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82-512: WCAT-FM has an effective radiated power (ERP) of 3,000 watts horizontal polarization and 2,750 watts vertical polarization. The transmitter is on Spring Road (Route 24) in Middlesex Township, Pennsylvania . In 1959, WHYL-FM first signed on the air. It was a simulcast of co-owned WHYL (960 AM). The two stations were owned by Mid-Atlantic Broadcasting. WHYL had a middle of the road format of popular adult music, news and sports. By

164-497: 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

246-446: A 3.5 dB/km fiber yields a loss of 0.35 dB = 3.5 dB/km × 0.1 km. The human perception of the intensity of sound and light more nearly approximates the logarithm of intensity rather than a linear relationship (see Weber–Fechner law ), making the dB scale a useful measure. The decibel is commonly used in acoustics as a unit of sound power level or sound pressure level . The reference pressure for sound in air

328-407: A bel would normally be written 0.05 dB, and not 5 mB. The method of expressing a ratio as a level in decibels depends on whether the measured property is a power quantity or a root-power quantity ; see Power, root-power, and field quantities for details. When referring to measurements of power quantities, a ratio can be expressed as a level in decibels by evaluating ten times

410-487: A brief period, WRKZ-FM flipped formats to all-1980s rock hits and re-branded itself as "Z102.3". Another format change came shortly thereafter when "Cat Country 106.7" WCAT-FM, on 106.7, changed its call sign to WCPP (known as "Cool Pop") and changed its format to hot AC . On February 17, 2004, the WCAT-FM call sign was moved to 102.3, the format was again changed to country, and it became "Red 102.3". Citadel Broadcasting ,

492-622: 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

574-422: A change in power by a factor of 10 corresponds to a 10 dB change in level. When expressing root-power quantities, a change in amplitude by a factor of 10 corresponds to a 20 dB change in level. The decibel scales differ by a factor of two, so that the related power and root-power levels change by the same value in linear systems, where power is proportional to the square of amplitude. The definition of

656-502: A decibel is one-tenth of a bel). P and P 0 must measure the same type of quantity, and have the same units before calculating the ratio. If P = P 0 in the above equation, then L P = 0. If P is greater than P 0 then L P is positive; if P is less than P 0 then L P is negative. Rearranging the above equation gives the following formula for P in terms of P 0 and L P  : When referring to measurements of root-power quantities, it

738-670: A favorable response to a new unit definition among members of the International Advisory Committee on Long Distance Telephony in Europe and replaced the MSC with the Transmission Unit (TU). 1 TU was defined such that the number of TUs was ten times the base-10 logarithm of the ratio of measured power to a reference power. The definition was conveniently chosen such that 1 TU approximated 1 MSC; specifically, 1 MSC

820-437: A frequency of 5000   radians per second (795.8 Hz), and matched closely the smallest attenuation detectable to a listener. A standard telephone cable was "a cable having uniformly distributed resistance of 88 ohms per loop-mile and uniformly distributed shunt capacitance of 0.054  microfarads per mile" (approximately corresponding to 19  gauge wire). In 1924, Bell Telephone Laboratories received

902-464: 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

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984-453: A linear scale, adding there, and then taking logarithms to return. For example, where operations on decibels are logarithmic addition/subtraction and logarithmic multiplication/division, while operations on the linear scale are the usual operations: The logarithmic mean is obtained from the logarithmic sum by subtracting 10 log 10 ⁡ 2 {\displaystyle 10\log _{10}2} , since logarithmic division

1066-428: A manner similar to scientific notation . This allows one to clearly visualize huge changes of some quantity. See Bode plot and Semi-log plot . For example, 120 dB SPL may be clearer than "a trillion times more intense than the threshold of hearing". Level values in decibels can be added instead of multiplying the underlying power values, which means that the overall gain of a multi-component system, such as

1148-434: A power ratio of 10 , or 1.9953 , about 0.24% different from exactly 2, and a voltage ratio of 1.4125 , 0.12% different from exactly √ 2 . Similarly, an increase of 6.000 dB corresponds to the power ratio is 10 ≈ 3.9811 , about 0.5% different from 4. The decibel is useful for representing large ratios and for simplifying representation of multiplicative effects, such as attenuation from multiple sources along

1230-459: A ratio between two root-power quantities of √ 10 :1. Two signals whose levels differ by one decibel have a power ratio of 10 , which is approximately 1.258 93 , and an amplitude (root-power quantity) ratio of 10 ( 1.122 02 ). The bel is rarely used either without a prefix or with SI unit prefixes other than deci ; it is customary, for example, to use hundredths of a decibel rather than millibels . Thus, five one-thousandths of

1312-418: A series of amplifier stages, can be calculated by summing the gains in decibels of the individual components, rather than multiply the amplification factors; that is, log( A × B × C ) = log( A ) + log( B ) + log( C ). Practically, this means that, armed only with the knowledge that 1 dB is a power gain of approximately 26%, 3 dB is approximately 2× power gain, and 10 dB is 10× power gain, it

1394-406: A signal chain. Its application in systems with additive effects is less intuitive, such as in the combined sound pressure level of two machines operating together. Care is also necessary with decibels directly in fractions and with the units of multiplicative operations. The logarithmic scale nature of the decibel means that a very large range of ratios can be represented by a convenient number, in

1476-423: 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

1558-421: A subtraction ( C / N 0 ) dB = C dB − N 0 dB . However, the linear-scale units still simplify in the implied fraction, so that the results would be expressed in dB-Hz. According to Mitschke, "The advantage of using a logarithmic measure is that in a transmission chain, there are many elements concatenated, and each has its own gain or attenuation. To obtain the total, addition of decibel values

1640-886: 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

1722-400: A unit of logarithmic power ratio, while the neper is used for logarithmic root-power (amplitude) ratio. The unit dBW is often used to denote a ratio for which the reference is 1 W, and similarly dBm for a 1 mW reference point. (31.62 V / 1 V) ≈ 1 kW / 1 W , illustrating the consequence from the definitions above that L G has the same value, 30 dB, regardless of whether it

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1804-983: 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

1886-402: 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

1968-422: 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

2050-428: 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 10 (approximately 1.26 ) or root-power ratio of 10 (approximately 1.12 ). The unit fundamentally expresses a relative change but may also be used to express an absolute value as

2132-469: Is almost universally rounded to 3 dB in technical writing. This implies an increase in voltage by a factor of √ 2 ≈ 1.4142 . Likewise, a doubling or halving of the voltage, corresponding to a quadrupling or quartering of the power, is commonly described as 6 dB rather than ± 6.0206  dB. Should it be necessary to make the distinction, the number of decibels is written with additional significant figures . 3.000 dB corresponds to

2214-538: 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

2296-411: 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

2378-402: Is deprecated by that standard and root-power is used throughout this article. Although power and root-power quantities are different quantities, their respective levels are historically measured in the same units, typically decibels. A factor of 2 is introduced to make changes in the respective levels match under restricted conditions such as when the medium is linear and the same waveform

2460-406: 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

2542-416: Is linear subtraction. Attenuation constants, in topics such as optical fiber communication and radio propagation path loss , are often expressed as a fraction or ratio to distance of transmission. In this case, dB/m represents decibel per meter, dB/mi represents decibel per mile, for example. These quantities are to be manipulated obeying the rules of dimensional analysis , e.g., a 100-meter run with

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2624-490: Is much more convenient than multiplication of the individual factors." However, for the same reason that humans excel at additive operation over multiplication, decibels are awkward in inherently additive operations: if two machines each individually produce a sound pressure level of, say, 90 dB at a certain point, then when both are operating together we should expect the combined sound pressure level to increase to 93 dB, but certainly not to 180 dB!; suppose that

2706-411: Is obtained from powers or from amplitudes, provided that in the specific system being considered power ratios are equal to amplitude ratios squared. A change in power ratio by a factor of 10 corresponds to a change in level of 10 dB . A change in power ratio by a factor of 2 or ⁠ 1 / 2 ⁠ is approximately a change of 3 dB . More precisely, the change is ± 3.0103  dB, but this

2788-830: 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 Decibel The decibel (symbol: dB )

2870-791: Is possible to determine the power ratio of a system from the gain in dB with only simple addition and multiplication. For example: However, according to its critics, the decibel creates confusion, obscures reasoning, is more related to the era of slide rules than to modern digital processing, and is cumbersome and difficult to interpret. Quantities in decibels are not necessarily additive , thus being "of unacceptable form for use in dimensional analysis ". Thus, units require special care in decibel operations. Take, for example, carrier-to-noise-density ratio C / N 0 (in hertz), involving carrier power C (in watts) and noise power spectral density N 0 (in W/Hz). Expressed in decibels, this ratio would be

2952-438: 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

3034-574: Is recognized by other international bodies such as the International Electrotechnical Commission (IEC) and International Organization for Standardization (ISO). The IEC permits the use of the decibel with root-power quantities as well as power and this recommendation is followed by many national standards bodies, such as NIST , which justifies the use of the decibel for voltage ratios. In spite of their widespread use, suffixes (such as in dBA or dBV) are not recognized by

3116-452: Is set at the typical threshold of perception of an average human and there are common comparisons used to illustrate different levels of sound pressure . As sound pressure is a root-power quantity, the appropriate version of the unit definition is used: where p rms is the root mean square of the measured sound pressure and p ref is the standard reference sound pressure of 20 micropascals in air or 1 micropascal in water. Use of

3198-475: 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

3280-448: 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

3362-409: Is under consideration with changes in amplitude, or the medium impedance is linear and independent of both frequency and time. This relies on the relationship holding. In a nonlinear system, this relationship does not hold by the definition of linearity. However, even in a linear system in which the power quantity is the product of two linearly related quantities (e.g. voltage and current ), if

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3444-440: Is usual to consider the ratio of the squares of F (measured) and F 0 (reference). This is because the definitions were originally formulated to give the same value for relative ratios for both power and root-power quantities. Thus, the following definition is used: The formula may be rearranged to give Similarly, in electrical circuits , dissipated power is typically proportional to the square of voltage or current when

3526-486: 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

3608-441: Is widely used among the foreign telephone organizations and recently it was termed the "decibel" at the suggestion of the International Advisory Committee on Long Distance Telephony. The decibel may be defined by the statement that two amounts of power differ by 1 decibel when they are in the ratio of 10 and any two amounts of power differ by N decibels when they are in the ratio of 10 . The number of transmission units expressing

3690-414: The base-10 logarithm of the ratio of the measured quantity to reference value. Thus, the ratio of P (measured power) to P 0 (reference power) is represented by L P , that ratio expressed in decibels, which is calculated using the formula: The base-10 logarithm of the ratio of the two power quantities is the number of bels. The number of decibels is ten times the number of bels (equivalently,

3772-414: The gains of amplifiers, attenuation of signals, and signal-to-noise ratios are often expressed in decibels. The decibel originates from methods used to quantify signal loss in telegraph and telephone circuits. Until the mid-1920s, the unit for loss was miles of standard cable (MSC). 1 MSC corresponded to the loss of power over one mile (approximately 1.6 km) of standard telephone cable at

3854-399: The impedance is constant. Taking voltage as an example, this leads to the equation for power gain level L G : where V out is the root-mean-square (rms) output voltage, V in is the rms input voltage. A similar formula holds for current. The term root-power quantity is introduced by ISO Standard 80000-1:2009 as a substitute of field quantity . The term field quantity

3936-415: The impedance is frequency- or time-dependent, this relationship does not hold in general, for example if the energy spectrum of the waveform changes. For differences in level, the required relationship is relaxed from that above to one of proportionality (i.e., the reference quantities P 0 and F 0 need not be related), or equivalently, must hold to allow the power level difference to be equal to

4018-434: The 1970s, WHYL-FM began playing country music using broadcast automation . On December 31, 1979, the call sign changed to WZUE and was branded as "Zoo 102". The WZUE calls were short-lived as the call sign reverted to WHYL-FM on October 14, 1981, branded as "Country 102". On April 26, 2002, the call sign was changed to WRKZ-FM. It began as a simulcast of WCAT-FM 106.7 , and branded itself as "Cat Country 106.7". After

4100-1191: 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

4182-570: 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

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4264-456: The IEC or ISO. The IEC Standard 60027-3:2002 defines the following quantities. The decibel (dB) is one-tenth of a bel: 1 dB = 0.1 B . The bel (B) is 1 ⁄ 2  ln(10) nepers : 1 B = 1 ⁄ 2 ln(10) Np . The neper is the change in the level of a root-power quantity when the root-power quantity changes by a factor of e , that is 1 Np = ln(e) = 1 , thereby relating all of

4346-539: 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

4428-428: 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

4510-426: 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

4592-505: 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

4674-1002: 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

4756-426: 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

4838-568: 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,

4920-401: The decibel in underwater acoustics leads to confusion, in part because of this difference in reference value. Sound intensity is proportional to the square of sound pressure. Therefore, the sound intensity level can also be defined as: The human ear has a large dynamic range in sound reception. The ratio of the sound intensity that causes permanent damage during short exposure to that of

5002-492: The decibel originated in the measurement of transmission loss and power in telephony of the early 20th century in the Bell System in the United States. The bel was named in honor of Alexander Graham Bell , but the bel is seldom used. Instead, the decibel is used for a wide variety of measurements in science and engineering , most prominently for sound power in acoustics , in electronics and control theory . In electronics,

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5084-403: 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

5166-473: 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

5248-441: The earliest days of the telephone, the need for a unit in which to measure the transmission efficiency of telephone facilities has been recognized. The introduction of cable in 1896 afforded a stable basis for a convenient unit and the "mile of standard" cable came into general use shortly thereafter. This unit was employed up to 1923 when a new unit was adopted as being more suitable for modern telephone work. The new transmission unit

5330-434: 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

5412-536: The name logit for "standard magnitudes which combine by multiplication", to contrast with the name unit for "standard magnitudes which combine by addition". In April 2003, the International Committee for Weights and Measures (CIPM) considered a recommendation for the inclusion of the decibel in the International System of Units (SI), but decided against the proposal. However, the decibel

5494-416: The noise from a machine is measured (including the contribution of background noise) and found to be 87 dBA but when the machine is switched off the background noise alone is measured as 83 dBA. [...] the machine noise [level (alone)] may be obtained by 'subtracting' the 83 dBA background noise from the combined level of 87 dBA; i.e., 84.8 dBA.; in order to find a representative value of

5576-428: 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

5658-441: 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

5740-456: The quantities power spectral density and the associated root-power quantities via the Fourier transform , which allows elimination of the frequency dependence in the analysis by analyzing the system at each frequency independently. Since logarithm differences measured in these units often represent power ratios and root-power ratios, values for both are shown below. The bel is traditionally used as

5822-428: The ratio of a value to a fixed reference value; when used in this way, the unit symbol is often suffixed with letter codes that indicate the reference value. For example, for the reference value of 1  volt , a common suffix is " V " (e.g., "20 dBV"). Two principal types of scaling of the decibel are in common use. When expressing a power ratio, it is defined as ten times the logarithm with base 10 . That is,

5904-427: The ratio of any two powers is therefore ten times the common logarithm of that ratio. This method of designating the gain or loss of power in telephone circuits permits direct addition or subtraction of the units expressing the efficiency of different parts of the circuit ... In 1954, J. W. Horton argued that the use of the decibel as a unit for quantities other than transmission loss led to confusion, and suggested

5986-449: 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

6068-464: 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,

6150-459: The root-power level difference from power P 1 and F 1 to P 2 and F 2 . An example might be an amplifier with unity voltage gain independent of load and frequency driving a load with a frequency-dependent impedance: the relative voltage gain of the amplifier is always 0 dB, but the power gain depends on the changing spectral composition of the waveform being amplified. Frequency-dependent impedances may be analyzed by considering

6232-442: 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

6314-420: The sound level in a room a number of measurements are taken at different positions within the room, and an average value is calculated. [...] Compare the logarithmic and arithmetic averages of [...] 70 dB and 90 dB: logarithmic average = 87 dB; arithmetic average = 80 dB. Addition on a logarithmic scale is called logarithmic addition , and can be defined by taking exponentials to convert to

6396-518: The station's former owner, merged with Cumulus Media on September 16, 2011. To comply with Department of Justice regulations, WCAT-FM, the license for WWKL , and the intellectual property of WTPA , along with WRSR in Flint, Michigan , were transferred to Potential Broadcasting LLC. In August 2012, Potential Broadcasting sold WCAT-FM to Harold Z. Swidler, owner of WIOO in Carlisle, Pennsylvania. The sale

6478-789: 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

6560-399: The units as nondimensional natural log of root-power-quantity ratios, 1 dB =  0.115 13 ... Np =  0.115 13 ... . Finally, the level of a quantity is the logarithm of the ratio of the value of that quantity to a reference value of the same kind of quantity. Therefore, the bel represents the logarithm of a ratio between two power quantities of 10:1, or the logarithm of

6642-586: Was 1.056 TU. In 1928, the Bell system renamed the TU into the decibel, being one tenth of a newly defined unit for the base-10 logarithm of the power ratio. It was named the bel , in honor of the telecommunications pioneer Alexander Graham Bell . The bel is seldom used, as the decibel was the proposed working unit. The naming and early definition of the decibel is described in the NBS Standard's Yearbook of 1931: Since

6724-509: Was consummated on November 7, 2012. The studio facilities were relocated from Camp Hill, Pennsylvania , at the former home of Citadel Harrisburg, to Carlisle, Pennsylvania. The station has a "New Country & The Legends" format, with an emphasis on the local community, as reflected on the official website, boasting "Community-Minded Local Radio. Local Personalities. Local Owners." Effective radiated power Effective radiated power ( ERP ), synonymous with equivalent radiated power ,

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