Effective radiated power
Effective radiated power, synonymous with equivalent radiated power, is an IEEE standardized definition of directional radio frequency 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 as the actual source antenna at a distant receiver located in the direction of the antenna's strongest beam. 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 equivalent isotropically radiated power. Equivalent isotropically radiated power is the hypothetical power that would have to be radiated by an isotropic antenna to give the same 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 compared to an isotropic radiator, if ERP and EIRP are expressed in watts their relation is
If they are expressed in decibels
Definitions
Effective radiated power and effective isotropic radiated power both measure the amount of power a radio transmitter and antenna radiates in a specific direction: in the direction of maximum signal strength 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 desired direction. The latter factor is quantified by the antenna gain, which is the ratio of the signal strength radiated by an antenna to that radiated by a standard antenna. For example, a 1,000-watt transmitter feeding an antenna with a gain of 4 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. 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:
- Isotropic gain is the ratio of the power density received at a point far from the antenna in the direction of its maximum radiation, to the power received at the same point from a hypothetical lossless isotropic antenna, which radiates equal power in all directions
- Dipole gain is the ratio of the power density received from the antenna in the direction of its maximum radiation to the power density received from a lossless half-wave dipole antenna in the direction of its maximum radiation
In decibels
The two measures EIRP and ERP are based on the two different standard antennas above:
- EIRP is defined as the RMS power input in watts required to a lossless isotropic antenna to give the same maximum power density far from the antenna as the actual transmitter. It is equal to the power input to the transmitter's antenna multiplied by the isotropic antenna gain
- ERP is defined as the RMS power input in watts required to a lossless half-wave dipole antenna to give the same maximum power density far from the antenna as the actual transmitter. It is equal to the power input to the transmitter's antenna multiplied by the antenna gain relative to a half-wave dipole
In decibels
Relation to transmitter output power
The transmitter is usually connected to the antenna through a transmission line. Since the transmission line may have significant losses, the power applied to the antenna is usually less than the output power of the transmitter. The relation of ERP and EIRP to transmitter output power isLosses in the antenna itself are included in the gain.
Relation to signal strength
If the signal path is in free space the signal strength of the radio signal on the main lobe axis at any particular distance from the antenna can be calculated from the EIRP or ERP. Since an isotropic antenna radiates equal power flux density over a sphere centered on the antenna, and the area of a sphere with radius is thenSince,
However if the radio waves travel by ground wave as is typical for medium or longwave broadcasting, skywave, or indirect paths play a part in transmission, the waves will suffer additional attenuation which depends on the terrain between the antennas, so these formulas are not valid.
Dipole vs. isotropic radiators
Because ERP is calculated as antenna gain 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, and the receiver cannot know the difference so long as the input power is increased by 2.15 dB.Unfortunately, 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 better energy focusing than a simple dipole. Since it is constructed from dipoles, often its antenna gain is expressed in dBd, but listed only as dB. Obviously 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 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 or an isotropic radiator with antenna input power increased by 1.57 dB.
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
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 of such a station typically may be 10,000 to 20,000 watts, with a gain factor of 5 to 10. 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. Rather than the average power over all directions, it is the apparent power in the direction of the antenna's main lobe that is quoted as a station's 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.. To deal with antenna polarization, the Federal Communications Commission 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 or 50,000 watts, though exact restrictions vary depending on the class of license and the antenna height above average terrain. Some stations have been grandfathered in or, very infrequently, been given a waiver, and can exceed normal restrictions.