thumb|upright=1.6|Illustration of definition of effective isotropically radiated power (EIRP). The axes have units of signal strength in decibels. <math>R_\mathsf{a}</math> is the [[radiation pattern of a given transmitter driving a directional antenna, emitting a beam of radio waves along the z axis. It radiates a far field signal strength of <math>S</math> in its direction of maximum radiation (main lobe) along the z-axis. The <span style="color:green;">green</span> sphere <math>R_\mathsf{iso}</math> is the radiation pattern of an ideal isotropic antenna that radiates the same maximum signal strength as the directive antenna does. The transmitter power that would have to be applied to the isotropic antenna to radiate this much power is the EIRP.]]
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 that would have to be radiated by a half-wave dipole antenna to give the same radiation intensity (signal strength, or power flux density, expressed as power per area) 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 about 1.64 (or about 2.15 dB) compared to an isotropic radiator, if ERP and EIRP are expressed as power their relation is
<math display="block">\ \mathsf{EIRP}_\mathsf{(W)} \approx 1.64 \times \mathsf{ERP}_\mathsf{(W)}\ </math>
If they are expressed in decibels
<math display="block">\ \mathsf{EIRP}_\mathrm{(dBm)} \approx \mathsf{ERP}_\mathrm{(dBm)} + 2.15\ \mathsf{dB}\ </math>
Definitions
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.
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 some necessarily named standard antenna. (Without specifying a standard for comparison there can be no ratio.) For example, a 1,000 watt transmitter feeding an antenna with a gain of 4× compared to a theoretical isotropic antenna, or about 6 dBi, will radiate the same power in the direction of its main lobe, and thus the same EIRP, as a 4,000 watt transmitter feeding the theoretical isotropic antenna radiates in all directions equally. 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 measures 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, both theoretical; an isotropic antenna and a (perfect, lossless) half-wave dipole:
- Isotropic gain is the ratio of the power density (signal strength, in power per area) received at a point far from the antenna (i.e. in its far field) in the direction of its maximum radiation (i.e. its main lobe), <math>\ S_\mathsf{max}\ </math>, to the power density received at the same point from a hypothetical lossless isotropic antenna, which radiates equally in all directions, <math>\ S_\mathsf{max,iso}\ </math>: <math display="block">\ \mathrm{G}_\mathsf{i} = \frac{\ S_\mathsf{max}\ }{\ S_\mathsf{max,iso}\ }\ </math> Gain is often expressed in logarithmic units of decibels (dB). The gain relative to an isotropic antenna and expressed in decibels, dB, is given by
: <math display="block">\ \mathrm{G}_\mathsf{(dB_i)} = 10\ \log_{10}\left( \frac{\ S_\mathsf{max}\ }{\ S_\mathsf{max,iso}\ } \right)\ </math>
- Dipole gain is the ratio of the power density (signal strength, in power per area) received at a point far from the antenna (i.e. in its far field) in the direction of its maximum radiation (i.e. its main lobe), <math>\ S_\mathsf{max}\ </math>, to the power density received at the same point from a hypothetical lossless half-wave dipole antenna, <math>S_\mathsf{max,dipole}</math>:<math display="block">\ \mathrm{G}_\mathsf{d} = \frac{\ S_\mathsf{max}\ }{\ S_\mathsf{max,dipole}\ }\ </math> The gain relative to a half-wave dipole antenna and expressed in decibels, dB, is given by <math display="block">\ \mathrm{G}_\mathsf{(dB_d)} = 10\ \log_{10}\left( \frac{\ S_\mathsf{max}\ }{\ S_\mathsf{max,dipole}\ } \right)\ </math>
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 (assuming the antenna axis is vertical), the gain of a half-wave dipole is greater than that of an isotropic antenna. The isotropic gain of a half-wave dipole is about 1.64, or, in decibels, <math>\ 10\ \log_{10}(1.64) \approx 2.15\ \mathsf{dB}\ ,</math> so
<math display="block">\ G_\mathsf{i} \approx 1.64\ G_\mathsf{d} ~.</math>
In decibels
<math display="block">\ G_\mathsf{(dB_i)} \approx G_\mathsf{(dB_d)} + 2.15\ \mathsf{dB} ~.</math>
The two measures EIRP and ERP are based on the two different standard antennas above:
Polarization
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.
FM example
thumb|upright=0.5|Four-bay crossed-dipole antenna of an FM broadcasting station
For example, an FM radio station which advertises that it has 100,000 watts of power actually has 100,000 watts ERP, and not an actual 100,000-watt transmitter. The transmitter power output (TPO) of such a station typically may be 10,000–20,000 watts, with a gain factor of 5–10× (5–10×, or 7–10 dB). In most antenna designs, gain is realized primarily by concentrating power toward the horizontal plane and suppressing it at upward and downward angles, through the use of phased arrays of antenna elements. The distribution of power versus elevation angle is known as the vertical pattern. When an antenna is also directional horizontally, gain and ERP will vary with azimuth (compass direction). Rather than the average power over all directions, it is the apparent power in the direction of the peak of the antenna's main lobe that is quoted as a station's ERP (this statement is just another way of stating the definition of ERP). This is particularly applicable to the huge ERPs reported for shortwave broadcasting stations, which use very narrow beam widths to get their signals across continents and oceans.
United States regulatory usage
ERP for FM radio in the United States is always relative to a theoretical reference half-wave dipole antenna. (That is, when calculating ERP, the most direct approach is to work with antenna gain in dB). To deal with antenna polarization, the Federal Communications Commission (FCC) lists ERP in both the horizontal and vertical measurements for FM and TV. Horizontal is the standard for both, but if the vertical ERP is larger it will be used instead.
The maximum ERP for US FM broadcasting is usually 100,000 watts (FM Zone II) or 50,000 watts (in the generally more densely populated Zones I and I-A), though exact restrictions vary depending on the class of license and the antenna height above average terrain (HAAT). Some stations have been grandfathered in or, very infrequently, been given a waiver, and can exceed normal restrictions.
Microwave band issues
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
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.
Related terms
According to the Institution of Electrical Engineers (UK), ERP is often used as a general reference term for radiated power, but strictly speaking should only be used when the antenna is a half-wave dipole, and is used when referring to FM transmission.
It relates to AM broadcasting only, and expresses the field strength in "microvolts per metre at a distance of 1 kilometre from the transmitting antenna".
HAAT
The height above average terrain for VHF and higher frequencies is extremely important when considering ERP, as the signal coverage (broadcast range) produced by a given ERP dramatically increases with antenna height. Because of this, it is possible for a station of only a few hundred watts ERP to cover more area than a station of a few thousand watts ERP, if its signal travels above obstructions on the ground.
See also
- Nominal power (radio broadcasting)
- List of North American broadcast station classes