Effective radiated power

Effective radiated power and effective isotropic radiated power both measure the power density a radio transmitter and antenna (or other source of electromagnetic waves) radiates 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 desired direction. 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:

• Isotropic gain is the ratio of the power density ${\displaystyle S_{\text{max}}}$ (signal strength in watts per square meter) received at a point far from the antenna (in the far field) in the direction of its maximum radiation (main lobe), to the power ${\displaystyle S_{\text{max,isotropic}}}$ received at the same point from a hypothetical lossless isotropic antenna, which radiates equal power in all directions
  $${\displaystyle \mathrm {G} _{\text{i}}={S_{\text{max}} \over S_{\text{max,isotropic}}}}$$

  
  Gain is often expressed in logarithmic units of decibels (dB). The decibel gain relative to an isotropic antenna (dBi) is given by
  $${\displaystyle \mathrm {G} {\text{(dBi)}}=10\log {S_{\text{max}} \over S_{\text{max,isotropic}}}}$$

  
• Dipole gain is the ratio of the power density received from the antenna in the direction of its maximum radiation to the power density ${\displaystyle S_{\text{max,dipole}}}$ received from a lossless half-wave dipole antenna in the direction of its maximum radiation
  $${\displaystyle \mathrm {G} _{\text{d}}={S_{\text{max}} \over S_{\text{max,dipole}}}}$$

  
  The decibel gain relative to a dipole (dBd) is given by
  $${\displaystyle \mathrm {G} {\text{(dBd)}}=10\log {S_{\text{max}} \over S_{\text{max,dipole}}}}$$

  

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

$${\displaystyle G_{\text{i}}=1.64G_{\text{d}}}$$

$${\displaystyle G{\text{(dBi)}}=G{\text{(dBd)}}+2.15}$$

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

• 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
  $${\displaystyle \mathrm {EIRP} =G_{\text{i}}P_{\text{in}}}$$

  
  The ERP and EIRP are also often expressed in decibels (dB). The input power in decibels is usually calculated with comparison to a reference level of one watt (W): ${\displaystyle P_{\text{in}}\mathrm {(dBW)} =10\log P_{\text{in}}}$. Since multiplication of two factors is equivalent to addition of their decibel values
  $${\displaystyle \mathrm {EIRP(dBW)} =G{\text{(dBi)}}+P_{\text{in}}\mathrm {(dBW)} }$$

  
• 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
  $${\displaystyle \mathrm {ERP} =G_{\text{d}}P_{\text{in}}}$$

  
  In decibels
  $${\displaystyle \mathrm {ERP(dBW)} =G{\text{(dBd)}}+P_{\text{in}}\mathrm {(dBW)} }$$

  

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

$${\displaystyle \mathrm {EIRP(W)} =1.64\cdot \mathrm {ERP(W)} }$$

$${\displaystyle \mathrm {EIRP(dBW)} =\mathrm {ERP} {\text{(dBW)}}+2.15}$$

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Main lobe

Main lobe

In a radio antenna's radiation pattern, the main lobe, or main beam, is the lobe containing the higher power. This is the lobe that exhibits the greater field strength.

Radiation pattern

Radiation pattern

In the field of antenna design the term radiation pattern refers to the directional (angular) dependence of the strength of the radio waves from the antenna or other source.

Decibel

Decibel

The decibel is a relative unit of measurement equal to one tenth of a bel (B). It expresses the ratio of two values of a power or root-power quantity on a logarithmic scale. Two signals whose levels differ by one decibel have a power ratio of 101/10 or root-power ratio of 101⁄20.

The transmitter is usually connected to the antenna through a transmission line and impedance matching network. Since these components may have significant losses ${\displaystyle L}$, the power applied to the antenna is usually less than the output power of the transmitter ${\displaystyle P_{\text{TX}}}$. The relation of ERP and EIRP to transmitter output power is

$${\displaystyle \mathrm {EIRP(dBW)} =P_{\text{TX}}\mathrm {(dBW)} -L\mathrm {(dB)} +G{\text{(dBi)}}}$$

$${\displaystyle \mathrm {ERP(dBW)} =P_{\text{TX}}\mathrm {(dBW)} -L\mathrm {(dB)} +G{\text{(dBi)}}-2.15}$$

If the signal path is in free space (line-of-sight propagation with no multipath) the signal strength (power flux density in watts per square meter) ${\displaystyle S}$ of the radio signal on the main lobe axis at any particular distance ${\displaystyle r}$ 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 ${\displaystyle r}$ is ${\displaystyle A=4\pi r^{2}}$ then

$${\displaystyle S(r)={\mathrm {EIRP} \over 4\pi r^{2}}}$$

${\displaystyle \mathrm {EIRP} =\mathrm {ERP} \times 1.64}$

$${\displaystyle S(r)={\mathrm {0.41\times ERP} \over \pi r^{2}}}$$

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Line-of-sight propagation

Line-of-sight propagation

Line-of-sight propagation is a characteristic of electromagnetic radiation or acoustic wave propagation which means waves travel in a direct path from the source to the receiver. Electromagnetic transmission includes light emissions traveling in a straight line. The rays or waves may be diffracted, refracted, reflected, or absorbed by the atmosphere and obstructions with material and generally cannot travel over the horizon or behind obstacles.

Multipath propagation

Multipath propagation

In radio communication, multipath is the propagation phenomenon that results in radio signals reaching the receiving antenna by two or more paths. Causes of multipath include atmospheric ducting, ionospheric reflection and refraction, and reflection from water bodies and terrestrial objects such as mountains and buildings. When the same signal is received over more than one path, it can create interference and phase shifting of the signal. Destructive interference causes fading; this may cause a radio signal to become too weak in certain areas to be received adequately. For this reason, this effect is also known as multipath interference or multipath distortion.

Irradiance

Irradiance

In radiometry, irradiance is the radiant flux received by a surface per unit area. The SI unit of irradiance is the watt per square metre (W⋅m−2). The CGS unit erg per square centimetre per second (erg⋅cm−2⋅s−1) is often used in astronomy. Irradiance is often called intensity, but this term is avoided in radiometry where such usage leads to confusion with radiant intensity. In astrophysics, irradiance is called radiant flux.

Ground wave

Ground wave

Ground waves are radio waves propagating parallel to and adjacent to the surface of the Earth, following the curvature of the Earth. This radiation is known as Norton surface wave, or more properly Norton ground wave, because ground waves in radio propagation are not confined to the surface.

Skywave

Skywave

In radio communication, skywave or skip refers to the propagation of radio waves reflected or refracted back toward Earth from the ionosphere, an electrically charged layer of the upper atmosphere. Since it is not limited by the curvature of the Earth, skywave propagation can be used to communicate beyond the horizon, at intercontinental distances. It is mostly used in the shortwave frequency bands.

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.

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 (directivity) 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 (20 dBW) transmitter with losses of 6 dB prior to the antenna. ERP [5]

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.

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 to 20,000 watts, with a gain factor of 5 to 10 (5× to 10×, or 7 to 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 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 dBd). 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).^[6] Some stations have been grandfathered in or, very infrequently, been given a waiver, and can exceed normal restrictions.

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Frequency modulation

Frequency modulation

Frequency modulation (FM) is the encoding of information in a carrier wave by varying the instantaneous frequency of the wave. The technology is used in telecommunications, radio broadcasting, signal processing, and computing.

Watt

Watt

The watt is the unit of power or radiant flux in the International System of Units (SI), equal to 1 joule per second or 1 kg⋅m2⋅s−3. It is used to quantify the rate of energy transfer. The watt is named in honor of James Watt (1736–1819), an 18th-century Scottish inventor, mechanical engineer, and chemist who improved the Newcomen engine with his own steam engine in 1776. Watt's invention was fundamental for the Industrial Revolution.

Transmitter power output

Transmitter power output

In radio transmission, transmitter power output (TPO) is the actual amount of power of radio frequency (RF) energy that a transmitter produces at its output.

Decibel

Decibel

The decibel is a relative unit of measurement equal to one tenth of a bel (B). It expresses the ratio of two values of a power or root-power quantity on a logarithmic scale. Two signals whose levels differ by one decibel have a power ratio of 101/10 or root-power ratio of 101⁄20.

Phased array

Phased array

In antenna theory, a phased array usually means an electronically scanned array, a computer-controlled array of antennas which creates a beam of radio waves that can be electronically steered to point in different directions without moving the antennas.

Azimuth

Azimuth

An azimuth is an angular measurement in a spherical coordinate system. More specifically, it is the horizontal angle from a cardinal direction, most commonly north.

Compass

Compass

A compass is a device that shows the cardinal directions used for navigation and geographic orientation. It commonly consists of a magnetized needle or other element, such as a compass card or compass rose, which can pivot to align itself with magnetic north. Other methods may be used, including gyroscopes, magnetometers, and GPS receivers.

Federal Communications Commission

Federal Communications Commission

The Federal Communications Commission (FCC) is an independent agency of the United States federal government that regulates communications by radio, television, wire, satellite, and cable across the United States. The FCC maintains jurisdiction over the areas of broadband access, fair competition, radio frequency use, media responsibility, public safety, and homeland security.

Measurement

Measurement

Measurement is the quantification of attributes of an object or event, which can be used to compare with other objects or events. In other words, measurement is a process of determining how large or small a physical quantity is as compared to a basic reference quantity of the same kind. The scope and application of measurement are dependent on the context and discipline. In natural sciences and engineering, measurements do not apply to nominal properties of objects or events, which is consistent with the guidelines of the International vocabulary of metrology published by the International Bureau of Weights and Measures. However, in other fields such as statistics as well as the social and behavioural sciences, measurements can have multiple levels, which would include nominal, ordinal, interval and ratio scales.

Height above average terrain

Height above average terrain

Height above average terrain (HAAT), or effective height above average terrain (EHAAT), is the vertical position of an antenna site is above the surrounding landscape. HAAT is used extensively in FM radio and television, as it is more important than effective radiated power (ERP) in determining the range of broadcasts. For international coordination, it is officially measured in meters, even by the Federal Communications Commission in the United States, as Canada and Mexico have extensive border zones where stations can be received on either side of the international boundaries. Stations that want to increase above a certain HAAT must reduce their power accordingly, based on the maximum distance their station class is allowed to cover.

Grandfather clause

Grandfather clause

A grandfather clause, also known as grandfather policy, grandfathering, or grandfathered in, is a provision in which an old rule continues to apply to some existing situations while a new rule will apply to all future cases. Those exempt from the new rule are said to have grandfather rights or acquired rights, or to have been grandfathered in. Frequently, the exemption is limited, as it may extend for a set time, or it may be lost under certain circumstances; for example, a grandfathered power plant might be exempt from new, more restrictive pollution laws, but the exception may be revoked and the new rules would apply if the plant were expanded. Often, such a provision is used as a compromise or out of practicality, to allow new rules to be enacted without upsetting a well-established logistical or political situation. This extends the idea of a rule not being retroactively applied.

Waiver

Waiver

A waiver is the voluntary relinquishment or surrender of some known right or privilege.

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.

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Microwave

Microwave

Microwave is a form of electromagnetic radiation with wavelengths ranging from about one meter to one millimeter corresponding to frequencies between 300 MHz and 300 GHz respectively. Different sources define different frequency ranges as microwaves; the above broad definition includes both UHF and EHF bands. A more common definition in radio-frequency engineering is the range between 1 and 100 GHz. In all cases, microwaves include the entire SHF band at minimum. Frequencies in the microwave range are often referred to by their IEEE radar band designations: S, C, X, Ku, K, or Ka band, or by similar NATO or EU designations.

Radiation

Radiation

In physics, radiation is the emission or transmission of energy in the form of waves or particles through space or through a material medium. This includes:electromagnetic radiation, such as radio waves, microwaves, infrared, visible light, ultraviolet, x-rays, and gamma radiation (γ) particle radiation, such as alpha radiation (α), beta radiation (β), proton radiation and neutron radiation acoustic radiation, such as ultrasound, sound, and seismic waves gravitational radiation, that takes the form of gravitational waves, or ripples in the curvature of spacetime

Satellite

Satellite

A satellite or artificial satellite is an object intentionally placed into orbit in outer space. Satellites have a variety of uses, including communication relay, weather forecasting, navigation (GPS), broadcasting, scientific research, and Earth observation. Additional military uses are reconnaissance, early warning, signals intelligence and, potentially, weapon delivery. Other satellites include the final rocket stages that placed satellites in orbit and formerly useful satellites that are now defunct.

Transponder

Transponder

In telecommunications, a transponder is a device that, upon receiving a signal, emits a different signal in response. The term is a blend of transmitter and responder.

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 directions. Directional arrays are used to protect co- or adjacent channel stations, usually at night, but some run directionally 24 hours. 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.

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,^[7] and is used when referring to FM transmission.^[8]

EMRP

Effective monopole radiated power (EMRP) may be used in Europe, particularly in relation to medium wave broadcasting antennas. This is the same as ERP, except that a short vertical antenna (i.e. a short monopole) is used as the reference antenna instead of a half-wave dipole.^[7]

CMF

Cymomotive force (CMF) is an alternative term used for expressing radiation intensity in volts, particularly at the lower frequencies.^[7] It is used in Australian legislation regulating AM broadcasting services, which describes it as: "for a transmitter, [it] means the product, expressed in volts, of: (a) the electric field strength at a given point in space, due to the operation of the transmitter; and (b) the distance of that point from the transmitter's antenna".^[9]

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".^[8]

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Institution of Electrical Engineers

Institution of Electrical Engineers

The Institution of Electrical Engineers (IEE) was a British professional organisation of electronics, electrical, manufacturing, and Information Technology professionals, especially electrical engineers. It began in 1871 as the Society of Telegraph Engineers. In 2006, it changed its name to the Institution of Engineering and Technology (IET).

Medium wave

Medium wave

Medium wave (MW) is the part of the medium frequency (MF) radio band used mainly for AM radio broadcasting. The spectrum provides about 120 channels with more limited sound quality than FM stations on the FM broadcast band. During the daytime, reception is usually limited to more local stations, though this is dependent on the signal conditions and quality of radio receiver used. Improved signal propagation at night allows the reception of much longer distance signals. This can cause increased interference because on most channels multiple transmitters operate simultaneously worldwide. In addition, amplitude modulation (AM) is often more prone to interference by various electronic devices, especially power supplies and computers. Strong transmitters cover larger areas than on the FM broadcast band but require more energy and longer antennas. Digital modes are possible but have not reached momentum yet.

Monopole antenna

Monopole antenna

A monopole antenna is a class of radio antenna consisting of a straight rod-shaped conductor, often mounted perpendicularly over some type of conductive surface, called a ground plane. The driving signal from the transmitter is applied, or for receiving antennas the output signal to the receiver is taken, between the lower end of the monopole and the ground plane. One side of the antenna feedline is attached to the lower end of the monopole, and the other side is attached to the ground plane, which is often the Earth. This contrasts with a dipole antenna which consists of two identical rod conductors, with the signal from the transmitter applied between the two halves of the antenna.

Dipole

Dipole

In physics, a dipole is an electromagnetic phenomenon which occurs in two ways:An electric dipole deals with the separation of the positive and negative electric charges found in any electromagnetic system. A simple example of this system is a pair of charges of equal magnitude but opposite sign separated by some typically small distance. A magnetic dipole is the closed circulation of an electric current system. A simple example is a single loop of wire with constant current through it. A bar magnet is an example of a magnet with a permanent magnetic dipole moment.

Volt

Volt

The volt is the unit of electric potential, electric potential difference (voltage), and electromotive force in the International System of Units (SI). It is named after the Italian physicist Alessandro Volta (1745–1827).

AM broadcasting

AM broadcasting

AM broadcasting is radio broadcasting using amplitude modulation (AM) transmissions. It was the first method developed for making audio radio transmissions, and is still used worldwide, primarily for medium wave transmissions, but also on the longwave and shortwave radio bands.

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.