Misplaced Pages

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95-403: 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

190-458: A coherent isotropic radiator of linear polarization can be shown to be impossible. Its radiation field could not be consistent with the Helmholtz wave equation (derived from Maxwell's equations ) in all directions simultaneously. Consider a large sphere surrounding the hypothetical point source, in the far field of the radiation pattern so that at that radius the wave over a reasonable area

285-407: A coherent isotropic radiator of linear polarization can be shown to be impossible. Its radiation field could not be consistent with the Helmholtz wave equation (derived from Maxwell's equations ) in all directions simultaneously. Consider a large sphere surrounding the hypothetical point source, in the far field of the radiation pattern so that at that radius the wave over a reasonable area

380-643: A band-pass filter F ν to a matched resistor R in another thermal cavity CR (the characteristic impedance of the antenna, line and filter are all matched). Both cavities are at the same temperature   T   . {\displaystyle \ T~.} The filter F ν only allows through a narrow band of frequencies from   ν   {\displaystyle \ \nu \ } to   ν + Δ ν   . {\displaystyle \ \nu +\Delta \nu ~.} Both cavities are filled with blackbody radiation in equilibrium with

475-643: A band-pass filter F ν to a matched resistor R in another thermal cavity CR (the characteristic impedance of the antenna, line and filter are all matched). Both cavities are at the same temperature   T   . {\displaystyle \ T~.} The filter F ν only allows through a narrow band of frequencies from   ν   {\displaystyle \ \nu \ } to   ν + Δ ν   . {\displaystyle \ \nu +\Delta \nu ~.} Both cavities are filled with blackbody radiation in equilibrium with

570-645: A linearly polarized antenna cannot receive components of radio waves with electric field perpendicular to the antenna's linear elements; similarly a right circularly polarized antenna cannot receive left circularly polarized waves. Therefore, the antenna only receives the component of power density S in the cavity matched to its polarization, which is half of the total power density S matched =   1   2 S {\displaystyle S_{\text{matched}}={\frac {\ 1\ }{2}}S} Suppose   B ν   {\displaystyle \ B_{\nu }\ }

665-645: A linearly polarized antenna cannot receive components of radio waves with electric field perpendicular to the antenna's linear elements; similarly a right circularly polarized antenna cannot receive left circularly polarized waves. Therefore, the antenna only receives the component of power density S in the cavity matched to its polarization, which is half of the total power density S matched =   1   2 S {\displaystyle S_{\text{matched}}={\frac {\ 1\ }{2}}S} Suppose   B ν   {\displaystyle \ B_{\nu }\ }

760-497: A waiver , and can exceed normal restrictions. 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. In

855-424: A black thermal cavity at a constant temperature. In a cavity at equilibrium the power density of radiation is the same in every direction and every point in the cavity, meaning that the amount of power passing through a unit surface is constant at any location, and with the surface oriented in any direction. This radiation field is different from that of an isotropic radiator, in which the direction of power flow

950-424: A black thermal cavity at a constant temperature. In a cavity at equilibrium the power density of radiation is the same in every direction and every point in the cavity, meaning that the amount of power passing through a unit surface is constant at any location, and with the surface oriented in any direction. This radiation field is different from that of an isotropic radiator, in which the direction of power flow

1045-622: 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. 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

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1140-433: A coherent isotropic sound radiator is feasible; an example is a pulsing spherical membrane or diaphragm, whose surface expands and contracts radially with time, pushing on the air. The aperture of an isotropic antenna can be derived by a thermodynamic argument, which follows. Suppose an ideal (lossless) isotropic antenna A located within a thermal cavity CA is connected via a lossless transmission line through

1235-433: A coherent isotropic sound radiator is feasible; an example is a pulsing spherical membrane or diaphragm, whose surface expands and contracts radially with time, pushing on the air. The aperture of an isotropic antenna can be derived by a thermodynamic argument, which follows. Suppose an ideal (lossless) isotropic antenna A located within a thermal cavity CA is connected via a lossless transmission line through

1330-464: A gain of 1× (equiv. 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

1425-792: A perfect lossless isotropic antenna at the same distance. This is called isotropic gain G = I     I iso     . {\displaystyle G={\frac {I}{~\ I_{\text{iso}}\ }}~.} Gain is often expressed in logarithmic units called decibels (dB). When gain is calculated with respect to an isotropic antenna, these are called decibels isotropic (dBi) G (dBi) = 10   log 10 ⁡ ( I     I iso   )   . {\displaystyle G{\text{(dBi)}}=10\ \log _{10}\left({\frac {I}{~\ I_{\text{iso}}\ }}\right)~.} The gain of any perfectly efficient antenna averaged over all directions

1520-792: A perfect lossless isotropic antenna at the same distance. This is called isotropic gain G = I     I iso     . {\displaystyle G={\frac {I}{~\ I_{\text{iso}}\ }}~.} Gain is often expressed in logarithmic units called decibels (dB). When gain is calculated with respect to an isotropic antenna, these are called decibels isotropic (dBi) G (dBi) = 10   log 10 ⁡ ( I     I iso   )   . {\displaystyle G{\text{(dBi)}}=10\ \log _{10}\left({\frac {I}{~\ I_{\text{iso}}\ }}\right)~.} The gain of any perfectly efficient antenna averaged over all directions

1615-495: A radiator is isotropic is independent of whether it obeys Lambert's law . As radiators, a spherical black body is both, a flat black body is Lambertian but not isotropic, a flat chrome sheet is neither, and by symmetry the Sun is isotropic, but not Lambertian on account of limb darkening . An isotropic sound radiator is a theoretical loudspeaker radiating equal sound volume in all directions. Since sound waves are longitudinal waves ,

1710-449: A radiator is isotropic is independent of whether it obeys Lambert's law . As radiators, a spherical black body is both, a flat black body is Lambertian but not isotropic, a flat chrome sheet is neither, and by symmetry the Sun is isotropic, but not Lambertian on account of limb darkening . An isotropic sound radiator is a theoretical loudspeaker radiating equal sound volume in all directions. Since sound waves are longitudinal waves ,

1805-1130: A resistor at temperature   T   {\displaystyle \ T\ } over a frequency range   Δ ν   {\displaystyle \ \Delta \nu \ } is P R = k T   Δ ν {\displaystyle P_{\text{R}}=kT\ \Delta \nu } Since the cavities are in thermodynamic equilibrium   P A = P R   , {\displaystyle \ P_{\text{A}}=P_{\text{R}}\ ,} so   4 π A e k T   λ 2   Δ ν = k T   Δ ν {\displaystyle {\frac {\ 4\pi A_{\text{e}}kT\ }{\lambda ^{2}}}\ \Delta \nu =kT\ \Delta \nu }   A e =     λ 2   4 π   {\displaystyle \ A_{\text{e}}={~~\lambda ^{2}\ \over 4\pi }\ } Isotropic antenna An isotropic radiator

1900-423: 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

1995-983: Is   E I R P ( d B W ) = P T X   ( d B W ) − L ( d B ) + G ( d B i )   , {\displaystyle \ {\mathsf {EIRP}}_{\mathsf {(dB_{W})}}=P_{{\mathsf {TX}}\ {\mathsf {(dB_{W})}}}-L_{\mathsf {(dB)}}+G_{\mathsf {(dB_{i})}}\ ,}   E R P ( d B W ) = P T X   ( d B W ) − L ( d B ) + G ( d B i ) − 2.15   d B   . {\displaystyle \ {\mathsf {ERP}}_{\mathsf {(dB_{W})}}=P_{{\mathsf {TX}}\ {\mathsf {(dB_{W})}}}-L_{\mathsf {(dB)}}+G_{\mathsf {(dB_{i})}}-2.15\ {\mathsf {dB}}~.} Losses in

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2090-402: Is 8.77 dB d = 10.92 dB i . 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 dB d or dB i with ERP and EIRP. Let us assume a 100 watt (20 dB W ) transmitter with losses of 6 dB prior to

2185-422: Is a constant, i.e., 0 dB d = 2.15 dB i . 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 dB d and dB i is often left unstated and

2280-506: Is a point radiation or sound source. At a distance, the Sun is an isotropic radiator of electromagnetic radiation. The radiation field of an isotropic radiator in empty space can be found from conservation of energy . The waves travel in straight lines away from the source point, in the radial direction r ^ {\displaystyle {\hat {\mathbf {r} }}} . Since it has no preferred direction of radiation,

2375-461: Is a point radiation or sound source. At a distance, the Sun is an isotropic radiator of electromagnetic radiation. The radiation field of an isotropic radiator in empty space can be found from conservation of energy . The waves travel in straight lines away from the source point, in the radial direction r ^ {\displaystyle {\hat {\mathbf {r} }}} . Since it has no preferred direction of radiation,

2470-484: Is a theoretical point source of waves which radiates the same intensity of radiation in all directions. It may be based on sound waves or electromagnetic waves , in which case it is also known as an isotropic antenna . It has no preferred direction of radiation, i.e., it radiates uniformly in all directions over a sphere centred on the source. Isotropic radiators are used as reference radiators with which other sources are compared, for example in determining

2565-484: Is a theoretical point source of waves which radiates the same intensity of radiation in all directions. It may be based on sound waves or electromagnetic waves , in which case it is also known as an isotropic antenna . It has no preferred direction of radiation, i.e., it radiates uniformly in all directions over a sphere centred on the source. Isotropic radiators are used as reference radiators with which other sources are compared, for example in determining

2660-538: 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. ERP for FM radio in

2755-483: Is equal to the antenna's directivity multiplied by the antenna efficiency , is defined as the ratio of the intensity   I   {\displaystyle \scriptstyle \ I\ } (power per unit area) of the radio power received at a given distance from the antenna (in the direction of maximum radiation) to the intensity   I iso   {\displaystyle \scriptstyle \ I_{\text{iso}}\ } received from

2850-483: Is equal to the antenna's directivity multiplied by the antenna efficiency , is defined as the ratio of the intensity   I   {\displaystyle \scriptstyle \ I\ } (power per unit area) of the radio power received at a given distance from the antenna (in the direction of maximum radiation) to the intensity   I iso   {\displaystyle \scriptstyle \ I_{\text{iso}}\ } received from

2945-449: Is essentially planar. In the far field the electric (and magnetic) field of a plane wave in free space is always perpendicular to the direction of propagation of the wave. So the electric field would have to be tangent to the surface of the sphere everywhere, and continuous along that surface. However the hairy ball theorem shows that a continuous vector field tangent to the surface of a sphere must fall to zero at one or more points on

Effective radiated power - Misplaced Pages Continue

3040-449: Is essentially planar. In the far field the electric (and magnetic) field of a plane wave in free space is always perpendicular to the direction of propagation of the wave. So the electric field would have to be tangent to the surface of the sphere everywhere, and continuous along that surface. However the hairy ball theorem shows that a continuous vector field tangent to the surface of a sphere must fall to zero at one or more points on

3135-483: Is everywhere away from the source point, and decreases with the inverse square of distance from it. In antenna theory, an isotropic antenna is a hypothetical antenna radiating the same intensity of radio waves in all directions. It thus is said to have a directivity of 0 dBi (dB relative to isotropic) in all directions. Since it is entirely non-directional, it serves as a hypothetical worst-case against which directional antennas may be compared. In reality,

3230-483: Is everywhere away from the source point, and decreases with the inverse square of distance from it. In antenna theory, an isotropic antenna is a hypothetical antenna radiating the same intensity of radio waves in all directions. It thus is said to have a directivity of 0 dBi (dB relative to isotropic) in all directions. Since it is entirely non-directional, it serves as a hypothetical worst-case against which directional antennas may be compared. In reality,

3325-405: 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

3420-529: Is nothing to absorb the waves, the power striking a spherical surface enclosing the radiator, with the radiator at center, regardless of the radius r {\displaystyle r} , must be the total power ⟨ P ⟩ {\displaystyle \left\langle P\right\rangle } in watts emitted by the source. Since the power density ⟨ S ⟩ {\displaystyle \left\langle S\right\rangle } in watts per square meter striking each point of

3515-529: Is nothing to absorb the waves, the power striking a spherical surface enclosing the radiator, with the radiator at center, regardless of the radius r {\displaystyle r} , must be the total power ⟨ P ⟩ {\displaystyle \left\langle P\right\rangle } in watts emitted by the source. Since the power density ⟨ S ⟩ {\displaystyle \left\langle S\right\rangle } in watts per square meter striking each point of

3610-832: 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. ELF 3 Hz/100 Mm 30 Hz/10 Mm SLF 30 Hz/10 Mm 300 Hz/1 Mm ULF 300 Hz/1 Mm 3 kHz/100 km VLF 3 kHz/100 km 30 kHz/10 km LF 30 kHz/10 km 300 kHz/1 km MF 300 kHz/1 km 3 MHz/100 m HF 3 MHz/100 m 30 MHz/10 m VHF 30 MHz/10 m 300 MHz/1 m UHF 300 MHz/1 m 3 GHz/100 mm SHF 3 GHz/100 mm 30 GHz/10 mm EHF 30 GHz/10 mm 300 GHz/1 mm THF 300 GHz/1 mm 3 THz/0.1 mm Isotropic antenna An isotropic radiator

3705-438: 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× (equiv. 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

3800-510: Is the spectral radiance per hertz in the cavity; the power of black-body radiation per unit area (m ) per unit solid angle ( steradian ) per unit frequency ( hertz ) at frequency   ν   {\displaystyle \ \nu \ } and temperature   T   {\displaystyle \ T\ } in the cavity. If   A e ( θ , ϕ )   {\displaystyle \ A_{\text{e}}(\theta ,\phi )\ }

3895-510: Is the spectral radiance per hertz in the cavity; the power of black-body radiation per unit area (m ) per unit solid angle ( steradian ) per unit frequency ( hertz ) at frequency   ν   {\displaystyle \ \nu \ } and temperature   T   {\displaystyle \ T\ } in the cavity. If   A e ( θ , ϕ )   {\displaystyle \ A_{\text{e}}(\theta ,\phi )\ }

Effective radiated power - Misplaced Pages Continue

3990-422: Is the antenna's aperture, the amount of power in the frequency range   Δ ν   {\displaystyle \ \Delta \nu \ } the antenna receives from an increment of solid angle   d Ω = d θ d ϕ   {\displaystyle \ \mathrm {d} \Omega =\mathrm {d} \theta \;\mathrm {d} \phi \ } in

4085-422: Is the antenna's aperture, the amount of power in the frequency range   Δ ν   {\displaystyle \ \Delta \nu \ } the antenna receives from an increment of solid angle   d Ω = d θ d ϕ   {\displaystyle \ \mathrm {d} \Omega =\mathrm {d} \theta \;\mathrm {d} \phi \ } in

4180-473: 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 . Cymomotive force ( CMF ) is an alternative term used for expressing radiation intensity in volts , particularly at the lower frequencies. It is used in Australian legislation regulating AM broadcasting services, which describes it as: "for a transmitter, [it] means

4275-448: 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. 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

4370-431: Is unity, or 0 dBi. In EMF measurement applications, an isotropic receiver (also called isotropic antenna) is a calibrated radio receiver with an antenna which approximates an isotropic reception pattern ; that is, it has close to equal sensitivity to radio waves from any direction. It is used as a field measurement instrument to measure electromagnetic sources and calibrate antennas. The isotropic receiving antenna

4465-431: Is unity, or 0 dBi. In EMF measurement applications, an isotropic receiver (also called isotropic antenna) is a calibrated radio receiver with an antenna which approximates an isotropic reception pattern ; that is, it has close to equal sensitivity to radio waves from any direction. It is used as a field measurement instrument to measure electromagnetic sources and calibrate antennas. The isotropic receiving antenna

4560-569: Is usually approximated by three orthogonal antennas or sensing devices with a radiation pattern of the omnidirectional type sin ⁡ θ {\textstyle \sin \theta } such as short dipoles or small loop antennas . The parameter used to define accuracy in the measurements is called isotropic deviation . In optics, an isotropic radiator is a point source of light. The Sun approximates an (incoherent) isotropic radiator of light. Certain munitions such as flares and chaff have isotropic radiator properties. Whether

4655-569: Is usually approximated by three orthogonal antennas or sensing devices with a radiation pattern of the omnidirectional type sin ⁡ θ {\textstyle \sin \theta } such as short dipoles or small loop antennas . The parameter used to define accuracy in the measurements is called isotropic deviation . In optics, an isotropic radiator is a point source of light. The Sun approximates an (incoherent) isotropic radiator of light. Certain munitions such as flares and chaff have isotropic radiator properties. Whether

4750-486: Is usually connected to the antenna through a transmission line and impedance matching network . Since these components may have significant losses   L   , {\displaystyle \ L\ ,} the power applied to the antenna is usually less than the output power of the transmitter   P T X   . {\displaystyle \ P_{\mathsf {TX}}~.} The relation of ERP and EIRP to transmitter output power

4845-822: The Rayleigh–Jeans formula gives a very close approximation of the blackbody spectral radiance B ν =   2 ν 2 k T   c 2 =   2 k T   λ 2 {\displaystyle B_{\nu }={\frac {\ 2\nu ^{2}kT\ }{c^{2}}}={\frac {\ 2kT\ }{\lambda ^{2}}}} Therefore P A =   4 π   A e   k T   λ 2   Δ ν {\displaystyle P_{\text{A}}={\frac {\ 4\pi \ A_{\text{e}}\ kT\ }{\lambda ^{2}}}\ \Delta \nu } The Johnson–Nyquist noise power produced by

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4940-766: The Rayleigh–Jeans formula gives a very close approximation of the blackbody spectral radiance B ν =   2 ν 2 k T   c 2 =   2 k T   λ 2 {\displaystyle B_{\nu }={\frac {\ 2\nu ^{2}kT\ }{c^{2}}}={\frac {\ 2kT\ }{\lambda ^{2}}}} Therefore P A =   4 π   A e   k T   λ 2   Δ ν {\displaystyle P_{\text{A}}={\frac {\ 4\pi \ A_{\text{e}}\ kT\ }{\lambda ^{2}}}\ \Delta \nu } The Johnson–Nyquist noise power produced by

5035-460: The gain of antennas . A coherent isotropic radiator of electromagnetic waves is theoretically impossible, but incoherent radiators can be built. An isotropic sound radiator is possible because sound is a longitudinal wave . The term isotropic radiation means a radiation field which has the same intensity in all directions at each point; thus an isotropic radiator does not produce isotropic radiation. In physics, an isotropic radiator

5130-460: The gain of antennas . A coherent isotropic radiator of electromagnetic waves is theoretically impossible, but incoherent radiators can be built. An isotropic sound radiator is possible because sound is a longitudinal wave . The term isotropic radiation means a radiation field which has the same intensity in all directions at each point; thus an isotropic radiator does not produce isotropic radiation. In physics, an isotropic radiator

5225-437: The second law of thermodynamics . Therefore, the power flows in both directions must be equal P A = P R {\displaystyle P_{\text{A}}=P_{\text{R}}} The radio noise in the cavity is unpolarized , containing an equal mixture of polarization states. However any antenna with a single output is polarized, and can only receive one of two orthogonal polarization states. For example,

5320-437: The second law of thermodynamics . Therefore, the power flows in both directions must be equal P A = P R {\displaystyle P_{\text{A}}=P_{\text{R}}} The radio noise in the cavity is unpolarized , containing an equal mixture of polarization states. However any antenna with a single output is polarized, and can only receive one of two orthogonal polarization states. For example,

5415-1191: 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   r   {\displaystyle \ r\ } is   A = 4 π   r 2   {\displaystyle \ A=4\pi \ r^{2}\ } then   S ( r ) =   E I R P     4 π   r 2     . {\displaystyle \ S(r)={\frac {\ {\mathsf {EIRP}}\ }{\ 4\pi \ r^{2}\ }}~.} Since   E I R P = E R P × 1.64   , {\displaystyle \ \mathrm {EIRP} =\mathrm {ERP} \times 1.64\ ,}   S ( r ) =   0.410 × E R P     π   r 2     . {\displaystyle \ S(r)={\frac {\ 0.410\times {\mathsf {ERP}}\ }{\ \pi \ r^{2}\ }}~.} After dividing out

5510-617: 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, and is used when referring to FM transmission. Effective monopole radiated power ( EMRP ) may be used in Europe, particularly in relation to medium wave broadcasting antennas. This

5605-539: 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 d ). 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

5700-962: 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   E I R P ( W ) = 1.64 × E R P ( W )   {\displaystyle \ {\mathsf {EIRP}}_{\mathsf {(W)}}=1.64\times {\mathsf {ERP}}_{\mathsf {(W)}}\ } If they are expressed in decibels   E I R P ( d B ) = E R P ( d B ) + 2.15   d B   {\displaystyle \ {\mathsf {EIRP}}_{\mathrm {(dB)} }={\mathsf {ERP}}_{\mathrm {(dB)} }+2.15\ {\mathsf {dB}}\ } Effective radiated power and effective isotropic radiated power both measure

5795-428: 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

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5890-413: The antenna and resistor. Some of this radiation is received by the antenna. The amount of this power   P A   {\displaystyle \ P_{\text{A}}\ } within the band of frequencies   Δ ν   {\displaystyle \ \Delta \nu \ } passes through the transmission line and filter F ν and is dissipated as heat in

5985-413: The antenna and resistor. Some of this radiation is received by the antenna. The amount of this power   P A   {\displaystyle \ P_{\text{A}}\ } within the band of frequencies   Δ ν   {\displaystyle \ \Delta \nu \ } passes through the transmission line and filter F ν and is dissipated as heat in

6080-429: The antenna is isotropic, it has the same aperture   A e ( θ , ϕ ) = A e   {\displaystyle \ A_{\text{e}}(\theta ,\phi )=A_{\text{e}}\ } in any direction. So the aperture can be moved outside the integral. Similarly the radiance   B ν   {\displaystyle \ B_{\nu }\ } in

6175-429: The antenna is isotropic, it has the same aperture   A e ( θ , ϕ ) = A e   {\displaystyle \ A_{\text{e}}(\theta ,\phi )=A_{\text{e}}\ } in any direction. So the aperture can be moved outside the integral. Similarly the radiance   B ν   {\displaystyle \ B_{\nu }\ } in

6270-426: The antenna itself are included in the gain. 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)   S   {\displaystyle \ S\ } of the radio signal on the main lobe axis at any particular distance r {\displaystyle r} from the antenna can be calculated from

6365-1002: 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 10 ⁡ ( 1.64 ) = 2.15   d B   , {\displaystyle \ 10\ \log _{10}(1.64)=2.15\ {\mathsf {dB}}\ ,} so   G i = 1.64   G d   . {\displaystyle \ G_{\mathsf {i}}=1.64\ G_{\mathsf {d}}~.} In decibels   G ( d B i ) = G ( d B d ) + 2.15   d B   . {\displaystyle \ G_{\mathsf {(dB_{i})}}=G_{\mathsf {(dB_{d})}}+2.15\ {\mathsf {dB}}~.} The two measures EIRP and ERP are based on

6460-426: The antenna. ERP < 22.77 dB W and EIRP < 24.92 dB W , 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

6555-568: 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,

6650-690: The cavity is the same in any direction P A =   1   2 A e   B ν   Δ ν   ∫ 4 π d Ω {\displaystyle P_{\text{A}}={\frac {\ 1\ }{2}}A_{\text{e}}\ B_{\nu }\ \Delta \nu \ \int \limits _{4\pi }\mathrm {d} \Omega } P A = 2 π   A e   B ν   Δ ν {\displaystyle P_{\text{A}}=2\pi \ A_{\text{e}}\ B_{\nu }\ \Delta \nu } Radio waves are low enough in frequency so

6745-690: The cavity is the same in any direction P A =   1   2 A e   B ν   Δ ν   ∫ 4 π d Ω {\displaystyle P_{\text{A}}={\frac {\ 1\ }{2}}A_{\text{e}}\ B_{\nu }\ \Delta \nu \ \int \limits _{4\pi }\mathrm {d} \Omega } P A = 2 π   A e   B ν   Δ ν {\displaystyle P_{\text{A}}=2\pi \ A_{\text{e}}\ B_{\nu }\ \Delta \nu } Radio waves are low enough in frequency so

6840-402: 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. 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

6935-852: The direction   θ , ϕ   {\displaystyle \ \theta ,\phi \ } is d P A ( θ , ϕ )   =   A e ( θ , ϕ )   S matched   Δ ν d Ω   =     1   2 A e ( θ , ϕ )   B ν   Δ ν d Ω {\displaystyle \mathrm {d} P_{\text{A}}(\theta ,\phi )~=~A_{\text{e}}(\theta ,\phi )\ S_{\text{matched}}\ \Delta \nu \;{\text{d}}\Omega ~=~{\frac {\ 1\ }{2}}A_{\text{e}}(\theta ,\phi )\ B_{\nu }\ \Delta \nu \;\mathrm {d} \Omega } To find

7030-852: The direction   θ , ϕ   {\displaystyle \ \theta ,\phi \ } is d P A ( θ , ϕ )   =   A e ( θ , ϕ )   S matched   Δ ν d Ω   =     1   2 A e ( θ , ϕ )   B ν   Δ ν d Ω {\displaystyle \mathrm {d} P_{\text{A}}(\theta ,\phi )~=~A_{\text{e}}(\theta ,\phi )\ S_{\text{matched}}\ \Delta \nu \;{\text{d}}\Omega ~=~{\frac {\ 1\ }{2}}A_{\text{e}}(\theta ,\phi )\ B_{\nu }\ \Delta \nu \;\mathrm {d} \Omega } To find

7125-473: 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

7220-434: The factor of   π   , {\displaystyle \ \pi \ ,} we get:   S ( r ) =   0.131 × E R P     r 2     . {\displaystyle \ S(r)={\frac {\ 0.131\times {\mathsf {ERP}}\ }{\ r^{2}\ }}~.} However, if the radio waves travel by ground wave as

7315-407: The frequency band   Δ ν   {\displaystyle \ \Delta \nu \ } passes through the filter and is radiated by the antenna. Since the entire system is at the same temperature it is in thermodynamic equilibrium ; there can be no net transfer of power between the cavities, otherwise one cavity would heat up and the other would cool down in violation of

7410-407: The frequency band   Δ ν   {\displaystyle \ \Delta \nu \ } passes through the filter and is radiated by the antenna. Since the entire system is at the same temperature it is in thermodynamic equilibrium ; there can be no net transfer of power between the cavities, otherwise one cavity would heat up and the other would cool down in violation of

7505-422: The power density ⟨ S ⟩ {\displaystyle \left\langle S\right\rangle } of the waves at any point does not depend on the angular direction ( θ , ϕ ) {\displaystyle (\theta ,\phi )} , but only on the distance r {\displaystyle r} from the source. Assuming it is located in empty space where there

7600-422: The power density ⟨ S ⟩ {\displaystyle \left\langle S\right\rangle } of the waves at any point does not depend on the angular direction ( θ , ϕ ) {\displaystyle (\theta ,\phi )} , but only on the distance r {\displaystyle r} from the source. Assuming it is located in empty space where there

7695-424: 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

7790-412: The power density radiated by an isotropic radiator decreases with the inverse square of the distance from the source. The term isotropic radiation is not usually used for the radiation from an isotropic radiator because it has a different meaning in physics. In thermodynamics it refers to the electromagnetic radiation pattern which would be found in a region at thermodynamic equilibrium , as in

7885-412: The power density radiated by an isotropic radiator decreases with the inverse square of the distance from the source. The term isotropic radiation is not usually used for the radiation from an isotropic radiator because it has a different meaning in physics. In thermodynamics it refers to the electromagnetic radiation pattern which would be found in a region at thermodynamic equilibrium , as in

7980-440: The product, expressed in volts, of: 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". 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

8075-449: 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 dB d , but listed only as dB. This ambiguity is undesirable with respect to engineering specifications. A Yagi–Uda antenna's maximum directivity

8170-464: 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,

8265-425: The resistor. The rest is reflected by the filter back to the antenna and is reradiated into the cavity. The resistor also produces Johnson–Nyquist noise current due to the random motion of its molecules at the temperature   T   . {\displaystyle \ T~.} The amount of this power   P R   {\displaystyle \ P_{\text{R}}\ } within

8360-425: The resistor. The rest is reflected by the filter back to the antenna and is reradiated into the cavity. The resistor also produces Johnson–Nyquist noise current due to the random motion of its molecules at the temperature   T   . {\displaystyle \ T~.} The amount of this power   P R   {\displaystyle \ P_{\text{R}}\ } within

8455-516: The sphere is the same, it must equal the radiated power divided by the surface area 4 π r 2 {\displaystyle 4\pi r^{2}} of the sphere ⟨ S ⟩ = ⟨ P ⟩ 4 π r 2 r ^ {\displaystyle \quad \left\langle \mathbf {S} \right\rangle ={\left\langle P\right\rangle \over 4\pi r^{2}}{\hat {\mathbf {r} }}\;\;} Thus

8550-516: The sphere is the same, it must equal the radiated power divided by the surface area 4 π r 2 {\displaystyle 4\pi r^{2}} of the sphere ⟨ S ⟩ = ⟨ P ⟩ 4 π r 2 r ^ {\displaystyle \quad \left\langle \mathbf {S} \right\rangle ={\left\langle P\right\rangle \over 4\pi r^{2}}{\hat {\mathbf {r} }}\;\;} Thus

8645-464: The sphere, which is inconsistent with the assumption of an isotropic radiator with linear polarization. Incoherent isotropic antennas are possible and do not violate Maxwell's equations. Even though an exactly isotropic antenna cannot exist in practice, it is used as a base of comparison to calculate the directivity of actual antennas. Antenna gain   G   , {\displaystyle \scriptstyle \ G\ ,} which

8740-464: The sphere, which is inconsistent with the assumption of an isotropic radiator with linear polarization. Incoherent isotropic antennas are possible and do not violate Maxwell's equations. Even though an exactly isotropic antenna cannot exist in practice, it is used as a base of comparison to calculate the directivity of actual antennas. Antenna gain   G   , {\displaystyle \scriptstyle \ G\ ,} which

8835-745: The total power in the frequency range   Δ ν   {\displaystyle \ \Delta \nu \ } the antenna receives, this is integrated over all directions (a solid angle of   4 π   {\displaystyle \ 4\pi \ } ) P A =   1   2   ∫ 4 π A e ( θ , ϕ )   B ν   Δ ν d Ω {\displaystyle P_{\text{A}}={\frac {\ 1\ }{2}}\ \int \limits _{4\pi }A_{\text{e}}(\theta ,\phi )\ B_{\nu }\ \Delta \nu \;\mathrm {d} \Omega } Since

8930-745: The total power in the frequency range   Δ ν   {\displaystyle \ \Delta \nu \ } the antenna receives, this is integrated over all directions (a solid angle of   4 π   {\displaystyle \ 4\pi \ } ) P A =   1   2   ∫ 4 π A e ( θ , ϕ )   B ν   Δ ν d Ω {\displaystyle P_{\text{A}}={\frac {\ 1\ }{2}}\ \int \limits _{4\pi }A_{\text{e}}(\theta ,\phi )\ B_{\nu }\ \Delta \nu \;\mathrm {d} \Omega } Since

9025-785: The two different standard antennas above: Since the two definitions of gain only differ by a constant factor, so do ERP and EIRP   E I R P ( W ) = 1.64 × E R P ( W )   . {\displaystyle \ {\mathsf {EIRP}}_{\mathsf {(W)}}=1.64\times {\mathsf {ERP}}_{\mathsf {(W)}}~.} In decibels   E I R P ( d B W ) = E R P ( d B W ) + 2.15   d B   . {\displaystyle \ {\mathsf {EIRP}}_{\mathsf {(dB_{W})}}={\mathsf {ERP}}_{\mathsf {(dB_{W})}}+2.15\ {\mathsf {dB}}~.} The transmitter

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