factor is quantified by the antenna gain, which is the ratio of the signal strength radiated by an antenna in its direction of maximum radiation to that radiated by a standard antenna. For example, a 1,000-watt transmitter feeding an antenna with a gain of 4 (6 dBi) will have the same signal strength in the direction of its main lobe, and thus the same ERP and EIRP, as a 4,000-watt transmitter feeding an antenna with a gain of 1 (0 dBi). So ERP and EIRP are measures of radiated power that can compare different combinations of transmitters and antennas on an equal basis.

In spite of the names, ERP and EIRP do not measure transmitter power, or total power radiated by the antenna, they are just a measure of signal strength along the main lobe. They give no information about power radiated in other directions, or total power. ERP and EIRP are always greater than the actual total power radiated by the antenna.

The difference between ERP and EIRP is that antenna gain has traditionally been measured in two different units, comparing the antenna to two different standard antennas; an isotropic antenna and a half-wave dipole antenna:

In contrast to an isotropic antenna, the dipole has a "donut-shaped" radiation pattern, its radiated power is maximum in directions perpendicular to the antenna, declining to zero on the antenna axis. Since the radiation of the dipole is concentrated in horizontal directions, the gain of a half-wave dipole is greater than that of an isotropic antenna. The isotropic gain of a half-wave dipole is 1.64, or in decibels 10 log 1.64 = 2.15 dBi, so

The two measures EIRP and ERP are based on the two different standard antennas above:^[1]^[3]^[2]^[4]

Since the two definitions of gain only differ by a constant factor, so do ERP and EIRP

Dipole vs. isotropic radiators[edit]

Because ERP is calculated as antenna gain (in a given direction) as compared with the maximum directivity of a half-wave dipole antenna, it creates a mathematically virtual effective dipole antenna oriented in the direction of the receiver. 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 ideal dipole oriented with maximum directivity and matched polarization towards the receiver and with an antenna input power equal to the ERP. The receiver would not be able to determine a difference. Maximum directivity of an ideal half-wave dipole is a constant, i.e., 0 dBd = 2.15 dBi. Therefore, ERP is always 2.15 dB less than EIRP. The ideal dipole antenna could be further replaced by an isotropic radiator (a purely mathematical device which cannot exist in the real world), and the receiver cannot know the difference so long as the input power is increased by 2.15 dB.

The distinction between dBd and dBi is often left unstated and the reader is sometimes forced to infer which was used. For example, a Yagi–Uda antenna is constructed from several dipoles arranged at precise intervals to create greater energy focusing (directivity) than a simple dipole. Since it is constructed from dipoles, often its antenna gain is expressed in dBd, but listed only as dB. This ambiguity is undesirable with respect to engineering specifications. A Yagi–Uda antenna's maximum directivity is 8.77 dBd = 10.92 dBi. Its gain necessarily must be less than this by the factor η, which must be negative in units of dB. Neither ERP nor EIRP can be calculated without knowledge of the power accepted by the antenna, i.e., it is not correct to use units of dBd or dBi with ERP and EIRP. Let us assume a 100-watt (20 dBW) transmitter with losses of 6 dB prior to the antenna. ERP < 22.77dBW and EIRP < 24.92dBW, both less than ideal by η in dB. Assuming that the receiver is in the first side-lobe of the transmitting antenna, and each value is further reduced by 7.2 dB, which is the decrease in directivity from the main to side-lobe of a Yagi–Uda. Therefore, anywhere along the side-lobe direction from this transmitter, a blind receiver could not tell the difference if a Yagi–Uda was replaced with either an ideal dipole (oriented towards the receiver) or an isotropic radiator with antenna input power increased by 1.57 dB.^[5]

Polarization[edit]

Polarization has not been taken into account so far, but it must be properly clarified. When considering the dipole radiator previously we assumed that it was perfectly aligned with the receiver. Now assume, however, that the receiving antenna is circularly polarized, and there will be a minimum 3 dB polarization loss regardless of antenna orientation. If the receiver is also a dipole, it is possible to align it orthogonally to the transmitter such that theoretically zero energy is received. However, this polarization loss is not accounted for in the calculation of ERP or EIRP. Rather, the receiving system designer must account for this loss as appropriate. For example, a cellular telephone tower has a fixed linear polarization, but the mobile handset must function well at any arbitrary orientation. Therefore, a handset design might provide dual polarization receive on the handset so that captured energy is maximized regardless of orientation, or the designer might use a circularly polarized antenna and account for the extra 3 dB of loss with amplification.

Microwave band issues[edit]

For most microwave systems, a completely non-directional isotropic antenna (one which radiates equally and perfectly well in every direction – a physical impossibility) is used as a reference antenna, and then one speaks of EIRP (effective isotropic radiated power) rather than ERP. This includes satellite transponders, radar, and other systems which use microwave dishes and reflectors rather than dipole-style antennas.

Lower-frequency issues[edit]

In the case of medium wave (AM) stations in the United States, power limits are set to the actual transmitter power output, and ERP is not used in normal calculations. Omnidirectional antennas used by a number of stations radiate the signal equally in all horizontal directions. Directional arrays are used to protect co- or adjacent channel stations, usually at night, but some run directionally continuously. While antenna efficiency and ground conductivity are taken into account when designing such an array, the FCC database shows the station's transmitter power output, not ERP.