Decibel - Knowledge (XXG)

3048:

found to be 87 dBA but when the machine is switched off the background noise alone is measured as 83 dBA. the machine noise 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 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:

3528: 4183: 213:(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 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 8258: 3202: 2194:. 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 the quantities 4158:

of μV for microvolt), sometimes it is an acronym for the unit's name ("sm" for square meter, "m" for milliwatt), other times it is a mnemonic for the type of quantity being calculated ("i" for antenna gain with respect to an isotropic antenna, "λ" for anything normalized by the EM wavelength), or otherwise a general attribute or identifier about the nature of the quantity ("A" for

3523:{\displaystyle {\begin{aligned}M_{\text{lm}}(70,90)&=\left(70\,{\text{dBA}}+90\,{\text{dBA}}\right)/2\\&=10\cdot \log _{10}\left({\bigl (}10^{70/10}+10^{90/10}{\bigr )}/2\right)\,{\text{dBA}}\\&=10\cdot \left(\log _{10}{\bigl (}10^{70/10}+10^{90/10}{\bigr )}-\log _{10}2\right)\,{\text{dBA}}\approx 87\,{\text{dBA}}\end{aligned}}} 1703: 233:

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 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.

2937:). 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 is possible to determine the power ratio of a system from the gain in dB with only simple addition and multiplication. For example: 3064:, and can be defined by taking exponentials to convert to 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: 3038:

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 is much more convenient than multiplication of the individual factors."

7461:

Chand, N., Magill, P. D., Swaminathan, S. V., & Daugherty, T. H. (1999). Delivery of digital video and other multimedia services (> 1 Gb/s bandwidth) in passband above the 155 Mb/s baseband services on a FTTx full service access network. Journal of lightwave technology, 17(12),

4157:

Outside of documents adhering to SI units, the practice is very common as illustrated by the following examples. There is no general rule, with various discipline-specific practices. Sometimes the suffix is a unit symbol ("W","K","m"), sometimes it is a transliteration of a unit symbol ("uV" instead

4041:

quoted as 40 dB represents a ratio of 100:1 between optical signal intensity and optical-equivalent dark-noise intensity, not a 10,000:1 intensity (power) ratio as 40 dB might suggest. Sometimes the 20 log ratio definition is applied to electron counts or photon counts directly, which

240:

decibels when they are in the ratio of 10. The number of transmission units expressing 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

90:

The unit represents a relative value, expressed as a ratio. The relative value can sometimes represent an absolute value by using a fixed reference value in the denominator; when used in this way, the unit symbol is often suffixed with letter codes that indicate the reference value. For example, for

5289:

represents an audio level measurement, typically in a telephone circuit, relative to a -90 dBm reference level, with the measurement of this level frequency-weighted by a standard C-message weighting filter. The C-message weighting filter was chiefly used in North America. The Psophometric filter

4640:

to sound, although the measurement is still in dB (SPL). These measurements usually refer to noise and its effects on humans and other animals, and they are widely used in industry while discussing noise control issues, regulations and environmental standards. Other variations that may be seen

3047:

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 the noise from a machine is measured (including the contribution of background noise) and

5978:

2868:

The decibel is useful for representing large ratios and for simplifying representation of multiplicative effects, such as attenuation from multiple sources along a signal chain. Its application in systems with additive effects is less intuitive, such as in the combined sound pressure level of two

232:

Since 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

3196: 4045:

However, as mentioned above, the 10 log intensity convention prevails more generally in physical optics, including fiber optics, so the terminology can become murky between the conventions of digital photographic technology and physics. Most commonly, quantities called "dynamic range" or

6140:"When one gives the value of a quantity, any information concerning the quantity or its conditions of measurement must be presented in such a way as not to be associated with the unit. This means that quantities must be defined so that they can be expressed solely in acceptable units..." 4046:"signal-to-noise" (of the camera) would be specified in 20 log dB, but in related contexts (e.g. attenuation, gain, intensifier SNR, or rejection ratio) the term should be interpreted cautiously, as confusion of the two units can result in very large misunderstandings of the value. 1335: 4782:

of a signal compared with the maximum which a device can handle before clipping occurs. In digital systems, 0 dBTP would equal the highest level (number) the processor is capable of representing. Measured values are always negative or zero, since they are less than or equal to

114:

of the root-power quantity 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.

4153:

relative to 1 μV/m reference value. If the measurement result 20 dB is presented separately, it can be specified using the information in parentheses, which is then part of the surrounding text and not a part of the unit: 20 dB (re: 1 μV/m) or 20 dB (1 μV/m).

2210:

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 a unit of logarithmic power ratio, while the neper is used for logarithmic root-power (amplitude) ratio.

4069:

This form of attaching suffixes to dB is widespread in practice, albeit being against the rules promulgated by standards bodies (ISO and IEC), given the "unacceptability of attaching information to units" and the "unacceptability of mixing information with units". The

1533: 4029:, decibels generally represent ratios of video voltages or digitized light intensities, using 20 log of the ratio, even when the represented intensity (optical power) is directly proportional to the voltage generated by the sensor, not to its square, as in a 6131:"When one gives the value of a quantity, it is incorrect to attach letters or other symbols to the unit in order to provide information about the quantity or its conditions of measurement. Instead, the letters or other symbols should be attached to the quantity." 2474: 3854:

in sound reception. The ratio of the sound intensity that causes permanent damage during short exposure to that of the quietest sound that the ear can hear is equal to or greater than 1 trillion (10). Such large measurement ranges are conveniently expressed in

2588: 3859:: the base-10 logarithm of 10 is 12, which is expressed as a sound intensity level of 120 dB re 1 pW/m. The reference values of I and p in air have been chosen such that this corresponds approximately to a sound pressure level of 120 dB re 20 2712: 4404: 2950:

Calculated precisely, the output is 1 W × 10 ≈ 316.2 W. The approximate value has an error of only +0.4% with respect to the actual value, which is negligible given the precision of the values supplied and the accuracy of most measurement

3730: 1885: 4065:

In cases where the unit value of the reference is stated, the decibel value is known as "absolute". If the unit value of the reference is not explicitly stated, as in the dB gain of an amplifier, then the decibel value is considered relative.

5766: 186:

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

3845: 4307: 2941:

A system consists of 3 amplifiers in series, with gains (ratio of power out to in) of 10 dB, 8 dB, and 7 dB respectively, for a total gain of 25 dB. Broken into combinations of 10, 3, and 1 dB, this is:

4546:

networks, where the nominal strength of a single TV signal at the receiver terminals is about 0 dBmV. Cable TV uses 75 Ω coaxial cable, so 0 dBmV corresponds to −78.75 dBW (−48.75 dBm) or approximately

7251:

Zimmer, Walter MX, Mark P. Johnson, Peter T. Madsen, and Peter L. Tyack. "Echolocation clicks of free-ranging Cuvier’s beaked whales (Ziphius cavirostris)." The Journal of the Acoustical Society of America 117, no. 6 (2005):

3070: 2161: 4798:

dB(Z) – decibel relative to Z = 1 mm⋅m: energy of reflectivity (weather radar), related to the amount of transmitted power returned to the radar receiver. Values above 20 dBZ usually indicate falling

5133: 2039: 1217: 4006:, and the losses, in dB (decibels), of each component (e.g., connectors, splices, and lengths of fiber) are known, the overall link loss may be quickly calculated by addition and subtraction of decibel quantities. 2781: 4809:(RCS) of a target. The power reflected by the target is proportional to its RCS. "Stealth" aircraft and insects have negative RCS measured in dBsm, large flat plates or non-stealthy aircraft have positive values. 3951:

The decibel unit can also be combined with a reference level, often indicated via a suffix, to create an absolute unit of electric power. For example, it can be combined with "m" for "milliwatt" to produce the

3928:) can be calculated simply by summing the decibel gains of the individual components. Similarly, in telecommunications, decibels denote signal gain or loss from a transmitter to a receiver through some medium ( 4578:

referenced to the nominal threshold of human hearing: The measures of pressure (a root-power quantity) use the factor of 20, and the measures of power (e.g. dB SIL and dB SWL) use the factor of 10.

5482:. A signal measured with reference to a full-scale sine-wave appears 3 dB weaker when referenced to a full-scale square wave, thus: 0 dBFS(fullscale sine wave) = −3 dBFS(fullscale square wave). 4766:. A signal measured with reference to a full-scale sine-wave appears 3 dB weaker when referenced to a full-scale square wave, thus: 0 dBFS(fullscale sine wave) = −3 dBFS(fullscale square wave). 2605:

has the same value, 30 dB, regardless of whether it is obtained from powers or from amplitudes, provided that in the specific system being considered power ratios are equal to amplitude ratios squared.

4166:, as in "dB‑Hz", or with a space, as in "dB HL", or enclosed in parentheses, as in "dB(sm)", or with no intervening character, as in "dBm" (which is non-compliant with international standards). 2377: 2495: 4061:

Suffixes are commonly attached to the basic dB unit in order to indicate the reference value by which the ratio is calculated. For example, dBm indicates power measurement relative to 1 milliwatt.

2621: 1772: 1500: 7701:

Tuffentsammer, Karl (1956). "Das Dezilog, eine Brücke zwischen Logarithmen, Dezibel, Neper und Normzahlen" [The decilog, a bridge between logarithms, decibel, neper and preferred numbers].

1527:(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: 1698:{\displaystyle L_{F}=\ln \!\left({\frac {F}{F_{0}}}\right)\,{\text{Np}}=10\log _{10}\!\left({\frac {F^{2}}{F_{0}^{2}}}\right)\,{\text{dB}}=20\log _{10}\left({\frac {F}{F_{0}}}\right)\,{\text{dB}}} 4179:

Since the decibel is defined with respect to power, not amplitude, conversions of voltage ratios to decibels must square the amplitude, or use the factor of 20 instead of 10, as discussed above.

3599:

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

3207: 1939:

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

1340:

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, a decibel is one-tenth of a bel).

4426:.dBu can be used as a measure of voltage, regardless of impedance, but is derived from a 600 Ω load dissipating 0 dBm (1 mW). The reference voltage comes from the computation 4516:. Therefore, many devices offer dual voltage operation (with different gain or "trim" settings) for interoperability reasons. A switch or adjustment that covers at least the range between 4317: 5257: 4461: 7508:

209:

received 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

5220: 5193: 3650: 2905:

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 a series of

4986:

dB(quarterwave) – the gain of an antenna compared to the gain of a quarter wavelength whip. Rarely used, except in some marketing material. 0 dBq = −0.85 dBi

3571: 5652:

dB(relative) – simply a relative difference from something else, which is made apparent in context. The difference of a filter's response to nominal levels, for instance.

5265:

dB(relative) – simply a relative difference from something else, which is made apparent in context. The difference of a filter's response to nominal levels, for instance.

1808: 4726:. In audio and telephony, dBm is typically referenced relative to a 600 Ω impedance, which corresponds to a voltage level of 0.775 volts or 775 millivolts. 1947:

waveform 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

5712: 272:(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 5166: 257: 5680:, with the measurement of this level frequency-weighted by a standard C-message weighting filter. The C-message weighting filter was chiefly used in North America. 4931:

dB optical. A change of 1 dBo in optical power can result in a change of up to 2 dBe in electrical signal power in a system that is thermal noise limited.

5646:

dB(quarterwave) – the forward gain of an antenna compared to a quarter wavelength whip. Rarely used, except in some marketing material. 0 dBq = −0.85 dBi

5050: 269: 236:

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

225: 4502: 4482: 3896:. Similarly to the use in acoustics, a frequency weighted power is often used. For audio noise measurements in electrical circuits, the weightings are called 3772: 4254: 2827:. 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 ± 1107:

Therefore, the bel represents the logarithm of a ratio between two power quantities of 10:1, or the logarithm of a ratio between two root-power quantities of

2723: 8233: 3191:{\displaystyle 87\,{\text{dBA}}\ominus 83\,{\text{dBA}}=10\cdot \log _{10}{\bigl (}10^{87/10}-10^{83/10}{\bigr )}\,{\text{dBA}}\approx 84.8\,{\text{dBA}}} 7647: 5608:

dB optical. A change of 1 dBo in optical power can result in a change of up to 2 dBe in electrical signal power in system that is thermal noise limited.

245:

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 the name

6502:. International Electrotechnical Commission. 19 July 2002. Part 3: Logarithmic and related quantities, and their units. IEC 60027-3, Ed. 3.0. 5047:

occurs. Similar to dBFS, but also applicable to analog systems. According to ITU-T Rec. G.100.1 the level in dBov of a digital system is defined as:

265: 3616:

The human perception of the intensity of sound and light more nearly approximates the logarithm of intensity rather than a linear relationship (see

2083: 1104:. 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. 8297: 7095:"3.3 – What is the difference between dBv, dBu, dBV, dBm, dB SPL, and plain old dB? Why not just use regular voltage and power measurements?" 2909:

stages, can be calculated by summing the gains in decibels of the individual components, rather than multiply the amplification factors; that is,

1953: 1511: 1165: 68: 7312:

Tharr, D. (1998). Case Studies: Transient Sounds Through Communication Headsets. Applied Occupational and Environmental Hygiene, 13(10), 691–697.

4602:

and other liquids, a reference pressure of 1 μPa is used. An RMS sound pressure of one pascal corresponds to a level of 94 dB SPL.

3039:

However, for the same reason that humans excel at additive operation over multiplication, decibels are awkward in inherently additive operations:

1330:{\displaystyle L_{P}={\frac {1}{2}}\ln \!\left({\frac {P}{P_{0}}}\right)\,{\text{Np}}=10\log _{10}\!\left({\frac {P}{P_{0}}}\right)\,{\text{dB}}} 170:

The decibel originates from methods used to quantify signal loss in telegraph and telephone circuits. Until the mid-1920s, the unit for loss was

6058: 7094: 7198: 7171: 7077: 7050: 7021: 6994: 6967: 6907: 6584: 6337: 6287: 6210: 5519:

isotropic antenna. There is no fixed conversion rule between dBiC and dBi, as it depends on the receiving antenna and the field polarization.

4980:

isotropic antenna. There is no fixed conversion rule between dBiC and dBi, as it depends on the receiving antenna and the field polarization.

4661: = x dB. Nevertheless, the units dBA and dB(A) are still commonly used as a shorthand for A‑weighted measurements. Compare 8292: 7625: 2869:

machines operating together. Care is also necessary with decibels directly in fractions and with the units of multiplicative operations.

2063:

For differences in level, the required relationship is relaxed from that above to one of proportionality (i.e., the reference quantities

2060:

is frequency- or time-dependent, this relationship does not hold in general, for example if the energy spectrum of the waveform changes.

2814: dB, but this is almost universally rounded to 3 dB in technical writing. This implies an increase in voltage by a factor of 7949: 7420: 7297: 7496: 4508:, equipment may be calibrated to indicate a "0" on the VU meters some finite time after a signal has been applied at an amplitude of 7797: 7513: 6940: 6852:

Chapman, D. M., & Ellis, D. D. (1998). Elusive decibel: Thoughts on sonars and marine mammals. Canadian Acoustics, 26(2), 29-31.

5024: 4683:

as defined in ANSI and other standards, such that the resulting audiogram shows deviation from what is regarded as 'normal' hearing.

3874:

being the most common standard) to get the weighted acoustic power before converting to a sound level or noise level in decibels.

6479: 4224:

relative to 1 volt, regardless of impedance. This is used to measure microphone sensitivity, and also to specify the consumer

7363: 7137: 4828:, this indicates the relative levels of noise or sideband power, compared with the carrier power. Compare dBC, used in acoustics. 8139: 5019:

dB(Hz) – bandwidth relative to one hertz. E.g., 20 dB‑Hz corresponds to a bandwidth of 100 Hz. Commonly used in

3929: 2881:

nature of the decibel means that a very large range of ratios can be represented by a convenient number, in a manner similar to

2202:, which allows elimination of the frequency dependence in the analysis by analyzing the system at each frequency independently. 1714: 1442: 102:

Two principal types of scaling of the decibel are in common use. When expressing a power ratio, it is defined as ten times the

4565:

relative to 1 microvolt. Widely used in television and aerial amplifier specifications. 60 dBμV = 0 dBmV.

4042:

are proportional to sensor signal amplitude without the need to consider whether the voltage response to intensity is linear.

8243: 6702: 6559: 2968: 2959:

than to modern digital processing, and is cumbersome and difficult to interpret. Quantities in decibels are not necessarily

3024:. However, the linear-scale units still simplify in the implied fraction, so that the results would be expressed in dB-Hz. 7958: 7729: 7337: 6381: 6066: 4735: 3978:. When used in a 600-ohm circuit (historically, the standard reference impedance in telephone circuits), dBu and dBm are 3640:. The reference pressure for sound in air is set at the typical threshold of perception of an average human and there are 261: 7764: 7436: 7067: 5625: 5471: 5044: 4755: 1184: 1060: 76: 6263: 4860:. In the radio field, dBm is usually referenced to a 50 Ω load, with the resultant voltage being 0.224 volts. 2469:{\displaystyle L_{G}=10\log _{10}\left({\frac {1\,000\,{\text{W}}}{1\,{\text{W}}}}\right)\,{\text{dB}}=30\,{\text{dB}}} 7679: 3760:

Use of the decibel in underwater acoustics leads to confusion, in part because of this difference in reference value.

2583:{\displaystyle L_{G}=20\log _{10}\left({\frac {31.62\,{\text{V}}}{1\,{\text{V}}}}\right)\,{\text{dB}}=30\,{\text{dB}}} 6261:

Thompson and Taylor 2008, Guide for the Use of the International System of Units (SI), NIST Special Publication SP811

2044:

holding. In a nonlinear system, this relationship does not hold by the definition of linearity. However, even in a

264:(SI), but decided against the proposal. However, the decibel is recognized by other international bodies such as the 7389: 7262: 2955:

However, according to its critics, the decibel creates confusion, obscures reasoning, is more related to the era of

8287: 4613: 2897:. For example, 120 dB SPL may be clearer than "a trillion times more intense than the threshold of hearing". 2707:{\displaystyle L_{G}=10\log _{10}\left({\frac {10{\text{W}}}{0.001{\text{W}}}}\right)\,{\text{dB}}=40\,{\text{dB}}} 6680:

Andrew Clennel Palmer (2008), Dimensional Analysis and Intelligent Experimentation, World Scientific, 154 pp, p.13

3866:

Since the human ear is not equally sensitive to all sound frequencies, the acoustic power spectrum is modified by

3603:, e.g., a 100-meter run with a 3.5 dB/km fiber yields a loss of 0.35 dB = 3.5 dB/km × 0.1 km. 110:

by a factor of 10 corresponds to a 10 dB change in level. When expressing root-power quantities, a change in

6034:, in millibels (one hundredth of a decibel). 100 mBm = 1 dBm. This unit is in the Wi-Fi drivers of the 4690: 4399:{\displaystyle 20\cdot \log _{10}\left({\frac {1\,V_{\text{RMS}}}{{\sqrt {0.6}}\,V}}\right)=2.218\,{\text{dBu}}.} 3956:". A power level of 0 dBm corresponds to one milliwatt, and 1 dBm is one decibel greater (about 1.259 mW). 2314: 1068: 6659:

Hickling, R. (2006). Decibels and octaves, who needs them?. Journal of sound and vibration, 291(3-5), 1202-1207.

5294:

to see a comparison of frequency response curves for the C-message weighting and Psophometric weighting filters.

8197: 5332: 4680: 3925: 39: 3766:

is proportional to the square of sound pressure. Therefore the sound intensity level can also be defined as:

1516:

When referring to measurements of root-power quantities, it is usual to consider the ratio of the squares of

130:, but the bel is seldom used. Instead, the decibel is used for a wide variety of measurements in science and 8302: 8238: 6871: 6107: 5871: 5225: 4867: 4147: 2960: 7942: 6007: 5530: 5291: 5028: 4993: 4845: 4430: 3897: 3596: 2986: 2354:

The unit dBW is often used to denote a ratio for which the reference is 1 W, and similarly dBm for a

2195: 3617: 7790: 7661: 5975: 5912: 5516: 5431: 4977: 4963: 4637: 4609: 4034: 2166:

must hold to allow the power level difference to be equal to the root-power level difference from power

218: 159: 127: 3725:{\displaystyle L_{p}=20\log _{10}\!\left({\frac {p_{\text{rms}}}{p_{\text{ref}}}}\right)\,{\text{dB}},} 6282:(7th ed.). New York: The Institute of Electrical and Electronics Engineering. 2000. p. 288. 3644:. As sound pressure is a root-power quantity, the appropriate version of the unit definition is used: 1155:

The method of expressing a ratio as a level in decibels depends on whether the measured property is a

6618: 6169: 5922: 5198: 5171: 4599: 4587: 4575: 3637: 3600: 3061: 3033: 2964: 2057: 1943:

in the respective levels match under restricted conditions such as when the medium is linear and the

1880:{\displaystyle L_{G}=20\log _{10}\!\left({\frac {V_{\text{out}}}{V_{\text{in}}}}\right)\,{\text{dB}}} 1790: 35: 7598: 6668:

Nicholas P. Cheremisinoff (1996) Noise Control in Industry: A Practical Guide, Elsevier, 203 pp, p.

4182: 8223: 6900:

The Impact of A-weighting Sound Pressure Level Measurements during the Evaluation of Noise Exposure

6759: 6609:

I M Mills; B N Taylor; A J Thor (2001), "Definitions of the units radian, neper, bel and decibel",

6308: 5761:{\displaystyle {\sqrt {0.6}}\,{\text{V}}\,\approx 0.7746\,{\text{V}}\,\approx -2.218\,{\text{dBV}}} 5677: 5506: 4953: 4806: 3867: 3540: 3049: 2882: 2835: 1064: 56: 6898: 2834:

Should it be necessary to make the distinction, the number of decibels is written with additional

1152:. Thus, five one-thousandths of a bel would normally be written 0.05 dB, and not 5 mB. 8282: 7916: 7239: 7116: 6634: 6454: 6077: 6048: 5404:, this indicates the relative levels of noise or sideband power, compared with the carrier power. 5401: 4825: 4505: 3909: 3053: 1778: 1351:

must measure the same type of quantity, and have the same units before calculating the ratio. If

188: 151: 1117:

Two signals whose levels differ by one decibel have a power ratio of 10, which is approximately

276:, which justifies the use of the decibel for voltage ratios. In spite of their widespread use, 7621: 6519:

Thompson, A. and Taylor, B. N. sec 8.7, "Logarithmic quantities and units: level, neper, bel",

5138: 4654: 8261: 8147: 7935: 7854: 7641: 7526: 7509: 7473: 7416: 7293: 7194: 7167: 7073: 7046: 7017: 7011: 6990: 6984: 6963: 6957: 6936: 6827: 6793: 6776: 6742: 6698: 6580: 6555: 6400: 6333: 6283: 6206: 6202: 5932: 5837: 5557: 5502: 5308: 4949: 4793: 4623: 3856: 3633: 3589: 2878: 2199: 1188: 1078: 118:

The definition of the decibel originated in the measurement of transmission loss and power in

72: 7574: 7550: 7188: 7038: 6810: 6694: 6499: 6323: 7901: 7842: 7837: 7783: 6669: 6626: 6446: 6353: 6234: 6092: 5971: 5856: 5801: 5702: 5594: 5343: 4633: 4557: 4543: 4534: 4311: 4244: 4216: 3964: 3743: 3534: 2807: 2053: 1898: 1786: 103: 5925:) – for sound in air and other gases, relative to 20 μPa in air or 1 μPa in water 1793:

is constant. Taking voltage as an example, this leads to the equation for power gain level

8014: 6267: 5661: 5328: 5274: 4014: 3840:{\displaystyle L_{p}=10\log _{10}\!\left({\frac {I}{I_{\text{ref}}}}\right)\,{\text{dB}},} 3763: 1179: 7759: 7289: 7282: 5676:

represents an audio level measurement, typically in a telephone circuit, relative to the

4574:

Probably the most common usage of "decibels" in reference to sound level is dB SPL,

4302:{\displaystyle V={\sqrt {600\,\Omega \cdot 0.001\,{\text{W}}}}\approx 0.7746\,{\text{V}}} 7760:

Conversion of sound level units: dBSPL or dBA to sound pressure p and sound intensity J

6861:

C. S. Clay (1999), Underwater sound transmission and SI units, J Acoust Soc Am 106, 3047

6622: 6472: 6173: 8167: 8099: 7359: 7141: 6572: 6072: 6020: 5696:

of a signal compared with the maximum which a device can handle before clipping occurs.

5693: 5624:

of a signal (usually audio) compared with the maximum which a device can handle before

5435: 5043:

of a signal (usually audio) compared with the maximum which a device can handle before

5003: 4967: 4779: 4679:

as a measure of hearing loss. The reference level varies with frequency according to a

4487: 4467: 4191: 3908:

In electronics, the decibel is often used to express power or amplitude ratios (as for

3878: 3641: 3044: 147: 6540:. International Electrotechnical Commission. Part 3: Logarithmic quantities and units. 4976:

dB(isotropic circular) – the gain of an antenna compared to the gain of a theoretical

8276: 8228: 8152: 8089: 8079: 7321: 6638: 6195: 5379: 4672: 4038: 4003: 3937: 3860: 3851: 3585: 2893: 2045: 1916: 1135: 249:

for "standard magnitudes which combine by multiplication", to contrast with the name

6458: 6069:(Ldl), European and American standards for expressing noise level over an entire day 2048:

in which the power quantity is the product of two linearly related quantities (e.g.

8172: 8129: 8114: 8069: 8049: 7966: 7911: 7827: 6832: 6815: 6798: 6781: 6764: 6747: 6630: 6405: 6053: 5498: 5336: 4945: 4026: 3991: 3941: 3893: 6305:

Transmission Circuits for Telephonic Communication: Methods of analysis and design

3920:. One advantage is that the total decibel gain of a series of components (such as 6357: 4590:) – for sound in air and other gases, relative to 20 micropascals (μPa), or 8044: 7999: 7906: 7849: 7112: 6379:

Martin, W. H. (January 1929). "DeciBel—The New Name for the Transmission Unit".

6329: 5984: 5479: 5020: 4763: 4646: 4159: 4071: 3945: 3871: 3754: 3581: 281: 191: 155: 143: 135: 131: 123: 7715: 7333: 7224:

IEC 61672-1:2013 Electroacoustics - Sound Level meters - Part 1: Specifications

1020:

ISO 80000-3 describes definitions for quantities and units of space and time.

7600:

Reference Data for Engineers: Radio, Electronics, Computers and Communications

7497:

The use of the decibel and of relative levels in speechband telecommunications

7122: 5488: 5463: 4879: 4747: 4225: 4030: 4010: 3913: 2967:". Thus, units require special care in decibel operations. Take, for example, 2956: 2786:

A change in power ratio by a factor of 10 corresponds to a change in level of

2156:{\displaystyle {\frac {P_{2}}{P_{1}}}=\left({\frac {F_{2}}{F_{1}}}\right)^{2}} 199: 195: 4649:. According to standards from the International Electro-technical Committee ( 2853:. Similarly, an increase of 6.000 dB corresponds to the power ratio is 1191:

of the ratio of the measured quantity to reference value. Thus, the ratio of

8109: 8024: 7769: 6524: 6450: 6260: 6031: 5896: 5875: 5621: 5569: 5475: 5467: 5451: 5128:{\displaystyle L_{\text{ov}}=10\log _{10}\left({\frac {P}{P_{0}}}\right)\ ,} 5040: 4896: 4882: 4871: 4857: 4759: 4751: 4723: 4676: 4650: 3933: 3921: 3889: 3629: 3592: 2906: 2887: 2034:{\displaystyle {\frac {P(t)}{P_{0}}}=\left({\frac {F(t)}{F_{0}}}\right)^{2}} 1024: 206: 139: 119: 1211:, that ratio expressed in decibels, which is calculated using the formula: 260:(CIPM) considered a recommendation for the inclusion of the decibel in the 4844:. 1 joule = 1 watt second = 1 watt per hertz, so 3967:

voltage which delivers 1 mW (0 dBm) into a 600-ohm resistor, or

2885:. This allows one to clearly visualize huge changes of some quantity. See 1027:

defines the following quantities. The decibel (dB) is one-tenth of a bel:

178:(approximately 1.6 km) of standard telephone cable at a frequency of 7989: 7754: 7266: 7213:

Morfey, C. L. (2001). Dictionary of Acoustics. Academic Press, San Diego.

6650:

R. Hickling (1999), Noise Control and SI Units, J Acoust Soc Am 106, 3048

6082: 5540: 4916: 4423: 4203: 4050: 7775: 7722:

Logarithms, preferred numbers, decibel, neper, phon - naturally related!

6521:

Guide for the Use of the International System of Units (SI) 2008 Edition

4406:

Originally dBv, it was changed to dBu to avoid confusion with dBV. The

4310:(i.e. the voltage that would dissipate 1 mW into a 600 Ω load). An 3642:

common comparisons used to illustrate different levels of sound pressure

2944:

25 dB = 10 dB + 10 dB + 3 dB + 1 dB + 1 dB

221:. The bel is seldom used, as the decibel was the proposed working unit. 8177: 8104: 8034: 8029: 7979: 5470:

of a signal compared with the maximum which a device can handle before

4754:

of a signal compared with the maximum which a device can handle before

4232:, in order to reduce manufacturing costs relative to equipment using a 3917: 2049: 1782: 5515:

dB(isotropic circular) – the forward gain of an antenna compared to a

4512:. Consumer equipment typically uses a lower "nominal" signal level of 2776:{\displaystyle G=10^{\frac {3}{10}}\times 1=1.995\,26\ldots \approx 2} 8192: 8094: 8004: 7984: 7974: 6418:

Harrison, William H. (1931). "Standards for Transmission of Speech".

6011: 5831: 5553: 5474:

occurs. Full-scale may be defined as the power level of a full-scale

5304: 4758:

occurs. Full-scale may be defined as the power level of a full-scale

4163: 3995: 2995:(in W/Hz). Expressed in decibels, this ratio would be a subtraction ( 2215:

Conversion between units of level and a list of corresponding ratios

183: 17: 7385: 6523:, NIST Special Publication 811, 2nd printing (November 2008), SP811 241:

expressing the efficiency of different parts of the circuit ...

30:

This article is about the logarithmic unit. For use of this unit in

7717:

Logarithmen, Normzahlen, Dezibel, Neper, Phon - natürlich verwandt!

224:

The naming and early definition of the decibel is described in the

8207: 8202: 8187: 8064: 8059: 8054: 8039: 7994: 6087: 6035: 5965: 5961: 5957: 5953: 5949: 5945: 5879: 5526: 5421: 5411: 5389: 5369: 4875: 4841: 4689:

sometimes used to denote weighted noise level, commonly using the

4181: 2230: 1140: 1042: 31: 8182: 8124: 8119: 7880: 7875: 7236: 7164:

The IEEE Standard Dictionary of Electrical and Electronics terms

6112: 6102: 6019:

dB(m) – decibel relative to reciprocal of meter: measure of the

5861: 5822: 5806: 5705: 5655: 5599: 5575: 5457: 5268: 5034: 5002:

dB(m) – decibel relative to reciprocal of meter: measure of the

4906: 4741: 4729: 4562: 4539: 4247: 4221: 4199: 4049:

Photographers typically use an alternative base-2 log unit, the

273: 175: 92: 7931: 7779: 5195:. The level of a tone with a digital amplitude (peak value) of 2842:, about 0.24% different from exactly 2, and a voltage ratio of 2596:, illustrating the consequence from the definitions above that 1908:

is the rms input voltage. A similar formula holds for current.

1416:

Rearranging the above equation gives the following formula for

8157: 8084: 8074: 7865: 7821: 7437:"The dBμ vs. dBu Mystery: Signal Strength vs. Field Strength?" 6897:

Richard L. St. Pierre, Jr. and Daniel J. Maguire (July 2004),

5563: 5395: 5323: 4851: 4819: 4717: 4662: 4542:

relative to 1 millivolt across 75 Ω. Widely used in

4195: 4187: 4033:

where response voltage is linear in intensity. Thus, a camera

3999: 3960: 3953: 1781:, dissipated power is typically proportional to the square of 79:

differ by one decibel have a power ratio of 10 (approximately

7043:

Image sensors and signal processing for digital still cameras

4992:

dB(m) – decibel relative to one square meter: measure of the

4878:. The unit is often used to specify the signal strength of a 4805:

dB(m) – decibel relative to one square meter: measure of the

174:(MSC). 1 MSC corresponded to the loss of power over one 7552:

Comprehensive Glossary of Telecom Abbreviations and Acronyms

6933:

Subscriber Loop Signaling and Transmission Handbook – Analog

6878:. Centers for Disease Control and Prevention. 7 October 2019 6426:. National Bureau of Standards, U. S. Govt. Printing Office. 5970:

These symbols are often used to denote the use of different

4632:

These symbols are often used to denote the use of different

4162:

sound pressure level). The suffix is often connected with a

3959:

In professional audio specifications, a popular unit is the

27:

Logarithmic unit expressing the ratio of physical quantities

7927: 6280:

IEEE Standard 100: a dictionary of IEEE standards and terms

6178:

the decibel represents a reduction in power of 1.258 times

6097: 4598:, approximately the quietest sound a human can hear. For 1767:{\displaystyle F=10^{\frac {L_{F}}{20\,{\text{dB}}}}F_{0}} 1495:{\displaystyle P=10^{\frac {L_{P}}{10\,{\text{dB}}}}P_{0}} 7226:. Geneva: International Electrotechnical Committee. 2013. 7069:

The Audio Expert: Everything You Need to Know About Audio

5580:

Power in dBm measured at a zero transmission level point.

5290:

is used for this purpose on international circuits. See

5505:, which uniformly distributes energy in all directions. 4952:, which uniformly distributes energy in all directions. 2838:. 3.000 dB corresponds to a power ratio of 10, or 6201:(Second ed.). Holt, Rinehart and Winston. p. 4053:, to describe light intensity ratios or dynamic range. 1134:

The bel is rarely used either without a prefix or with

6777:

Visual Perception: Physiology, Psychology, and Ecology

6536:"Letter symbols to be used in electrical technology". 5168:, for a rectangular signal with the maximum amplitude 1124:, and an amplitude (root-power quantity) ratio of 10 ( 1077:, thereby relating all of the units as nondimensional 5715: 5228: 5201: 5174: 5141: 5053: 4490: 4470: 4433: 4320: 4257: 3775: 3653: 3543: 3205: 3073: 2946:

With an input of 1 watt, the output is approximately

2726: 2624: 2498: 2380: 2086: 1956: 1811: 1717: 1536: 1445: 1220: 253:

for "standard magnitudes which combine by addition".

7662:"en:users:documentation:iw [Linux Wireless]" 6732:, Routledge, 12 November 2013, 400 pages, p. 13 6500:"Letter symbols to be used in electrical technology" 3573:, since logarithmic division is linear subtraction. 3537:

is obtained from the logarithmic sum by subtracting

2948:

1 W × 10 × 10 × 2 × 1.26 × 1.26 ≈ 317.5 W

1067:

when the root-power quantity changes by a factor of

126:

in the United States. The bel was named in honor of

8216: 8138: 8013: 7965: 5317:dB(K) – decibels relative to 1 K. — 4532:

Defined by Recommendation ITU-R V.574.; dBmV: dB(mV

7755:What is a decibel? With sound files and animations 7528:Satellite Communication: Concepts And Applications 7281: 6983:Stephen J. Sangwine and Robin E. N. Horne (1998). 6194: 5760: 5509:of the EM field is assumed unless noted otherwise. 5251: 5214: 5187: 5160: 5127: 4956:of the EM field is assumed unless noted otherwise. 4496: 4476: 4455: 4398: 4301: 3839: 3724: 3565: 3522: 3190: 2775: 2706: 2582: 2468: 2155: 2033: 1879: 1766: 1697: 1494: 1329: 277: 198:per mile" (approximately corresponding to 19 6437:Horton, J. W. (1954). "The bewildering decibel". 5529:. 1 joule = 1 watt second = 1 watt per hertz, so 4653:) and the American National Standards Institute, 3802: 3680: 2198:and the associated root-power quantities via the 1838: 1601: 1553: 1295: 1247: 7016:. Cambridge University Press. pp. 102–103. 6760:Introduction to Understandable Physics, Volume 2 5640:relative to the maximum value of the peak power. 4834:relative to the maximum value of the peak power. 4612:– relative to 10 W/m, which is roughly the 3879:Sound pressure § Examples of sound pressure 1935:Relationship between power and root-power levels 258:International Committee for Weights and Measures 7765:OSHA Regulations on Occupational Noise Exposure 7680:"Is your WiFi AP Missing Channels 12 & 13?" 7240:S1.4-19823 Specification for Sound Level Meters 6478:. Consultative Committee for Units. Section 3. 3753:is the standard reference sound pressure of 20 2963:, thus being "of unacceptable form for use in 230: 6962:. McGraw-Hill Professional. pp. 123–126. 4122:is the value of the reference quantity, e.g., 4002:(referenced to 1 mW), is launched into a 2790:. A change in power ratio by a factor of 2 or 2618:(one milliwatt) is obtained with the formula: 284:or dBV) are not recognized by the IEC or ISO. 270:International Organization for Standardization 7943: 7791: 7475:EW 102: A Second Course in Electronic Warfare 6494: 6492: 5905:sometimes used to denote weighted noise level 4734:Power in dBm (described above) measured at a 4314:voltage of 1 V therefore corresponds to 4186:A schematic showing the relationship between 3469: 3423: 3363: 3317: 3165: 3119: 217:, in honor of the telecommunications pioneer 67:). It expresses the ratio of two values of a 8: 7118:Creation of the dBu standard level reference 7010:Francis T. S. Yu and Xiangyang Yang (1997). 5809:relative to 1 volt, regardless of impedance. 5686:dB(m) – decibel relative to one square meter 5634:relative to the peak to peak sound pressure. 4698:relative to the peak to peak sound pressure. 3043:if two machines each individually produce a 8234:Historical definitions of the SI base units 6515: 6513: 6511: 6509: 5842:dB(Z) – decibel relative to Z = 1 mm⋅m 2901:Representation of multiplication operations 83:) or root-power ratio of 10 (approximately 7950: 7936: 7928: 7798: 7784: 7776: 6217:a pressure ratio of 1.122 equals + 1.0 dB 6038:kernel and the regulatory domain sections. 4074:standard recommends the following format: 3060:Addition on a logarithmic scale is called 1183:quantities, a ratio can be expressed as a 291: 7870: 7597:Mac E. Van Valkenburg (19 October 2001). 5753: 5752: 5742: 5737: 5736: 5729: 5724: 5723: 5716: 5714: 5244: 5227: 5206: 5200: 5179: 5173: 5146: 5140: 5114: 5096: 5087: 5074: 5058: 5052: 4885:at a receiving site (the signal measured 4489: 4469: 4440: 4432: 4388: 4387: 4370: 4363: 4355: 4350: 4344: 4331: 4319: 4294: 4293: 4280: 4279: 4269: 4264: 4256: 3829: 3828: 3816: 3807: 3796: 3780: 3774: 3714: 3713: 3701: 3691: 3685: 3674: 3658: 3652: 3620:), making the dB scale a useful measure. 3551: 3542: 3511: 3510: 3499: 3498: 3481: 3468: 3467: 3457: 3453: 3436: 3432: 3422: 3421: 3412: 3382: 3381: 3368: 3362: 3361: 3351: 3347: 3330: 3326: 3316: 3315: 3301: 3273: 3263: 3262: 3251: 3250: 3214: 3206: 3204: 3183: 3182: 3171: 3170: 3164: 3163: 3153: 3149: 3132: 3128: 3118: 3117: 3108: 3090: 3089: 3078: 3077: 3072: 2760: 2737: 2725: 2699: 2698: 2687: 2686: 2674: 2664: 2658: 2645: 2629: 2623: 2575: 2574: 2563: 2562: 2550: 2549: 2539: 2538: 2532: 2519: 2503: 2497: 2461: 2460: 2449: 2448: 2436: 2435: 2425: 2424: 2420: 2414: 2401: 2385: 2379: 2147: 2135: 2125: 2119: 2103: 2093: 2087: 2085: 2025: 2013: 1993: 1977: 1957: 1955: 1872: 1871: 1859: 1849: 1843: 1832: 1816: 1810: 1758: 1745: 1744: 1734: 1728: 1716: 1690: 1689: 1677: 1668: 1655: 1640: 1639: 1627: 1622: 1612: 1606: 1595: 1580: 1579: 1567: 1558: 1541: 1535: 1486: 1473: 1472: 1462: 1456: 1444: 1322: 1321: 1309: 1300: 1289: 1274: 1273: 1261: 1252: 1234: 1225: 1219: 266:International Electrotechnical Commission 7360:"RIDGE Radar Frequently Asked Questions" 6229: 6227: 6225: 6197:Fundamentals of Hearing: An Introduction 6166:Physical Properties of Polymers Handbook 6000:dB(Hz) – bandwidth relative to one hertz 4948:compared with the gain of a theoretical 2213: 1187:in decibels by evaluating ten times the 7885: 6408:, Robert J. Chapuis, Amos E. Joel, 2003 6188: 6186: 6153: 6124: 4814:Radio power, energy, and field strength 2077:need not be related), or equivalently, 1512:Power, root-power, and field quantities 1166:Power, root-power, and field quantities 1144:; it is preferred, for example, to use 7646:: CS1 maint: archived copy as title ( 7639: 7190:Audio postproduction for digital video 6159: 6157: 5974:, used to approximate the human ear's 5775:Defined by Recommendation ITU-R V.574. 5586:Defined by Recommendation ITU-R V.574. 5355:List of suffixes in alphabetical order 5252:{\displaystyle L=-3.01\ {\text{dBov}}} 4636:, used to approximate the human ear's 3028:Representation of addition operations 1708:The formula may be rearranged to give 994:An example scale showing power ratios 7735:from the original on 18 December 2016 6913:from the original on 22 December 2015 4025:In connection with video and digital 2362:Calculating the ratio in decibels of 300: 297: 7: 6986:The Colour Image Processing Handbook 6959:Fiber optic installer's field manual 6552:Fiber Optics: Physics and Technology 6485:from the original on 6 October 2014. 5602:relative to 1 millivolt across 75 Ω. 5430:dB(dipole) – the forward gain of an 5346:system noise equivalent temperature 5303: – decibels relative to 1 4524:is common in professional equipment. 4456:{\displaystyle V={\sqrt {R\cdot P}}} 2981:(in hertz), involving carrier power 1202:(reference power) is represented by 7284:Understanding Telephone Electronics 7013:Introduction to optical engineering 6872:"Loud Noise Can Cause Hearing Loss" 6579:(3rd ed.). Wiley. p. 63. 6538:International Standard CEI-IEC 27-3 6322:Davis, Don; Davis, Carolyn (1997). 4966:compared with the gain a half-wave 4657:, the preferred usage is to write L 3746:of the measured sound pressure and 2716:The power ratio corresponding to a 1927:is deprecated by that standard and 7714:Paulin, Eugen (1 September 2007). 7525:K. N. Raja Rao (31 January 2013). 7366:from the original on 31 March 2019 7340:from the original on 8 August 2019 5321:decibels per kelvin: Used for the 4915:dB(kW) – power relative to 1 4895:dB(fW) – power relative to 1 4856:dB(mW) – power relative to 1 4722:dB(mW) – power relative to 1 4270: 3757:in air or 1 micropascal in water. 1177:When referring to measurements of 25: 7628:from the original on 3 March 2016 7576:The Digital Satellite TV Handbook 7392:from the original on 10 June 2019 6303:Johnson, Kenneth Simonds (1944). 4970:. 0 dBd = 2.15 dBi 4905:dB(W) – power relative to 1 2810:. More precisely, the change is ± 1931:is used throughout this article. 1059:. The neper is the change in the 162:are often expressed in decibels. 122:of the early 20th century in the 8257: 8256: 7441:radio-timetraveller.blogspot.com 7140:. Deltamedia.com. Archived from 6401:100 Years of Telephone Switching 4009:In spectrometry and optics, the 3628:The decibel is commonly used in 1007:, and dB equivalents 10 log 7772:(RF signal and field strengths) 6093:One-third octave § Base 10 5501:compared with the hypothetical 5215:{\displaystyle x_{\text{over}}} 5188:{\displaystyle x_{\text{over}}} 3979: 2860:, about 0.5% different from 4. 2846:, 0.12% different from exactly 1084:of root-power-quantity ratios, 8298:Telecommunications engineering 8244:System of units of measurement 6989:. Springer. pp. 127–130. 5478:or alternatively a full-scale 5135:with the maximum signal power 5119: 5111: 5025:carrier-to-noise-density ratio 4762:or alternatively a full-scale 4057:Suffixes and reference values 3232: 3220: 2969:carrier-to-noise-density ratio 2005: 1999: 1969: 1963: 1915:is introduced by ISO Standard 91:the reference value of 1 1: 7809: 7166:(6th ed.). IEEE. 1996 . 7045:. CRC Press. pp. 79–83. 7041:. In Junichi Nakamura (ed.). 6828:Fitting The Task To The Human 6382:Bell System Technical Journal 6067:day-night average sound level 6059:Day–evening–night noise level 6030:mB(mW) – power relative to 1 6006:dB(K) – decibels relative to 5899:as a measure of hearing loss. 5568:dB(mW) – power relative to 1 5539:dB(kW) – power relative to 1 5450:dB(fW) – power relative to 1 4736:zero transmission level point 4665:, used in telecommunications. 3584:constants, in topics such as 3566:{\displaystyle 10\log _{10}2} 2720:change in level is given by: 1506:Root-power (field) quantities 262:International System of Units 228:Standard's Yearbook of 1931: 7832: 7336:. National Weather Service. 7263:"Turbine Sound Measurements" 7072:. Focal Press. p. 107. 6935:(1st ed.). IEEE Press. 6240:/ dBm / dBu / dBV calculator 5895:dB hearing level is used in 5887:Suffixes preceded by a space 5821:dB(W) – power relative to 1 5497:dB(isotropic) – the forward 5438:. 0 dBd = 2.15 dBi 4962:dB(dipole) – the gain of an 4713:See also dBV and dBu above. 4134: = 20 dB or 4017:is equivalent to −1 B. 2594:(31.62 V / 1 V) ≈ 1 kW / 1 W 1364:in the above equation, then 96: 69:power or root-power quantity 8293:Radio frequency propagation 7386:"Definition at Everything2" 7193:. Focal Press. p. 25. 6730:Acoustics and Noise Control 5940:Suffixes within parentheses 5023:calculations. Also used in 4115:is the quantity symbol and 3963:. This is relative to the 3595:, are often expressed as a 207:Bell Telephone Laboratories 8319: 7860: 7415:. Newnes. pp. 45–46. 7413:RF Components and Circuits 7242:, 2.3 Sound Level, p. 2–3. 6931:Reeve, William D. (1992). 6168:. Springer. p. 1025. 5434:compared with a half-wave 4840:energy relative to 1 4704:G‑weighted spectrum 4614:threshold of human hearing 4146:= 20 dB for the 3971:1 mW×600 Ω 3876: 3850:The human ear has a large 3031: 1509: 29: 8252: 7894: 7817: 7280:Bigelow, Stephen (2001). 7039:"Basics of Image Sensors" 7037:Junichi Nakamura (2006). 6811:Foundations of Perception 5915:– relative to 10 W/m 5400:relative to carrier – in 5161:{\displaystyle P_{0}=1.0} 5027:(not to be confused with 4824:relative to carrier – in 4691:ITU-R 468 noise weighting 4198:(the power dissipated as 4021:Video and digital imaging 2610:The ratio in decibels of 2478:The ratio in decibels of 993: 294: 99:" (e.g., "20 dBV"). 8198:minute and second of arc 6743:Sensation and Perception 6631:10.1088/0026-1394/38/4/8 6362:Bell Laboratories Record 6358:"'TU' becomes 'Decibel'" 6325:Sound system engineering 5935:– relative to 10 W. 5864:relative to 1 microvolt. 5533:can be expressed in dBJ. 5333:satellite communications 4848:can be expressed in dBJ. 4681:minimum audibility curve 4626:– relative to 10 W. 256:In April 2003, the 59:equal to one tenth of a 40:Decibel (disambiguation) 8239:2019 revision of the SI 6451:10.1109/EE.1954.6438830 6368:(4). AT&T: 137–139. 6164:Mark, James E. (2007). 6108:Richter magnitude scale 5872:electric field strength 5552:– decibels relative to 4868:electric field strength 4148:electric field strength 3994:, if a known amount of 3898:psophometric weightings 3888:The decibel is used in 1146:hundredths of a decibel 172:miles of standard cable 134:, most prominently for 106:. That is, a change in 6439:Electrical Engineering 6193:Yost, William (1985). 5867:dBμV/m, dBuV/m, or dBμ 5762: 5531:power spectral density 5292:Psophometric weighting 5253: 5216: 5189: 5162: 5129: 5029:carrier-to-noise ratio 4994:antenna effective area 4863:dBμV/m, dBuV/m, or dBμ 4846:power spectral density 4498: 4484:is the resistance and 4478: 4457: 4418:comes from the volume 4400: 4303: 4207: 3841: 3726: 3567: 3524: 3192: 3058: 2987:power spectral density 2873:Reporting large ratios 2777: 2708: 2584: 2470: 2196:power spectral density 2157: 2035: 1901:(rms) output voltage, 1881: 1768: 1699: 1496: 1331: 243: 160:signal-to-noise ratios 150:. In electronics, the 104:logarithm with base 10 95:, a common suffix is " 38:. For other uses, see 7770:Working with Decibels 7495:ITU-T Rec. G.100.1, " 7411:Carr, Joseph (2002). 7066:Winer, Ethan (2013). 6956:Chomycz, Bob (2000). 6577:Microwave Engineering 5913:sound intensity level 5763: 5525:energy relative to 1 5360:Unpunctuated suffixes 5254: 5217: 5190: 5163: 5130: 4889:is reported in dBμV). 4887:at the antenna output 4610:sound intensity level 4499: 4479: 4458: 4401: 4304: 4185: 4035:signal-to-noise ratio 3877:Further information: 3842: 3727: 3568: 3525: 3193: 3041: 3032:Further information: 2985:(in watts) and noise 2778: 2709: 2585: 2471: 2158: 2036: 1882: 1769: 1700: 1497: 1332: 219:Alexander Graham Bell 128:Alexander Graham Bell 8140:Other accepted units 7269:on 12 December 2010. 6691:Dimensional Analysis 5923:sound pressure level 5834:relative to 1 W·m·Hz 5713: 5517:circularly polarized 5226: 5199: 5172: 5139: 5051: 4978:circularly polarized 4944:dB(isotropic) – the 4936:Antenna measurements 4588:sound pressure level 4576:sound pressure level 4488: 4468: 4431: 4318: 4255: 3773: 3651: 3638:sound pressure level 3601:dimensional analysis 3541: 3203: 3071: 3062:logarithmic addition 3034:Logarithmic addition 2965:dimensional analysis 2724: 2622: 2496: 2378: 2084: 1954: 1809: 1715: 1534: 1443: 1218: 1195:(measured power) to 75:. Two signals whose 36:Sound pressure level 8224:Conversion of units 7666:wireless.kernel.org 6794:Exercise Psychology 6623:2001Metro..38..353M 6309:D. Van Nostrand Co. 6174:2007ppph.book.....M 5678:circuit noise level 5620:dB(overload) – the 5507:Linear polarization 5039:dB(overload) – the 4954:Linear polarization 4870:relative to 1 4807:radar cross section 3912:) in preference to 3868:frequency weighting 3050:logarithmic average 2883:scientific notation 2836:significant figures 2808:change of 3 dB 2806:is approximately a 2343:10 ≈ 3.162 28 2216: 1919:as a substitute of 1913:root-power quantity 1779:electrical circuits 1632: 1161:root-power quantity 1065:root-power quantity 998:, amplitude ratios 57:unit of measurement 8017:with special names 7917:telecommunications 7443:. 24 February 2015 7288:. Newnes. p. 7125:on 30 October 2021 6763:, p. SA19-PA9, at 6420:Standards Yearbook 6266:2016-06-03 at the 6236:Utilities : V 6078:Decade (log scale) 6049:Apparent magnitude 5758: 5556:: Used to express 5499:gain of an antenna 5402:telecommunications 5307:; used to express 5249: 5212: 5185: 5158: 5125: 5011:Other measurements 4946:gain of an antenna 4826:telecommunications 4506:professional audio 4494: 4474: 4453: 4396: 4299: 4236:line-level signal. 4208: 4202:by the 600 Ω 3837: 3722: 3588:communication and 3563: 3520: 3518: 3188: 3054:arithmetic average 2773: 2704: 2580: 2466: 2366:(one kilowatt, or 2214: 2153: 2031: 1877: 1764: 1695: 1618: 1492: 1327: 34:measurements, see 8288:Audio electronics 8270: 8269: 8148:astronomical unit 7925: 7924: 7549:Ali Akbar Arabi. 7200:978-1-57820-116-7 7187:Jay Rose (2002). 7173:978-1-55937-833-8 7079:978-0-240-82100-9 7052:978-0-8493-3545-7 7023:978-0-521-57493-8 6996:978-0-412-80620-9 6969:978-0-07-135604-6 6718:. Springer. 2010. 6697:, Springer, 2011 6586:978-0-471-44878-5 6554:, Springer, 2010 6473:"Meeting minutes" 6356:(December 1928). 6354:Hartley, R. V. L. 6339:978-0-240-80305-0 6289:978-0-7381-2601-2 6212:978-0-12-772690-8 5972:weighting filters 5933:sound power level 5756: 5740: 5727: 5721: 5558:noise temperature 5503:isotropic antenna 5309:noise temperature 5247: 5243: 5209: 5182: 5117: 5110: 5102: 5061: 4950:isotropic antenna 4709:Audio electronics 4634:weighting filters 4629:dBA, dBB, and dBC 4624:sound power level 4504:is the power. In 4497:{\displaystyle P} 4477:{\displaystyle R} 4451: 4391: 4375: 4368: 4358: 4297: 4285: 4283: 3857:logarithmic scale 3832: 3822: 3819: 3717: 3707: 3704: 3694: 3634:sound power level 3618:Weber–Fechner law 3590:radio propagation 3514: 3502: 3385: 3266: 3254: 3217: 3186: 3174: 3093: 3081: 2879:logarithmic scale 2745: 2702: 2690: 2680: 2677: 2667: 2578: 2566: 2556: 2553: 2542: 2464: 2452: 2442: 2439: 2428: 2358:reference point. 2347: 2346: 2238:Root-power ratio 2200:Fourier transform 2141: 2109: 2019: 1983: 1875: 1865: 1862: 1852: 1751: 1748: 1693: 1683: 1643: 1633: 1583: 1573: 1479: 1476: 1325: 1315: 1277: 1267: 1242: 1189:base-10 logarithm 1031:. The bel (B) is 1023:The IEC Standard 1018: 1017: 211:Transmission Unit 73:logarithmic scale 16:(Redirected from 8310: 8260: 8259: 7952: 7945: 7938: 7929: 7902:logarithmic unit 7800: 7793: 7786: 7777: 7744: 7742: 7740: 7734: 7727: 7710: 7688: 7687: 7676: 7670: 7669: 7658: 7652: 7651: 7645: 7637: 7635: 7633: 7618: 7612: 7611: 7609: 7607: 7594: 7588: 7587: 7585: 7583: 7570: 7564: 7563: 7561: 7559: 7546: 7540: 7539: 7537: 7535: 7522: 7516: 7506: 7500: 7493: 7487: 7486: 7484: 7482: 7469: 7463: 7459: 7453: 7452: 7450: 7448: 7433: 7427: 7426: 7408: 7402: 7401: 7399: 7397: 7382: 7376: 7375: 7373: 7371: 7356: 7350: 7349: 7347: 7345: 7330: 7324: 7319: 7313: 7310: 7304: 7303: 7287: 7277: 7271: 7270: 7265:. Archived from 7259: 7253: 7249: 7243: 7234: 7228: 7227: 7220: 7214: 7211: 7205: 7204: 7184: 7178: 7177: 7160: 7154: 7153: 7151: 7149: 7136:deltamedia.com. 7133: 7127: 7126: 7121:, archived from 7109: 7103: 7102: 7090: 7084: 7083: 7063: 7057: 7056: 7034: 7028: 7027: 7007: 7001: 7000: 6980: 6974: 6973: 6953: 6947: 6946: 6928: 6922: 6921: 6920: 6918: 6912: 6905: 6894: 6888: 6887: 6885: 6883: 6868: 6862: 6859: 6853: 6850: 6844: 6841: 6835: 6824: 6818: 6807: 6801: 6790: 6784: 6773: 6767: 6756: 6750: 6739: 6733: 6726: 6720: 6719: 6712: 6706: 6689:J. C. Gibbings, 6687: 6681: 6678: 6672: 6666: 6660: 6657: 6651: 6648: 6642: 6641: 6606: 6600: 6599:IEC 60027-3:2002 6597: 6591: 6590: 6569: 6563: 6550:Fedor Mitschke, 6548: 6542: 6541: 6533: 6527: 6517: 6504: 6503: 6496: 6487: 6486: 6484: 6477: 6469: 6463: 6462: 6434: 6428: 6427: 6415: 6409: 6397: 6391: 6390: 6376: 6370: 6369: 6350: 6344: 6343: 6328:(2nd ed.). 6319: 6313: 6312: 6300: 6294: 6293: 6276: 6270: 6258: 6252: 6251: 6250: 6248: 6243:, Analog Devices 6231: 6220: 6219: 6200: 6190: 6181: 6180: 6161: 6141: 6138: 6132: 6129: 5832:spectral density 5768: 5767: 5765: 5764: 5759: 5757: 5754: 5741: 5738: 5728: 5725: 5722: 5717: 5692:dB(true peak) – 5258: 5256: 5255: 5250: 5248: 5245: 5241: 5221: 5219: 5218: 5213: 5211: 5210: 5207: 5194: 5192: 5191: 5186: 5184: 5183: 5180: 5167: 5165: 5164: 5159: 5151: 5150: 5134: 5132: 5131: 5126: 5118: 5115: 5108: 5107: 5103: 5101: 5100: 5088: 5079: 5078: 5063: 5062: 5059: 4778:dB(true peak) – 4597: 4595: 4544:cable television 4523: 4519: 4515: 4511: 4503: 4501: 4500: 4495: 4483: 4481: 4480: 4475: 4463: 4462: 4460: 4459: 4454: 4452: 4441: 4405: 4403: 4402: 4397: 4392: 4389: 4380: 4376: 4374: 4369: 4364: 4361: 4360: 4359: 4356: 4345: 4336: 4335: 4309: 4308: 4306: 4305: 4300: 4298: 4295: 4286: 4284: 4281: 4265: 4235: 4231: 4170:List of suffixes 4145: 4133: 4110: 4092: 4013:used to measure 3973: 3972: 3965:root mean square 3944:, etc.) using a 3846: 3844: 3843: 3838: 3833: 3830: 3827: 3823: 3821: 3820: 3817: 3808: 3801: 3800: 3785: 3784: 3744:root mean square 3731: 3729: 3728: 3723: 3718: 3715: 3712: 3708: 3706: 3705: 3702: 3696: 3695: 3692: 3686: 3679: 3678: 3663: 3662: 3572: 3570: 3569: 3564: 3556: 3555: 3535:logarithmic mean 3529: 3527: 3526: 3521: 3519: 3515: 3512: 3503: 3500: 3497: 3493: 3486: 3485: 3473: 3472: 3466: 3465: 3461: 3445: 3444: 3440: 3427: 3426: 3417: 3416: 3390: 3386: 3383: 3380: 3376: 3372: 3367: 3366: 3360: 3359: 3355: 3339: 3338: 3334: 3321: 3320: 3306: 3305: 3284: 3277: 3272: 3268: 3267: 3264: 3255: 3252: 3219: 3218: 3215: 3197: 3195: 3194: 3189: 3187: 3184: 3175: 3172: 3169: 3168: 3162: 3161: 3157: 3141: 3140: 3136: 3123: 3122: 3113: 3112: 3094: 3091: 3082: 3079: 2951:instrumentation. 2924: 2859: 2856: 2852: 2851: 2845: 2841: 2830: 2826: 2823: 2821: 2820: 2813: 2805: 2803: 2802: 2799: 2796: 2789: 2782: 2780: 2779: 2774: 2747: 2746: 2738: 2719: 2713: 2711: 2710: 2705: 2703: 2700: 2691: 2688: 2685: 2681: 2679: 2678: 2675: 2669: 2668: 2665: 2659: 2650: 2649: 2634: 2633: 2617: 2613: 2595: 2589: 2587: 2586: 2581: 2579: 2576: 2567: 2564: 2561: 2557: 2555: 2554: 2551: 2544: 2543: 2540: 2533: 2524: 2523: 2508: 2507: 2491: 2487: 2485: 2484: 2475: 2473: 2472: 2467: 2465: 2462: 2453: 2450: 2447: 2443: 2441: 2440: 2437: 2430: 2429: 2426: 2415: 2406: 2405: 2390: 2389: 2373: 2369: 2365: 2357: 2323: 2322: 2311: 2310: 2298: 2297: 2289: 2288: 2276: 2275: 2267: 2266: 2257: 2256: 2217: 2162: 2160: 2159: 2154: 2152: 2151: 2146: 2142: 2140: 2139: 2130: 2129: 2120: 2110: 2108: 2107: 2098: 2097: 2088: 2040: 2038: 2037: 2032: 2030: 2029: 2024: 2020: 2018: 2017: 2008: 1994: 1984: 1982: 1981: 1972: 1958: 1899:root-mean-square 1886: 1884: 1883: 1878: 1876: 1873: 1870: 1866: 1864: 1863: 1860: 1854: 1853: 1850: 1844: 1837: 1836: 1821: 1820: 1773: 1771: 1770: 1765: 1763: 1762: 1753: 1752: 1750: 1749: 1746: 1739: 1738: 1729: 1704: 1702: 1701: 1696: 1694: 1691: 1688: 1684: 1682: 1681: 1669: 1660: 1659: 1644: 1641: 1638: 1634: 1631: 1626: 1617: 1616: 1607: 1600: 1599: 1584: 1581: 1578: 1574: 1572: 1571: 1559: 1546: 1545: 1501: 1499: 1498: 1493: 1491: 1490: 1481: 1480: 1478: 1477: 1474: 1467: 1466: 1457: 1393:is positive; if 1377:is greater than 1363: 1336: 1334: 1333: 1328: 1326: 1323: 1320: 1316: 1314: 1313: 1301: 1294: 1293: 1278: 1275: 1272: 1268: 1266: 1265: 1253: 1243: 1235: 1230: 1229: 1173:Power quantities 1136:SI unit prefixes 1130: 1129: 1123: 1122: 1113: 1112: 1103: 1101: 1095: 1093: 1087: 1076: 1075:1 Np = ln(e) = 1 1058: 1056: 1055: 1051: 1040: 1039: 1035: 1030: 1006: 1005: 989: 988: 978: 977: 974: 971: 956: 955: 952: 942: 941: 938: 923: 922: 912: 911: 908: 893: 892: 889: 879: 878: 875: 854: 853: 838: 837: 827: 826: 805: 804: 789: 788: 750: 749: 728: 726: 725: 722: 719: 707: 705: 704: 701: 698: 681: 680: 679: 677: 676: 673: 670: 655: 653: 652: 649: 646: 580: 579: 501: 500: 481: 480: 460: 459: 445: 444: 435: 434: 431: 417: 416: 407: 406: 403: 389: 388: 379: 378: 375: 361: 360: 351: 350: 347: 344: 330: 329: 320: 319: 316: 313: 301:Amplitude ratio 292: 181: 158:of signals, and 86: 82: 55:) is a relative 21: 8318: 8317: 8313: 8312: 8311: 8309: 8308: 8307: 8273: 8272: 8271: 8266: 8248: 8229:Metric prefixes 8212: 8134: 8016: 8009: 7961: 7956: 7926: 7921: 7890: 7813: 7804: 7751: 7738: 7736: 7732: 7725: 7713: 7703:VDI-Zeitschrift 7700: 7697: 7695:Further reading 7692: 7691: 7678: 7677: 7673: 7660: 7659: 7655: 7638: 7631: 7629: 7622:"Archived copy" 7620: 7619: 7615: 7605: 7603: 7596: 7595: 7591: 7581: 7579: 7572: 7571: 7567: 7557: 7555: 7548: 7547: 7543: 7533: 7531: 7524: 7523: 7519: 7507: 7503: 7494: 7490: 7480: 7478: 7471: 7470: 7466: 7460: 7456: 7446: 7444: 7435: 7434: 7430: 7423: 7410: 7409: 7405: 7395: 7393: 7384: 7383: 7379: 7369: 7367: 7358: 7357: 7353: 7343: 7341: 7334:"Glossary: D's" 7332: 7331: 7327: 7320: 7316: 7311: 7307: 7300: 7279: 7278: 7274: 7261: 7260: 7256: 7250: 7246: 7235: 7231: 7222: 7221: 7217: 7212: 7208: 7201: 7186: 7185: 7181: 7174: 7162: 7161: 7157: 7147: 7145: 7144:on 20 June 2013 7135: 7134: 7130: 7111: 7110: 7106: 7092: 7091: 7087: 7080: 7065: 7064: 7060: 7053: 7036: 7035: 7031: 7024: 7009: 7008: 7004: 6997: 6982: 6981: 6977: 6970: 6955: 6954: 6950: 6943: 6930: 6929: 6925: 6916: 6914: 6910: 6903: 6896: 6895: 6891: 6881: 6879: 6870: 6869: 6865: 6860: 6856: 6851: 6847: 6842: 6838: 6825: 6821: 6808: 6804: 6791: 6787: 6774: 6770: 6757: 6753: 6740: 6736: 6727: 6723: 6714: 6713: 6709: 6688: 6684: 6679: 6675: 6667: 6663: 6658: 6654: 6649: 6645: 6608: 6607: 6603: 6598: 6594: 6587: 6573:Pozar, David M. 6571: 6570: 6566: 6549: 6545: 6535: 6534: 6530: 6518: 6507: 6498: 6497: 6490: 6482: 6475: 6471: 6470: 6466: 6436: 6435: 6431: 6417: 6416: 6412: 6398: 6394: 6378: 6377: 6373: 6352: 6351: 6347: 6340: 6321: 6320: 6316: 6302: 6301: 6297: 6290: 6278: 6277: 6273: 6268:Wayback Machine 6259: 6255: 6246: 6244: 6239: 6233: 6232: 6223: 6213: 6192: 6191: 6184: 6163: 6162: 6155: 6150: 6145: 6144: 6139: 6135: 6130: 6126: 6121: 6064: 6045: 5994: 5982: 5942: 5889: 5859: 5804: 5711: 5710: 5709: 5662:reference noise 5597: 5362: 5357: 5335:, relating the 5329:figure of merit 5275:reference noise 5224: 5223: 5202: 5197: 5196: 5175: 5170: 5169: 5142: 5137: 5136: 5092: 5083: 5070: 5054: 5049: 5048: 5013: 4938: 4816: 4790: 4711: 4660: 4644: 4593: 4591: 4572: 4560: 4537: 4521: 4517: 4513: 4509: 4486: 4485: 4466: 4465: 4429: 4428: 4427: 4362: 4351: 4346: 4340: 4327: 4316: 4315: 4253: 4252: 4251: 4233: 4229: 4219: 4177: 4172: 4144: 4135: 4131: 4123: 4121: 4109: 4108: 4094: 4090: 4083: 4075: 4059: 4023: 4015:optical density 3988: 3977: 3970: 3968: 3906: 3886: 3881: 3812: 3803: 3792: 3776: 3771: 3770: 3764:Sound intensity 3752: 3741: 3697: 3687: 3681: 3670: 3654: 3649: 3648: 3626: 3614: 3609: 3579: 3547: 3539: 3538: 3517: 3516: 3477: 3449: 3428: 3408: 3407: 3403: 3388: 3387: 3343: 3322: 3314: 3310: 3297: 3282: 3281: 3246: 3242: 3235: 3210: 3201: 3200: 3145: 3124: 3104: 3069: 3068: 3036: 3030: 3023: 3016: 3009: 3005: 2994: 2980: 2949: 2945: 2910: 2903: 2875: 2866: 2857: 2854: 2849: 2847: 2843: 2839: 2828: 2824: 2818: 2816: 2815: 2811: 2800: 2797: 2794: 2793: 2791: 2787: 2733: 2722: 2721: 2717: 2670: 2660: 2654: 2641: 2625: 2620: 2619: 2615: 2611: 2604: 2593: 2545: 2534: 2528: 2515: 2499: 2494: 2493: 2489: 2482: 2480: 2479: 2431: 2416: 2410: 2397: 2381: 2376: 2375: 2371: 2367: 2363: 2355: 2352: 2337:1.151 3 Np 2320: 2318: 2308: 2306: 2295: 2293: 2286: 2284: 2273: 2271: 2264: 2262: 2254: 2252: 2208: 2193: 2186: 2179: 2172: 2131: 2121: 2115: 2114: 2099: 2089: 2082: 2081: 2076: 2069: 2009: 1995: 1989: 1988: 1973: 1959: 1952: 1951: 1937: 1907: 1896: 1855: 1845: 1839: 1828: 1812: 1807: 1806: 1801: 1754: 1740: 1730: 1724: 1713: 1712: 1673: 1664: 1651: 1608: 1602: 1591: 1563: 1554: 1537: 1532: 1531: 1526: 1520:(measured) and 1514: 1508: 1482: 1468: 1458: 1452: 1441: 1440: 1435: 1426: 1412: 1403: 1392: 1383: 1372: 1362: 1352: 1350: 1305: 1296: 1285: 1257: 1248: 1221: 1216: 1215: 1210: 1201: 1175: 1127: 1125: 1120: 1118: 1110: 1108: 1099: 1097: 1091: 1089: 1085: 1074: 1053: 1049: 1048: 1046: 1037: 1033: 1032: 1028: 1010: 1001: 999: 986: 984: 975: 972: 969: 967: 953: 950: 948: 939: 936: 934: 920: 918: 909: 906: 904: 890: 887: 885: 876: 873: 871: 851: 849: 835: 833: 824: 822: 802: 800: 786: 784: 747: 745: 723: 720: 717: 716: 714: 702: 699: 696: 695: 693: 674: 671: 668: 667: 665: 664: 662: 650: 647: 644: 643: 641: 577: 575: 498: 496: 478: 476: 457: 455: 442: 440: 432: 429: 427: 414: 412: 404: 401: 399: 386: 384: 376: 373: 371: 358: 356: 348: 345: 342: 340: 327: 325: 317: 314: 311: 309: 290: 179: 168: 154:of amplifiers, 84: 80: 43: 28: 23: 22: 15: 12: 11: 5: 8316: 8314: 8306: 8305: 8303:Units of level 8300: 8295: 8290: 8285: 8275: 8274: 8268: 8267: 8265: 8264: 8253: 8250: 8249: 8247: 8246: 8241: 8236: 8231: 8226: 8220: 8218: 8214: 8213: 8211: 8210: 8205: 8200: 8195: 8190: 8185: 8180: 8175: 8170: 8165: 8160: 8155: 8150: 8144: 8142: 8136: 8135: 8133: 8132: 8127: 8122: 8117: 8112: 8107: 8102: 8097: 8092: 8087: 8082: 8077: 8072: 8067: 8062: 8057: 8052: 8047: 8042: 8037: 8035:degree Celsius 8032: 8027: 8021: 8019: 8015:Derived units 8011: 8010: 8008: 8007: 8002: 7997: 7992: 7987: 7982: 7977: 7971: 7969: 7963: 7962: 7957: 7955: 7954: 7947: 7940: 7932: 7923: 7922: 7920: 7919: 7914: 7909: 7904: 7899: 7895: 7892: 7891: 7889: 7888: 7883: 7878: 7873: 7868: 7863: 7858: 7852: 7847: 7846: 7845: 7835: 7830: 7825: 7818: 7815: 7814: 7805: 7803: 7802: 7795: 7788: 7780: 7774: 7773: 7767: 7762: 7757: 7750: 7749:External links 7747: 7746: 7745: 7711: 7696: 7693: 7690: 7689: 7686:. 16 May 2013. 7671: 7653: 7613: 7589: 7573:Mark E. Long. 7565: 7541: 7517: 7501: 7488: 7464: 7454: 7428: 7422:978-0750648448 7421: 7403: 7377: 7351: 7325: 7314: 7305: 7299:978-0750671750 7298: 7272: 7254: 7244: 7229: 7215: 7206: 7199: 7179: 7172: 7155: 7138:"DB or Not DB" 7128: 7104: 7085: 7078: 7058: 7051: 7029: 7022: 7002: 6995: 6975: 6968: 6948: 6941: 6923: 6889: 6863: 6854: 6845: 6836: 6819: 6802: 6785: 6768: 6751: 6734: 6728:R. J. Peters, 6721: 6707: 6682: 6673: 6661: 6652: 6643: 6601: 6592: 6585: 6564: 6543: 6528: 6505: 6488: 6464: 6445:(6): 550–555. 6429: 6410: 6392: 6371: 6345: 6338: 6332:. p. 35. 6314: 6295: 6288: 6271: 6253: 6237: 6221: 6211: 6182: 6152: 6151: 6149: 6146: 6143: 6142: 6133: 6123: 6122: 6120: 6117: 6116: 6115: 6110: 6105: 6100: 6095: 6090: 6085: 6080: 6075: 6073:dB drag racing 6070: 6062: 6056: 6051: 6044: 6041: 6040: 6039: 6028: 6024: 6023: 6021:antenna factor 6017: 6014: 6004: 6001: 5998: 5993: 5992:Other suffixes 5990: 5989: 5988: 5980: 5968: 5941: 5938: 5937: 5936: 5929: 5926: 5919: 5916: 5909: 5906: 5903: 5900: 5893: 5888: 5885: 5884: 5883: 5874:relative to 1 5868: 5865: 5855: 5852: 5849: 5846: 5843: 5840: 5835: 5829: 5826: 5819: 5816: 5815:dB volume unit 5813: 5810: 5800: 5797: 5794: 5791: 5788: 5785: 5782: 5779: 5776: 5773: 5770: 5751: 5748: 5745: 5735: 5732: 5720: 5700: 5697: 5694:peak amplitude 5690: 5687: 5684: 5681: 5671: 5668: 5658: 5653: 5650: 5647: 5644: 5641: 5638: 5635: 5632: 5629: 5618: 5615: 5612: 5609: 5606: 5603: 5593: 5590: 5587: 5584: 5581: 5578: 5573: 5566: 5561: 5547: 5544: 5537: 5534: 5523: 5520: 5513: 5510: 5495: 5492: 5486: 5483: 5460: 5455: 5448: 5445: 5444:dB electrical. 5442: 5439: 5436:dipole antenna 5428: 5425: 5418: 5415: 5408: 5405: 5398: 5393: 5386: 5383: 5376: 5373: 5366: 5361: 5358: 5356: 5353: 5352: 5351: 5315: 5312: 5298: 5295: 5284: 5281: 5271: 5266: 5263: 5260: 5240: 5237: 5234: 5231: 5205: 5178: 5157: 5154: 5149: 5145: 5124: 5121: 5113: 5106: 5099: 5095: 5091: 5086: 5082: 5077: 5073: 5069: 5066: 5057: 5037: 5032: 5017: 5012: 5009: 5008: 5007: 5004:antenna factor 5000: 4997: 4990: 4987: 4984: 4981: 4974: 4971: 4968:dipole antenna 4960: 4957: 4942: 4937: 4934: 4933: 4932: 4929: 4926: 4925:dB electrical. 4923: 4920: 4913: 4910: 4903: 4900: 4893: 4890: 4864: 4861: 4854: 4849: 4838: 4835: 4832: 4829: 4822: 4815: 4812: 4811: 4810: 4803: 4800: 4799:precipitation. 4796: 4789: 4786: 4785: 4784: 4780:peak amplitude 4776: 4773: 4772:dB volume unit 4770: 4767: 4744: 4739: 4732: 4727: 4720: 4710: 4707: 4706: 4705: 4702: 4699: 4696: 4693: 4687: 4684: 4669: 4666: 4658: 4651:IEC 61672-2013 4642: 4630: 4627: 4620: 4617: 4606: 4603: 4600:sound in water 4584: 4571: 4568: 4567: 4566: 4556: 4553: 4549: 4548: 4533: 4530: 4526: 4525: 4493: 4473: 4450: 4447: 4444: 4439: 4436: 4395: 4386: 4383: 4379: 4373: 4367: 4354: 4349: 4343: 4339: 4334: 4330: 4326: 4323: 4292: 4289: 4278: 4275: 4272: 4268: 4263: 4260: 4242: 4238: 4237: 4215: 4212: 4192:voltage source 4176: 4173: 4171: 4168: 4139: 4127: 4119: 4106: 4098: 4088: 4079: 4058: 4055: 4022: 4019: 3987: 3984: 3975: 3974:≈ 0.775 V 3905: 3902: 3885: 3882: 3848: 3847: 3836: 3826: 3815: 3811: 3806: 3799: 3795: 3791: 3788: 3783: 3779: 3750: 3739: 3733: 3732: 3721: 3711: 3700: 3690: 3684: 3677: 3673: 3669: 3666: 3661: 3657: 3625: 3622: 3613: 3610: 3608: 3605: 3578: 3575: 3562: 3559: 3554: 3550: 3546: 3531: 3530: 3509: 3506: 3496: 3492: 3489: 3484: 3480: 3476: 3471: 3464: 3460: 3456: 3452: 3448: 3443: 3439: 3435: 3431: 3425: 3420: 3415: 3411: 3406: 3402: 3399: 3396: 3393: 3391: 3389: 3379: 3375: 3371: 3365: 3358: 3354: 3350: 3346: 3342: 3337: 3333: 3329: 3325: 3319: 3313: 3309: 3304: 3300: 3296: 3293: 3290: 3287: 3285: 3283: 3280: 3276: 3271: 3261: 3258: 3249: 3245: 3241: 3238: 3236: 3234: 3231: 3228: 3225: 3222: 3213: 3209: 3208: 3198: 3181: 3178: 3167: 3160: 3156: 3152: 3148: 3144: 3139: 3135: 3131: 3127: 3121: 3116: 3111: 3107: 3103: 3100: 3097: 3088: 3085: 3076: 3052:= 87 dB; 3045:sound pressure 3029: 3026: 3021: 3014: 3007: 3003: 2992: 2978: 2953: 2952: 2947: 2943: 2902: 2899: 2874: 2871: 2865: 2862: 2784: 2783: 2772: 2769: 2766: 2763: 2759: 2756: 2753: 2750: 2744: 2741: 2736: 2732: 2729: 2714: 2697: 2694: 2684: 2673: 2663: 2657: 2653: 2648: 2644: 2640: 2637: 2632: 2628: 2600: 2591: 2590: 2573: 2570: 2560: 2548: 2537: 2531: 2527: 2522: 2518: 2514: 2511: 2506: 2502: 2476: 2459: 2456: 2446: 2434: 2423: 2419: 2413: 2409: 2404: 2400: 2396: 2393: 2388: 2384: 2351: 2348: 2345: 2344: 2341: 2338: 2335: 2332: 2329: 2325: 2324: 2312: 2303: 2300: 2291: 2282: 2278: 2277: 2268: 2259: 2250: 2247: 2244: 2240: 2239: 2236: 2233: 2227: 2224: 2221: 2207: 2204: 2191: 2184: 2177: 2170: 2164: 2163: 2150: 2145: 2138: 2134: 2128: 2124: 2118: 2113: 2106: 2102: 2096: 2092: 2074: 2067: 2042: 2041: 2028: 2023: 2016: 2012: 2007: 2004: 2001: 1998: 1992: 1987: 1980: 1976: 1971: 1968: 1965: 1962: 1936: 1933: 1925:field quantity 1921:field quantity 1905: 1894: 1888: 1887: 1869: 1858: 1848: 1842: 1835: 1831: 1827: 1824: 1819: 1815: 1797: 1777:Similarly, in 1775: 1774: 1761: 1757: 1743: 1737: 1733: 1727: 1723: 1720: 1706: 1705: 1687: 1680: 1676: 1672: 1667: 1663: 1658: 1654: 1650: 1647: 1637: 1630: 1625: 1621: 1615: 1611: 1605: 1598: 1594: 1590: 1587: 1577: 1570: 1566: 1562: 1557: 1552: 1549: 1544: 1540: 1524: 1510:Main article: 1507: 1504: 1503: 1502: 1489: 1485: 1471: 1465: 1461: 1455: 1451: 1448: 1431: 1424: 1408: 1401: 1388: 1381: 1368: 1360: 1348: 1338: 1337: 1319: 1312: 1308: 1304: 1299: 1292: 1288: 1284: 1281: 1271: 1264: 1260: 1256: 1251: 1246: 1241: 1238: 1233: 1228: 1224: 1206: 1199: 1174: 1171: 1157:power quantity 1016: 1015: 1008: 991: 990: 982: 979: 965: 962: 958: 957: 946: 943: 932: 929: 925: 924: 916: 913: 902: 899: 895: 894: 883: 880: 869: 866: 862: 861: 858: 855: 847: 844: 840: 839: 831: 828: 820: 817: 813: 812: 809: 806: 798: 795: 791: 790: 782: 779: 776: 773: 769: 768: 765: 762: 759: 756: 752: 751: 743: 740: 737: 734: 730: 729: 711: 708: 690: 687: 683: 682: 659: 656: 638: 635: 631: 630: 627: 624: 621: 618: 614: 613: 611: 608: 606: 603: 599: 598: 595: 592: 589: 586: 582: 581: 572: 569: 566: 563: 559: 558: 555: 552: 549: 546: 542: 541: 538: 535: 533: 530: 526: 525: 523: 520: 518: 515: 511: 510: 507: 504: 502: 494: 490: 489: 487: 484: 482: 474: 470: 469: 466: 463: 461: 453: 449: 448: 446: 438: 436: 425: 421: 420: 418: 410: 408: 397: 393: 392: 390: 382: 380: 369: 365: 364: 362: 354: 352: 338: 334: 333: 331: 323: 321: 307: 303: 302: 299: 296: 289: 286: 194:of 0.054 167: 164: 148:control theory 26: 24: 14: 13: 10: 9: 6: 4: 3: 2: 8315: 8304: 8301: 8299: 8296: 8294: 8291: 8289: 8286: 8284: 8281: 8280: 8278: 8263: 8255: 8254: 8251: 8245: 8242: 8240: 8237: 8235: 8232: 8230: 8227: 8225: 8222: 8221: 8219: 8215: 8209: 8206: 8204: 8201: 8199: 8196: 8194: 8191: 8189: 8186: 8184: 8181: 8179: 8176: 8174: 8171: 8169: 8168:degree of arc 8166: 8164: 8161: 8159: 8156: 8154: 8151: 8149: 8146: 8145: 8143: 8141: 8137: 8131: 8128: 8126: 8123: 8121: 8118: 8116: 8113: 8111: 8108: 8106: 8103: 8101: 8098: 8096: 8093: 8091: 8088: 8086: 8083: 8081: 8078: 8076: 8073: 8071: 8068: 8066: 8063: 8061: 8058: 8056: 8053: 8051: 8048: 8046: 8043: 8041: 8038: 8036: 8033: 8031: 8028: 8026: 8023: 8022: 8020: 8018: 8012: 8006: 8003: 8001: 7998: 7996: 7993: 7991: 7988: 7986: 7983: 7981: 7978: 7976: 7973: 7972: 7970: 7968: 7964: 7960: 7953: 7948: 7946: 7941: 7939: 7934: 7933: 7930: 7918: 7915: 7913: 7910: 7908: 7905: 7903: 7900: 7897: 7896: 7893: 7887: 7884: 7882: 7879: 7877: 7874: 7872: 7869: 7867: 7864: 7862: 7859: 7856: 7853: 7851: 7848: 7844: 7841: 7840: 7839: 7836: 7834: 7831: 7829: 7826: 7823: 7820: 7819: 7816: 7811: 7808: 7801: 7796: 7794: 7789: 7787: 7782: 7781: 7778: 7771: 7768: 7766: 7763: 7761: 7758: 7756: 7753: 7752: 7748: 7731: 7728:(in German). 7723: 7719: 7718: 7712: 7708: 7705:(in German). 7704: 7699: 7698: 7694: 7685: 7684:wordpress.com 7681: 7675: 7672: 7667: 7663: 7657: 7654: 7649: 7643: 7627: 7623: 7617: 7614: 7602: 7601: 7593: 7590: 7578: 7577: 7569: 7566: 7554: 7553: 7545: 7542: 7530: 7529: 7521: 7518: 7515: 7514:0-932764-04-5 7511: 7505: 7502: 7498: 7492: 7489: 7477: 7476: 7472:David Adamy. 7468: 7465: 7458: 7455: 7442: 7438: 7432: 7429: 7424: 7418: 7414: 7407: 7404: 7391: 7387: 7381: 7378: 7365: 7361: 7355: 7352: 7339: 7335: 7329: 7326: 7323: 7322:ITU-R BS.1770 7318: 7315: 7309: 7306: 7301: 7295: 7291: 7286: 7285: 7276: 7273: 7268: 7264: 7258: 7255: 7248: 7245: 7241: 7238: 7233: 7230: 7225: 7219: 7216: 7210: 7207: 7202: 7196: 7192: 7191: 7183: 7180: 7175: 7169: 7165: 7159: 7156: 7143: 7139: 7132: 7129: 7124: 7120: 7119: 7114: 7108: 7105: 7100: 7096: 7093:Stas Bekman. 7089: 7086: 7081: 7075: 7071: 7070: 7062: 7059: 7054: 7048: 7044: 7040: 7033: 7030: 7025: 7019: 7015: 7014: 7006: 7003: 6998: 6992: 6988: 6987: 6979: 6976: 6971: 6965: 6961: 6960: 6952: 6949: 6944: 6942:0-87942-274-2 6938: 6934: 6927: 6924: 6909: 6902: 6901: 6893: 6890: 6877: 6873: 6867: 6864: 6858: 6855: 6849: 6846: 6843:ISO 1683:2015 6840: 6837: 6834: 6831:, p. 304, at 6830: 6829: 6823: 6820: 6817: 6813: 6812: 6806: 6803: 6800: 6797:, p. 407, at 6796: 6795: 6789: 6786: 6783: 6780:, p. 356, at 6779: 6778: 6772: 6769: 6766: 6762: 6761: 6755: 6752: 6749: 6746:, p. 268, at 6745: 6744: 6738: 6735: 6731: 6725: 6722: 6717: 6711: 6708: 6704: 6700: 6696: 6692: 6686: 6683: 6677: 6674: 6671: 6665: 6662: 6656: 6653: 6647: 6644: 6640: 6636: 6632: 6628: 6624: 6620: 6616: 6612: 6605: 6602: 6596: 6593: 6588: 6582: 6578: 6574: 6568: 6565: 6561: 6557: 6553: 6547: 6544: 6539: 6532: 6529: 6526: 6522: 6516: 6514: 6512: 6510: 6506: 6501: 6495: 6493: 6489: 6481: 6474: 6468: 6465: 6460: 6456: 6452: 6448: 6444: 6440: 6433: 6430: 6425: 6421: 6414: 6411: 6407: 6404:, p. 276, at 6403: 6402: 6396: 6393: 6388: 6384: 6383: 6375: 6372: 6367: 6363: 6359: 6355: 6349: 6346: 6341: 6335: 6331: 6327: 6326: 6318: 6315: 6310: 6306: 6299: 6296: 6291: 6285: 6281: 6275: 6272: 6269: 6265: 6262: 6257: 6254: 6242: 6241: 6230: 6228: 6226: 6222: 6218: 6214: 6208: 6204: 6199: 6198: 6189: 6187: 6183: 6179: 6175: 6171: 6167: 6160: 6158: 6154: 6147: 6137: 6134: 6128: 6125: 6118: 6114: 6111: 6109: 6106: 6104: 6101: 6099: 6096: 6094: 6091: 6089: 6086: 6084: 6081: 6079: 6076: 6074: 6071: 6068: 6060: 6057: 6055: 6052: 6050: 6047: 6046: 6042: 6037: 6033: 6029: 6026: 6025: 6022: 6018: 6015: 6013: 6009: 6005: 6002: 5999: 5996: 5995: 5991: 5986: 5977: 5973: 5969: 5967: 5963: 5959: 5955: 5951: 5947: 5944: 5943: 5939: 5934: 5930: 5927: 5924: 5920: 5917: 5914: 5910: 5907: 5904: 5901: 5898: 5894: 5891: 5890: 5886: 5881: 5877: 5873: 5869: 5866: 5863: 5858: 5853: 5850: 5847: 5844: 5841: 5839: 5836: 5833: 5830: 5827: 5824: 5820: 5817: 5814: 5811: 5808: 5803: 5798: 5795: 5792: 5789: 5786: 5783: 5780: 5777: 5774: 5771: 5749: 5746: 5743: 5733: 5730: 5718: 5707: 5704: 5701: 5698: 5695: 5691: 5688: 5685: 5682: 5679: 5675: 5672: 5669: 5667: 5663: 5659: 5657: 5654: 5651: 5648: 5645: 5642: 5639: 5636: 5633: 5630: 5627: 5623: 5619: 5616: 5613: 5610: 5607: 5604: 5601: 5596: 5591: 5588: 5585: 5582: 5579: 5577: 5574: 5571: 5567: 5565: 5562: 5559: 5555: 5551: 5548: 5545: 5542: 5538: 5535: 5532: 5528: 5524: 5521: 5518: 5514: 5511: 5508: 5504: 5500: 5496: 5493: 5490: 5487: 5484: 5481: 5477: 5473: 5469: 5465: 5461: 5459: 5456: 5453: 5449: 5446: 5443: 5440: 5437: 5433: 5429: 5426: 5423: 5419: 5416: 5413: 5409: 5406: 5403: 5399: 5397: 5394: 5391: 5387: 5384: 5381: 5380:dBrn adjusted 5377: 5374: 5371: 5367: 5364: 5363: 5359: 5354: 5349: 5345: 5341: 5338: 5334: 5330: 5326: 5325: 5320: 5316: 5313: 5310: 5306: 5302: 5299: 5296: 5293: 5288: 5285: 5282: 5280: 5276: 5272: 5270: 5267: 5264: 5261: 5238: 5235: 5232: 5229: 5222:is therefore 5203: 5176: 5155: 5152: 5147: 5143: 5122: 5104: 5097: 5093: 5089: 5084: 5080: 5075: 5071: 5067: 5064: 5055: 5046: 5042: 5038: 5036: 5033: 5030: 5026: 5022: 5018: 5015: 5014: 5010: 5005: 5001: 4998: 4995: 4991: 4988: 4985: 4982: 4979: 4975: 4972: 4969: 4965: 4961: 4958: 4955: 4951: 4947: 4943: 4940: 4939: 4935: 4930: 4927: 4924: 4921: 4918: 4914: 4911: 4908: 4904: 4901: 4898: 4894: 4891: 4888: 4884: 4881: 4877: 4873: 4869: 4865: 4862: 4859: 4855: 4853: 4850: 4847: 4843: 4839: 4836: 4833: 4830: 4827: 4823: 4821: 4818: 4817: 4813: 4808: 4804: 4801: 4797: 4795: 4792: 4791: 4787: 4781: 4777: 4774: 4771: 4768: 4765: 4761: 4757: 4753: 4749: 4745: 4743: 4740: 4737: 4733: 4731: 4728: 4725: 4721: 4719: 4716: 4715: 4714: 4708: 4703: 4700: 4697: 4694: 4692: 4688: 4685: 4682: 4678: 4674: 4673:hearing level 4670: 4667: 4664: 4656: 4652: 4648: 4639: 4635: 4631: 4628: 4625: 4621: 4618: 4615: 4611: 4607: 4604: 4601: 4589: 4586:dB SPL ( 4585: 4582: 4581: 4580: 4577: 4569: 4564: 4559: 4554: 4551: 4550: 4545: 4541: 4536: 4531: 4528: 4527: 4507: 4491: 4471: 4448: 4445: 4442: 4437: 4434: 4425: 4421: 4417: 4413: 4409: 4393: 4384: 4381: 4377: 4371: 4365: 4352: 4347: 4341: 4337: 4332: 4328: 4324: 4321: 4313: 4290: 4287: 4276: 4273: 4266: 4261: 4258: 4249: 4246: 4243: 4240: 4239: 4227: 4223: 4218: 4213: 4210: 4209: 4205: 4201: 4197: 4193: 4189: 4184: 4180: 4174: 4169: 4167: 4165: 4161: 4155: 4152: 4149: 4142: 4138: 4130: 4126: 4118: 4114: 4105: 4101: 4097: 4087: 4082: 4078: 4073: 4067: 4063: 4056: 4054: 4052: 4047: 4043: 4040: 4039:dynamic range 4036: 4032: 4028: 4027:image sensors 4020: 4018: 4016: 4012: 4011:blocking unit 4007: 4005: 4001: 3997: 3993: 3985: 3983: 3981: 3966: 3962: 3957: 3955: 3949: 3947: 3943: 3939: 3938:coaxial cable 3935: 3931: 3927: 3923: 3919: 3915: 3911: 3903: 3901: 3899: 3895: 3891: 3883: 3880: 3875: 3873: 3869: 3864: 3862: 3858: 3853: 3852:dynamic range 3834: 3824: 3813: 3809: 3804: 3797: 3793: 3789: 3786: 3781: 3777: 3769: 3768: 3767: 3765: 3761: 3758: 3756: 3749: 3745: 3738: 3719: 3709: 3698: 3688: 3682: 3675: 3671: 3667: 3664: 3659: 3655: 3647: 3646: 3645: 3643: 3639: 3635: 3632:as a unit of 3631: 3623: 3621: 3619: 3611: 3606: 3604: 3602: 3598: 3594: 3591: 3587: 3586:optical fiber 3583: 3576: 3574: 3560: 3557: 3552: 3548: 3544: 3536: 3507: 3504: 3494: 3490: 3487: 3482: 3478: 3474: 3462: 3458: 3454: 3450: 3446: 3441: 3437: 3433: 3429: 3418: 3413: 3409: 3404: 3400: 3397: 3394: 3392: 3377: 3373: 3369: 3356: 3352: 3348: 3344: 3340: 3335: 3331: 3327: 3323: 3311: 3307: 3302: 3298: 3294: 3291: 3288: 3286: 3278: 3274: 3269: 3259: 3256: 3247: 3243: 3239: 3237: 3229: 3226: 3223: 3211: 3199: 3179: 3176: 3158: 3154: 3150: 3146: 3142: 3137: 3133: 3129: 3125: 3114: 3109: 3105: 3101: 3098: 3095: 3086: 3083: 3074: 3067: 3066: 3065: 3063: 3057: 3056:= 80 dB. 3055: 3051: 3046: 3040: 3035: 3027: 3025: 3020: 3013: 3002: 2998: 2991: 2988: 2984: 2977: 2973: 2970: 2966: 2962: 2958: 2940: 2939: 2938: 2936: 2932: 2928: 2922: 2918: 2914: 2908: 2900: 2898: 2896: 2895: 2894:Semi-log plot 2890: 2889: 2884: 2880: 2872: 2870: 2863: 2861: 2837: 2832: 2809: 2770: 2767: 2764: 2761: 2757: 2754: 2751: 2748: 2742: 2739: 2734: 2730: 2727: 2715: 2695: 2692: 2682: 2671: 2661: 2655: 2651: 2646: 2642: 2638: 2635: 2630: 2626: 2609: 2608: 2607: 2603: 2599: 2571: 2568: 2558: 2546: 2535: 2529: 2525: 2520: 2516: 2512: 2509: 2504: 2500: 2477: 2457: 2454: 2444: 2432: 2421: 2417: 2411: 2407: 2402: 2398: 2394: 2391: 2386: 2382: 2361: 2360: 2359: 2349: 2342: 2339: 2336: 2333: 2330: 2327: 2326: 2316: 2313: 2304: 2301: 2292: 2283: 2280: 2279: 2269: 2260: 2251: 2248: 2245: 2242: 2241: 2237: 2234: 2232: 2228: 2225: 2222: 2219: 2218: 2212: 2205: 2203: 2201: 2197: 2190: 2183: 2176: 2169: 2148: 2143: 2136: 2132: 2126: 2122: 2116: 2111: 2104: 2100: 2094: 2090: 2080: 2079: 2078: 2073: 2066: 2061: 2059: 2055: 2051: 2047: 2046:linear system 2026: 2021: 2014: 2010: 2002: 1996: 1990: 1985: 1978: 1974: 1966: 1960: 1950: 1949: 1948: 1946: 1942: 1934: 1932: 1930: 1926: 1922: 1918: 1914: 1909: 1904: 1900: 1893: 1867: 1856: 1846: 1840: 1833: 1829: 1825: 1822: 1817: 1813: 1805: 1804: 1803: 1800: 1796: 1792: 1788: 1784: 1780: 1759: 1755: 1741: 1735: 1731: 1725: 1721: 1718: 1711: 1710: 1709: 1685: 1678: 1674: 1670: 1665: 1661: 1656: 1652: 1648: 1645: 1635: 1628: 1623: 1619: 1613: 1609: 1603: 1596: 1592: 1588: 1585: 1575: 1568: 1564: 1560: 1555: 1550: 1547: 1542: 1538: 1530: 1529: 1528: 1523: 1519: 1513: 1505: 1487: 1483: 1469: 1463: 1459: 1453: 1449: 1446: 1439: 1438: 1437: 1434: 1430: 1423: 1419: 1414: 1413:is negative. 1411: 1407: 1400: 1397:is less than 1396: 1391: 1387: 1380: 1376: 1371: 1367: 1359: 1355: 1347: 1343: 1317: 1310: 1306: 1302: 1297: 1290: 1286: 1282: 1279: 1269: 1262: 1258: 1254: 1249: 1244: 1239: 1236: 1231: 1226: 1222: 1214: 1213: 1212: 1209: 1205: 1198: 1194: 1190: 1186: 1182: 1181: 1172: 1170: 1169:for details. 1168: 1167: 1162: 1158: 1153: 1151: 1147: 1143: 1142: 1137: 1132: 1115: 1105: 1083: 1082: 1072: 1071: 1066: 1062: 1044: 1041: ln(10) 1026: 1021: 1014: 1004: 997: 992: 983: 980: 966: 963: 960: 959: 947: 944: 933: 930: 927: 926: 917: 914: 903: 900: 897: 896: 884: 881: 870: 867: 864: 863: 859: 856: 848: 845: 842: 841: 832: 829: 821: 818: 815: 814: 810: 807: 799: 796: 793: 792: 783: 780: 777: 774: 771: 770: 766: 763: 760: 757: 754: 753: 744: 741: 738: 735: 732: 731: 712: 709: 691: 688: 685: 684: 660: 657: 639: 636: 633: 632: 628: 625: 622: 619: 616: 615: 612: 609: 607: 604: 601: 600: 596: 593: 590: 587: 584: 583: 573: 570: 567: 564: 561: 560: 556: 553: 550: 547: 544: 543: 539: 536: 534: 531: 528: 527: 524: 521: 519: 516: 513: 512: 508: 505: 503: 495: 492: 491: 488: 485: 483: 475: 472: 471: 467: 464: 462: 454: 451: 450: 447: 439: 437: 426: 423: 422: 419: 411: 409: 398: 395: 394: 391: 383: 381: 370: 367: 366: 363: 355: 353: 339: 336: 335: 332: 324: 322: 308: 305: 304: 293: 287: 285: 283: 279: 275: 271: 267: 263: 259: 254: 252: 248: 242: 239: 234: 229: 227: 222: 220: 216: 212: 208: 203: 201: 197: 193: 190: 185: 177: 173: 165: 163: 161: 157: 153: 149: 145: 141: 137: 133: 129: 125: 121: 116: 113: 109: 105: 100: 98: 94: 88: 78: 74: 70: 66: 62: 58: 54: 50: 45: 41: 37: 33: 19: 8173:electronvolt 8162: 7912:signal noise 7806: 7737:. Retrieved 7721: 7716: 7706: 7702: 7683: 7674: 7665: 7656: 7630:. Retrieved 7616: 7606:16 September 7604:. Retrieved 7599: 7592: 7582:16 September 7580:. Retrieved 7575: 7568: 7558:16 September 7556:. Retrieved 7551: 7544: 7534:16 September 7532:. Retrieved 7527: 7520: 7504: 7491: 7481:16 September 7479:. Retrieved 7474: 7467: 7457: 7445:. Retrieved 7440: 7431: 7412: 7406: 7394:. Retrieved 7380: 7368:. Retrieved 7354: 7342:. Retrieved 7328: 7317: 7308: 7283: 7275: 7267:the original 7257: 7247: 7232: 7223: 7218: 7209: 7189: 7182: 7163: 7158: 7148:16 September 7146:. Retrieved 7142:the original 7131: 7123:the original 7117: 7107: 7098: 7088: 7068: 7061: 7042: 7032: 7012: 7005: 6985: 6978: 6958: 6951: 6932: 6926: 6917:13 September 6915:, retrieved 6899: 6892: 6880:. Retrieved 6875: 6866: 6857: 6848: 6839: 6833:Google Books 6826: 6822: 6816:Google Books 6814:, p. 83, at 6809: 6805: 6799:Google Books 6792: 6788: 6782:Google Books 6775: 6771: 6765:Google Books 6758: 6754: 6748:Google Books 6741: 6737: 6729: 6724: 6716:Fiber Optics 6715: 6710: 6690: 6685: 6676: 6664: 6655: 6646: 6614: 6610: 6604: 6595: 6576: 6567: 6551: 6546: 6537: 6531: 6520: 6467: 6442: 6438: 6432: 6423: 6419: 6413: 6406:Google Books 6399: 6395: 6386: 6380: 6374: 6365: 6361: 6348: 6324: 6317: 6307:. New York: 6304: 6298: 6279: 6274: 6256: 6247:16 September 6245:, retrieved 6235: 6216: 6196: 6177: 6165: 6136: 6127: 6054:Cent (music) 5851:dBμV or dBuV 5708:relative to 5673: 5665: 5664:. See also 5549: 5347: 5339: 5337:antenna gain 5331:utilized in 5322: 5318: 5300: 5286: 5278: 5277:. See also 5016:dB‑Hz 4886: 4712: 4573: 4552:dBμV or dBuV 4422:used in the 4419: 4415: 4411: 4407: 4250:relative to 4178: 4156: 4150: 4140: 4136: 4128: 4124: 4116: 4112: 4103: 4099: 4095: 4085: 4080: 4076: 4068: 4064: 4060: 4048: 4044: 4024: 4008: 3992:optical link 3989: 3958: 3950: 3942:fiber optics 3907: 3887: 3865: 3849: 3762: 3759: 3755:micropascals 3747: 3736: 3734: 3627: 3615: 3580: 3532: 3059: 3042: 3037: 3018: 3011: 3000: 2996: 2989: 2982: 2975: 2971: 2954: 2934: 2930: 2926: 2920: 2916: 2912: 2904: 2892: 2886: 2876: 2867: 2833: 2785: 2601: 2597: 2592: 2353: 2209: 2188: 2181: 2174: 2167: 2165: 2071: 2064: 2062: 2043: 1944: 1940: 1938: 1928: 1924: 1923:. The term 1920: 1917:80000-1:2009 1912: 1910: 1902: 1891: 1889: 1798: 1794: 1776: 1707: 1521: 1517: 1515: 1432: 1428: 1421: 1420:in terms of 1417: 1415: 1409: 1405: 1398: 1394: 1389: 1385: 1378: 1374: 1369: 1365: 1357: 1353: 1345: 1341: 1339: 1207: 1203: 1196: 1192: 1178: 1176: 1164: 1160: 1156: 1154: 1149: 1148:rather than 1145: 1139: 1133: 1116: 1106: 1080: 1069: 1029:1 dB = 0.1 B 1025:60027-3:2002 1022: 1019: 1012: 1002: 995: 298:Power ratio 280:(such as in 255: 250: 246: 244: 237: 235: 231: 223: 214: 210: 204: 171: 169: 117: 111: 107: 101: 89: 64: 60: 52: 48: 46: 44: 7907:link budget 7739:18 December 7113:Rupert Neve 6330:Focal Press 6311:p. 10. 5870:dB(μV/m) – 5617:dBov or dBO 5480:square wave 5035:dBov or dBO 5021:link budget 4866:dB(μV/m) – 4783:full-scale. 4764:square wave 4675:is used in 4619:dB SWL 4605:dB SIL 4583:dB SPL 4547:13 nW. 4410:comes from 4132:(re 1 μV/m) 4072:IEC 60027-3 3946:link budget 3926:attenuators 3918:percentages 3904:Electronics 3872:A-weighting 3582:Attenuation 2957:slide rules 2486:V ≈ 31.62 V 2235:Power ratio 2223:In decibels 2206:Conversions 1138:other than 1094:... Np 196:microfarads 192:capacitance 156:attenuation 144:electronics 136:sound power 132:engineering 124:Bell System 8277:Categories 7967:Base units 7709:: 267–274. 7462:2449–2460. 7447:13 October 7252:3919–3927. 7099:stason.org 6703:1849963177 6617:(4): 353, 6611:Metrologia 6560:3642037038 6148:References 6008:reciprocal 5897:audiograms 5848:see dBμV/m 5787:see dBμV/m 5699:dBu or dBv 5489:G-weighted 5464:full scale 5327:factor, a 4880:television 4748:full scale 4677:audiograms 4668:dB HL 4596:10 Pa 4241:dBu or dBv 4226:line-level 4160:A-weighted 4031:CCD imager 3998:power, in 3930:free space 3922:amplifiers 3916:ratios or 3914:arithmetic 3612:Perception 2864:Properties 2831: dB. 2370:watts) to 2331:10 dB 2056:), if the 1929:root-power 1073:, that is 288:Definition 268:(IEC) and 8283:Acoustics 8110:steradian 8025:becquerel 7824:(or dBmW) 7632:24 August 6639:250827251 6032:milliwatt 5876:microvolt 5747:− 5744:≈ 5731:≈ 5660:dB above 5622:amplitude 5570:milliwatt 5468:amplitude 5452:femtowatt 5273:dB above 5236:− 5081:⁡ 5041:amplitude 5031:, in dB). 4897:femtowatt 4883:broadcast 4872:microvolt 4858:milliwatt 4752:amplitude 4724:milliwatt 4686:dB Q 4655:ANSI S1.4 4570:Acoustics 4561:) – 4446:⋅ 4338:⁡ 4325:⋅ 4288:≈ 4274:⋅ 4271:Ω 4220:) – 4143:/(1 μV/m) 3980:identical 3934:waveguide 3890:telephony 3884:Telephony 3630:acoustics 3624:Acoustics 3593:path loss 3577:Fractions 3558:⁡ 3505:≈ 3488:⁡ 3475:− 3419:⁡ 3401:⋅ 3308:⁡ 3295:⋅ 3177:≈ 3143:− 3115:⁡ 3102:⋅ 3084:⊖ 2907:amplifier 2888:Bode plot 2768:≈ 2765:… 2749:× 2652:⁡ 2526:⁡ 2408:⁡ 2246:1 dB 2243:1 dB 2058:impedance 1911:The term 1791:impedance 1789:when the 1662:⁡ 1150:millibels 1086:1 dB 1057:ln(10) Np 568:.995 ≈ 2 557:.995 ≈ 2 551:.981 ≈ 4 205:In 1924, 140:acoustics 120:telephony 112:amplitude 51:(symbol: 8262:Category 8217:See also 7990:kilogram 7959:SI units 7898:See also 7810:suffixes 7730:Archived 7642:cite web 7626:Archived 7396:8 August 7390:Archived 7370:8 August 7364:Archived 7344:25 April 7338:Archived 6908:archived 6575:(2005). 6480:Archived 6459:51654766 6264:Archived 6083:Loudness 6043:See also 5976:response 5921:dB SPL ( 5828:dBW·m·Hz 5781:see dBμV 5626:clipping 5614:see dBov 5541:kilowatt 5491:spectrum 5476:sinusoid 5472:clipping 5466:) – the 5344:receiver 5045:clipping 4917:kilowatt 4760:sinusoid 4756:clipping 4750:) – the 4638:response 4424:VU meter 4414:, while 4204:resistor 4111:, where 3597:fraction 2961:additive 2933:) + log( 2929:) + log( 2374:yields: 2350:Examples 2290: dB 2258: Np 1373:= 0. If 1079:natural 278:suffixes 8178:hectare 8163:decibel 8105:sievert 8100:siemens 8030:coulomb 7980:candela 7857:(radar) 7807:Decibel 6882:30 July 6876:cdc.gov 6619:Bibcode 6170:Bibcode 5862:voltage 5807:voltage 5793:see dBu 5706:voltage 5628:occurs. 5600:voltage 5432:antenna 5342:to the 4964:antenna 4616:in air. 4563:voltage 4540:voltage 4522:−10 dBV 4514:−10 dBV 4248:voltage 4230:−10 dBV 4222:voltage 4175:Voltage 3996:optical 3969:√ 3742:is the 2848:√ 2817:√ 2804:⁠ 2792:⁠ 2481:√ 2299: B 2226:In bels 2054:current 2050:voltage 1941:changes 1897:is the 1787:current 1783:voltage 1109:√ 1096:= 1088:= 1052:⁄ 1036:⁄ 1000:√ 727:⁠ 715:⁠ 713:.501 ≈ 706:⁠ 694:⁠ 692:.251 ≈ 678:⁠ 666:⁠ 663:√ 661:.708 ≈ 654:⁠ 642:⁠ 640:.501 ≈ 576:√ 574:.413 ≈ 202:wire). 184:radians 166:History 49:decibel 8193:minute 8153:dalton 8095:radian 8090:pascal 8080:newton 8005:second 7985:kelvin 7975:ampere 7838:dBm/Hz 7724:] 7512: 7419: 7296: 7197: 7170: 7076: 7049: 7020: 6993: 6966: 6939: 6701: 6637: 6583: 6558: 6457: 6336: 6286: 6209: 6065:) and 6012:kelvin 5964:, and 5928:dB SWL 5918:dB SPL 5908:dB SIL 5784:dBuV/m 5734:0.7746 5554:kelvin 5242: 5109: 4641:are dB 4518:+4 dBu 4510:+4 dBu 4464:where 4291:0.7746 4234:+4 dBu 4194:) and 4164:hyphen 4093:or as 3990:In an 3986:Optics 3735:where 2925:= log( 2858:3.9811 2844:1.4125 2840:1.9953 2829:6.0206 2825:1.4142 2812:3.0103 2231:nepers 1890:where 1163:; see 1047:1 B = 1043:nepers 1011: 182: 77:levels 8208:tonne 8203:neper 8188:litre 8130:weber 8115:tesla 8070:lumen 8065:katal 8060:joule 8055:hertz 8050:henry 8040:farad 7995:metre 7886:dB-Hz 7733:(PDF) 7726:(PDF) 7720:[ 6911:(PDF) 6904:(PDF) 6635:S2CID 6483:(PDF) 6476:(PDF) 6455:S2CID 6119:Notes 6088:Neper 6036:Linux 5997:dB-Hz 5966:dB(Z) 5962:dB(G) 5958:dB(D) 5954:dB(C) 5950:dB(B) 5946:dB(A) 5892:dB HL 5880:meter 5854:dB(μV 5772:dBu0s 5750:2.218 5674:dBrnC 5670:dBrnC 5666:dBrnC 5592:dB(mV 5583:dBm0s 5550:dB(K) 5527:joule 5422:dB(D) 5412:dB(C) 5390:dB(B) 5370:dB(A) 5301:dB(K) 5287:dBrnC 5283:dBrnC 5279:dBrnC 4876:meter 4842:joule 4788:Radar 4647:dB(A) 4555:dB(μV 4529:dBm0s 4385:2.218 4277:0.001 4190:(the 4004:fiber 3910:gains 3894:audio 2788:10 dB 2758:1.995 2672:0.001 2536:31.62 2319:2.718 2307:7.389 2294:0.868 2285:8.685 2272:1.122 2270:10 ≈ 2263:1.258 2261:10 ≈ 2253:0.115 2249:0.1 B 1404:then 1384:then 1185:level 1180:power 1159:or a 1126:1.122 1119:1.258 1098:0.115 1090:0.115 1063:of a 1061:level 961:−100 860:.001 778:.001 629:.891 623:.794 597:.122 591:.259 540:.162 247:logit 200:gauge 189:shunt 152:gains 142:, in 108:power 71:on a 32:sound 18:DBrnC 8183:hour 8125:watt 8120:volt 8045:gray 8000:mole 7881:dBrn 7876:dBFS 7861:dBsm 7812:(dB) 7741:2016 7648:link 7634:2013 7608:2013 7584:2013 7560:2013 7536:2013 7510:ISBN 7483:2013 7449:2016 7417:ISBN 7398:2019 7372:2019 7346:2013 7294:ISBN 7237:ANSI 7195:ISBN 7168:ISBN 7150:2013 7074:ISBN 7047:ISBN 7018:ISBN 6991:ISBN 6964:ISBN 6937:ISBN 6919:2011 6884:2020 6699:ISBN 6695:p.37 6581:ISBN 6556:ISBN 6389:(1). 6334:ISBN 6284:ISBN 6249:2016 6207:ISBN 6113:Sone 6103:Phon 6003:dB/K 5902:dB Q 5878:per 5860:) – 5823:watt 5812:dBVU 5805:) – 5799:dB(V 5778:dBuV 5689:dBTP 5683:dBsm 5656:dBrn 5637:dBpp 5631:dBpp 5598:) – 5589:dBmV 5576:dBm0 5512:dBiC 5458:dBFS 5420:see 5410:see 5388:see 5378:see 5368:see 5314:dB/K 5269:dBrn 5246:dBov 5239:3.01 5208:over 5181:over 5116:dBov 4989:dBsm 4973:dBiC 4907:watt 4874:per 4831:dBpp 4802:dBsm 4775:dBTP 4769:dBVU 4742:dBFS 4730:dBm0 4695:dBpp 4538:) – 4520:and 4420:unit 4412:volt 4214:dB(V 4200:heat 4084:(re 4051:stop 3924:and 3892:and 3607:Uses 3533:The 3180:84.8 2911:log( 2891:and 2877:The 2855:10 ≈ 2718:3 dB 2616:1 mW 2612:10 W 2492:is: 2483:1000 2368:1000 2364:1 kW 2356:1 mW 2305:e ≈ 2302:1 Np 2281:1 Np 2220:Unit 2187:and 2173:and 2070:and 2052:and 1945:same 1427:and 1344:and 1141:deci 1114::1. 985:.000 968:.000 949:.000 935:.000 928:−90 919:.000 905:.000 898:−80 886:.000 872:.000 865:−70 850:.000 843:−60 834:.003 823:.000 816:−50 811:.01 801:.000 794:−40 785:.031 772:−30 761:.01 755:−20 746:.316 733:−10 509:.62 306:100 274:NIST 251:unit 180:5000 176:mile 146:and 93:volt 85:1.12 81:1.26 47:The 8158:day 8085:ohm 8075:lux 7871:dBi 7866:dBc 7855:dBZ 7850:dBA 7843:PSD 7833:dBV 7828:dBW 7822:dBm 6627:doi 6525:PDF 6447:doi 6424:119 6238:RMS 6203:206 6063:den 6027:mBm 6016:dBm 6010:of 5985:dBA 5983:or 5931:dB 5911:dB 5857:RMS 5845:dBμ 5838:dBZ 5818:dBW 5802:RMS 5796:dBV 5790:dBv 5755:dBV 5719:0.6 5703:RMS 5649:dBr 5643:dBq 5611:dBO 5605:dBo 5595:RMS 5564:dBm 5546:dBK 5536:dBk 5522:dBJ 5494:dBi 5485:dBG 5462:dB( 5447:dBf 5441:dBe 5427:dBd 5417:dBD 5407:dBC 5396:dBc 5385:dBB 5375:dBa 5365:dBA 5324:G/T 5319:not 5297:dBK 5262:dBr 5156:1.0 5072:log 4999:dBm 4983:dBq 4959:dBd 4941:dBi 4928:dBo 4922:dBe 4912:dBk 4902:dBW 4892:dBf 4852:dBm 4837:dBJ 4820:dBc 4794:dBZ 4746:dB( 4718:dBm 4701:dBG 4671:dB 4663:dBc 4645:or 4622:dB 4608:dB 4558:RMS 4535:RMS 4390:dBu 4366:0.6 4357:RMS 4329:log 4312:RMS 4267:600 4245:RMS 4228:of 4217:RMS 4211:dBV 4196:dBm 4188:dBu 4120:ref 4107:ref 4089:ref 4037:or 4000:dBm 3976:RMS 3961:dBu 3954:dBm 3861:μPa 3818:ref 3794:log 3751:ref 3740:rms 3703:ref 3693:rms 3672:log 3636:or 3549:log 3513:dBA 3501:dBA 3479:log 3410:log 3384:dBA 3299:log 3265:dBA 3253:dBA 3185:dBA 3173:dBA 3106:log 3092:dBA 3080:dBA 3022:0dB 2643:log 2614:to 2517:log 2490:1 V 2488:to 2422:000 2399:log 2372:1 W 2334:1 B 2328:1 B 2296:589 2229:In 2180:to 1895:out 1851:out 1830:log 1785:or 1653:log 1593:log 1287:log 1131:). 1102:... 1081:log 973:000 970:000 951:031 940:001 937:000 907:000 888:316 874:000 852:001 836:162 767:.1 739:.1 686:−6 634:−3 617:−1 529:10 517:100 514:20 499:000 493:30 486:100 479:000 473:40 468:.2 465:316 458:000 456:100 452:50 443:000 433:000 430:000 424:60 415:162 405:000 402:000 396:70 387:000 377:000 374:000 372:100 368:80 359:623 349:000 346:000 343:000 337:90 328:000 326:100 318:000 315:000 312:000 295:dB 282:dBA 226:NBS 215:bel 138:in 87:). 61:bel 8279:: 7707:98 7682:. 7664:. 7644:}} 7640:{{ 7624:. 7499:". 7439:. 7388:. 7362:. 7292:. 7290:16 7115:, 7097:. 6906:, 6874:. 6693:, 6633:, 6625:, 6615:38 6613:, 6508:^ 6491:^ 6453:. 6443:73 6441:. 6422:. 6385:. 6364:. 6360:. 6224:^ 6215:. 6205:. 6185:^ 6176:. 6156:^ 6098:pH 6061:(L 5979:dB 5960:, 5956:, 5952:, 5948:, 5076:10 5068:10 5060:ov 4333:10 4322:20 3982:. 3948:. 3940:, 3936:, 3932:, 3900:. 3863:. 3831:dB 3798:10 3790:10 3716:dB 3676:10 3668:20 3553:10 3545:10 3508:87 3483:10 3463:10 3455:90 3451:10 3442:10 3434:70 3430:10 3414:10 3398:10 3357:10 3349:90 3345:10 3336:10 3328:70 3324:10 3303:10 3292:10 3260:90 3248:70 3230:90 3224:70 3216:lm 3159:10 3151:83 3147:10 3138:10 3130:87 3126:10 3110:10 3099:10 3087:83 3075:87 3017:− 3015:dB 3010:= 3008:dB 2923:) 2919:× 2915:× 2762:26 2743:10 2735:10 2701:dB 2696:40 2689:dB 2662:10 2647:10 2639:10 2577:dB 2572:30 2565:dB 2521:10 2513:20 2463:dB 2458:30 2451:dB 2403:10 2395:10 2340:10 2321:28 2317:≈ 2309:06 2287:89 2274:02 2265:93 2255:13 1906:in 1874:dB 1861:in 1834:10 1826:20 1802:: 1747:dB 1742:20 1726:10 1692:dB 1657:10 1649:20 1642:dB 1597:10 1589:10 1582:Np 1551:ln 1475:dB 1470:10 1454:10 1436:: 1356:= 1324:dB 1291:10 1283:10 1276:Np 1245:ln 1128:02 1121:93 1111:10 1100:13 1092:13 1045:: 1009:10 987:01 954:62 910:01 825:01 787:62 602:0 585:1 562:3 545:6 532:10 522:10 506:31 477:10 400:10 385:10 357:31 310:10 53:dB 7951:e 7944:t 7937:v 7799:e 7792:t 7785:v 7743:. 7668:. 7650:) 7636:. 7610:. 7586:. 7562:. 7538:. 7485:. 7451:. 7425:. 7400:. 7374:. 7348:. 7302:. 7203:. 7176:. 7152:. 7101:. 7082:. 7055:. 7026:. 6999:. 6972:. 6945:. 6886:. 6705:. 6670:7 6629:: 6621:: 6589:. 6562:. 6461:. 6449:: 6387:8 6366:7 6342:. 6292:. 6172:: 5987:. 5981:A 5882:. 5825:. 5769:. 5739:V 5726:V 5572:. 5560:. 5543:. 5454:. 5424:. 5414:. 5392:. 5382:. 5372:. 5350:. 5348:T 5340:G 5311:. 5305:K 5259:. 5233:= 5230:L 5204:x 5177:x 5153:= 5148:0 5144:P 5123:, 5120:] 5112:[ 5105:) 5098:0 5094:P 5090:P 5085:( 5065:= 5056:L 5006:. 4996:. 4919:. 4909:. 4899:. 4738:. 4659:A 4643:A 4594:× 4592:2 4492:P 4472:R 4449:P 4443:R 4438:= 4435:V 4416:u 4408:v 4394:. 4382:= 4378:) 4372:V 4353:V 4348:1 4342:( 4296:V 4282:W 4262:= 4259:V 4206:) 4151:E 4141:E 4137:L 4129:E 4125:L 4117:x 4113:x 4104:x 4102:/ 4100:x 4096:L 4091:) 4086:x 4081:x 4077:L 3952:" 3870:( 3835:, 3825:) 3814:I 3810:I 3805:( 3787:= 3782:p 3778:L 3748:p 3737:p 3720:, 3710:) 3699:p 3689:p 3683:( 3665:= 3660:p 3656:L 3561:2 3495:) 3491:2 3470:) 3459:/ 3447:+ 3438:/ 3424:( 3405:( 3395:= 3378:) 3374:2 3370:/ 3364:) 3353:/ 3341:+ 3332:/ 3318:( 3312:( 3289:= 3279:2 3275:/ 3270:) 3257:+ 3244:( 3240:= 3233:) 3227:, 3221:( 3212:M 3166:) 3155:/ 3134:/ 3120:( 3096:= 3019:N 3012:C 3006:) 3004:0 3001:N 2999:/ 2997:C 2993:0 2990:N 2983:C 2979:0 2976:N 2974:/ 2972:C 2935:C 2931:B 2927:A 2921:C 2917:B 2913:A 2850:2 2822:≈ 2819:2 2801:2 2798:/ 2795:1 2771:2 2755:= 2752:1 2740:3 2731:= 2728:G 2693:= 2683:) 2676:W 2666:W 2656:( 2636:= 2631:G 2627:L 2602:G 2598:L 2569:= 2559:) 2552:V 2547:1 2541:V 2530:( 2510:= 2505:G 2501:L 2455:= 2445:) 2438:W 2433:1 2427:W 2418:1 2412:( 2392:= 2387:G 2383:L 2315:e 2192:2 2189:F 2185:2 2182:P 2178:1 2175:F 2171:1 2168:P 2149:2 2144:) 2137:1 2133:F 2127:2 2123:F 2117:( 2112:= 2105:1 2101:P 2095:2 2091:P 2075:0 2072:F 2068:0 2065:P 2027:2 2022:) 2015:0 2011:F 2006:) 2003:t 2000:( 1997:F 1991:( 1986:= 1979:0 1975:P 1970:) 1967:t 1964:( 1961:P 1903:V 1892:V 1868:) 1857:V 1847:V 1841:( 1823:= 1818:G 1814:L 1799:G 1795:L 1760:0 1756:F 1736:F 1732:L 1722:= 1719:F 1686:) 1679:0 1675:F 1671:F 1666:( 1646:= 1636:) 1629:2 1624:0 1620:F 1614:2 1610:F 1604:( 1586:= 1576:) 1569:0 1565:F 1561:F 1556:( 1548:= 1543:F 1539:L 1525:0 1522:F 1518:F 1488:0 1484:P 1464:P 1460:L 1450:= 1447:P 1433:P 1429:L 1425:0 1422:P 1418:P 1410:P 1406:L 1402:0 1399:P 1395:P 1390:P 1386:L 1382:0 1379:P 1375:P 1370:P 1366:L 1361:0 1358:P 1354:P 1349:0 1346:P 1342:P 1318:) 1311:0 1307:P 1303:P 1298:( 1280:= 1270:) 1263:0 1259:P 1255:P 1250:( 1240:2 1237:1 1232:= 1227:P 1223:L 1208:P 1204:L 1200:0 1197:P 1193:P 1070:e 1054:2 1050:1 1038:2 1034:1 1013:x 1003:x 996:x 981:0 976:1 964:0 945:0 931:0 921:1 915:0 901:0 891:2 882:0 877:1 868:0 857:0 846:0 830:0 819:0 808:0 803:1 797:0 781:0 775:0 764:0 758:0 748:2 742:0 736:0 724:2 721:/ 718:1 710:0 703:4 700:/ 697:1 689:0 675:2 672:/ 669:1 658:0 651:2 648:/ 645:1 637:0 626:0 620:0 610:1 605:1 594:1 588:1 578:2 571:1 565:1 554:1 548:3 537:3 497:1 441:1 428:1 413:3 341:1 238:N 97:V 65:B 63:( 42:. 20:)

Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.

Index