The decibel (dB) is a logarithmic unit of measurement that expresses the magnitude of a physical quantity (usually power or intensity) relative to a specified or implied reference level. Since it expresses a ratio of two quantities with the same unit, it is a dimensionless unit. A decibel is one tenth of a bel, a seldomused unit.
The decibel is widely known as a measure of sound pressure level, but is also used for a wide variety of other measurements in science and engineering (particularly acoustics, electronics, and control theory) and other disciplines. It confers a number of advantages, such as the ability to conveniently represent very large or small numbers, a logarithmic scaling that roughly corresponds to the human perception of sound and light, and the ability to carry out multiplication of ratios by simple addition and subtraction.
The decibel symbol is often qualified with a suffix, which indicates which reference quantity or frequency weighting function has been used. For example, "dBm" indicates that the reference quantity is one milliwatt, while "dBu" is referenced to 0.775 volts RMS.^{[1]}
The definitions of the decibel and bel use base10 logarithms. For a similar unit using natural logarithms to base e, see neper.
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The decibel originates from methods used to quantify reductions in audio levels in telephone circuits. These losses were originally measured in units of Miles of Standard Cable (MSC), where 1 MSC corresponded to the loss of power over a 1 mile (approximately 1.6 km) length of standard telephone cable at a frequency of 5000 radians per second (795.8 Hz) and roughly matched the smallest attenuation detectable to an average listener. Standard telephone cable was defined as "a cable having uniformly distributed resistances of 88 ohms per loop mile and uniformly distributed shunt capacitance of .054 microfarad per mile" (approximately 19 gauge).^{[citation needed]}
The transmission unit or TU was devised by engineers of the Bell Telephone Laboratories in the 1920s to replace the MSC. 1 TU was defined as ten times the base10 logarithm of the ratio of measured power to reference power.^{[2]} The definitions were conveniently chosen such that 1 TU approximately equalled 1 MSC (specifically, 1.056 TU = 1 MSC).^{[3]} Eventually, international standards bodies adopted the base10 logarithm of the power ratio as a standard unit, which was named the "bel" in honor of the Bell System's founder and telecommunications pioneer Alexander Graham Bell. The bel was a factor of ten larger than the TU, such that 1 TU equalled 1 decibel.^{[4]} In many situations, the bel proved inconveniently large, so the decibel has become more common.
In April 2003, the International Committee for Weights and Measures (CIPM) considered a recommendation for the decibel's inclusion in the SI system, but decided not to adopt the decibel as an SI unit.^{[5]} However, the decibel is recognized by other international bodies such as the International Electrotechnical Commission (IEC).^{[6]} The IEC permits the use of the decibel with field quantities as well as power and this recommendation is followed by many national standards bodies, such as NIST, which justifies the use of the decibel for voltage ratios.^{[7]}
When referring to measurements of power or intensity, a ratio can be expressed in decibels by evaluating ten times the base10 logarithm of the ratio of the measured quantity to the reference level. Thus, if L represents the ratio of a power value P_{1} to another power value P_{0}, then L_{dB} represents that ratio expressed in decibels and is calculated using the formula:
P_{1} and P_{0} must have the same dimension, i.e. they must measure the same type of quantity, and the same units before calculating the ratio: however, the choice of scale for this common unit is irrelevant, as it changes both quantities by the same factor, and thus cancels in the ratio—the ratio of two quantities is scaleinvariant. Note that if P_{1} = P_{0} in the above equation, then L_{dB} = 0. If P_{1} is greater than P_{0} then L_{dB} is positive; if P_{1} is less than P_{0} then L_{dB} is negative.
Rearranging the above equation gives the following formula for P_{1} in terms of P_{0} and L_{dB}:
Since a bel is equal to ten decibels, the corresponding formulae for measurement in bels (L_{B}) are
When referring to measurements of amplitude it is usual to consider the ratio of the squares of A_{1} (measured amplitude) and A_{0} (reference amplitude). This is because in most applications power is proportional to the square of amplitude, and it is desirable for the two decibel formulations to give the same result in such typical cases. Thus the following definition is used:
This formula is sometimes called the 20 log rule, and similarly the formula for ratios of powers is the 10 log rule, and similarly for other factors.^{[citation needed]} The equivalence of and is of the standard properties of logarithms.
The formula may be rearranged to give
Similarly, in electrical circuits, dissipated power is typically proportional to the square of voltage or current when the impedance is held constant. Taking voltage as an example, this leads to the equation:
where V_{1} is the voltage being measured, V_{0} is a specified reference voltage, and G_{dB} is the power gain expressed in decibels. A similar formula holds for current.
Note that all of these examples yield dimensionless answers in dB because they are relative ratios expressed in decibels.
Notice that , illustrating the consequence from the definitions above that G_{dB} has the same value, , regardless of whether it is obtained with the 10log or 20log rules; provided that in the specific system being considered power ratios are equal to amplitude ratios squared.
A change in power ratio by a factor of 10 is a 10 dB change. A change in power ratio by a factor of two is approximately a 3 dB change. More precisely, the factor is 10^{3/10}, or 1.9953, about 0.24% different from exactly 2. Similarly, an increase of 3 dB implies an increase in voltage by a factor of approximately , or about 1.41, an increase of 6 dB corresponds to approximately four times the power and twice the voltage, and so on. In exact terms the power ratio is 10^{6/10}, or about 3.9811, a relative error of about 0.5%.
The use of the decibel has a number of merits:
The decibel is commonly used in acoustics to quantify sound levels relative to some 0 dB reference. The reference level is typically set at the threshold of perception of an average human and there are common comparisons used to illustrate different levels of sound pressure. As with other decibel figures, normally the ratio expressed is a power ratio (rather than a pressure ratio).
The human ear has a large dynamic range in audio perception. The ratio of the sound pressure that causes permanent damage during short exposure to the quietest sound that the ear can hear is above a trillion. Such large measurement ranges are conveniently expressed in logarithmic units: the base10 logarithm of one trillion (10^{12}) is 12, which is expressed as an audio level of 120 dB. Since the human ear is not equally sensitive to all sound frequencies, noise levels at maximum human sensitivity — for example, the higher harmonics of middle A (between 2 and 4 kHz) — are factored more heavily into some measurements using frequency weighting.
In electronics, the decibel is often used to express power or amplitude ratios (gains), in preference to arithmetic ratios or percentages. One advantage is that the total decibel gain of a series of components (such as amplifiers and attenuators) can be calculated simply by summing the decibel gains of the individual components. Similarly, in telecommunications, decibels are used to account for the gains and losses of a signal from a transmitter to a receiver through some medium (free space, wave guides, coax, fiber optics, etc.) using a link budget.
The decibel unit can also be combined with a suffix to create an absolute unit of electric power. For example, it can be combined with "m" for "milliwatt" to produce the "dBm". Zero dBm is the power level corresponding to a power of one milliwatt, and 1 dBm is one decibel greater (about 1.259 mW).
In professional audio, a popular unit is the dBu (see below for all the units). The "u" stands for "unloaded", and was probably chosen to be similar to lowercase "v", as dBv was the older name for the same thing. It was changed to avoid confusion with dBV. This unit (dBu) is an RMS measurement of voltage which uses as its reference 0.775 V_{RMS}. Chosen for historical reasons, it is the voltage level which delivers 1 mW of power in a 600 ohm resistor, which used to be the standard reference impedance in telephone audio circuits.
The bel is used to represent noise power levels in hard drive specifications. It shares the same symbol (B) as the byte.
In an optical link, if a known amount of optical power, in dBm (referenced to 1 mW), is launched into a fiber, and the losses, in dB (decibels), of each electronic 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.
In spectrometry and optics, the blocking unit used to measure optical density is equivalent to −1 B. In astronomy, the apparent magnitude measures the brightness of a star logarithmically, since, just as the ear responds logarithmically to acoustic power, the eye responds logarithmically to brightness; however astronomical magnitudes reverse the sign with respect to the bel, so that the brightest stars have the lowest magnitudes, and the magnitude increases for fainter stars.
In connection with digital and video image sensors, decibels generally represent ratios of video voltages or digitized light levels, using 20 log of the ratio, even when the represented optical power is directly proportional to the voltage or level, not to its square. Thus, a camera signaltonoise ratio of 60 dB represents a power ratio of 1000:1 between signal power and noise power, not 1,000,000:1.^{[8]}
Although decibel measurements are always relative to a reference level, if the numerical value of that reference is explicitly and exactly stated, then the decibel measurement is called an "absolute" measurement, in the sense that the exact value of the measured quantity can be recovered using the formula given earlier. For example, since dBm indicates power measurement relative to 1 milliwatt,
If the numerical value of the reference is not explicitly stated, as in the dB gain of an amplifier, then the decibel measurement is purely relative. The practice of attaching a suffix to the basic dB unit, forming compound units such as dBm, dBu, dBA, etc, is not permitted by SI.^{[9]} However, outside of documents adhering to SI units, the practice is very common as illustrated by the following examples.
dBm or dBmW
Since the decibel is defined with respect to power, not amplitude, conversions of voltage ratios to decibels must square the amplitude, as discussed above.
dBV
dBu or dBv
dBmV
dBμV or dBuV
Probably the most common usage of "decibels" in reference to sound loudness is dB SPL, referenced to the nominal threshold of human hearing:^{[11]}
dB(SPL)
dB(PA)
dB SIL
dB SWL
dB(A), dB(B), and dB(C)
dB HL or dB hearing level is used in audiograms as a measure of hearing loss. The reference level varies with frequency according to a minimum audibility curve as defined in ANSI and other standards, such that the resulting audiogram shows deviation from what is regarded as 'normal' hearing.^{[citation needed]}
dB Q is sometimes used to denote weighted noise level, commonly using the ITUR 468 noise weighting^{[citation needed]}
dBsm
dBJ
dBμV/m or dBuV/m
dBf
dBW
dBk
dBi
dBd
dBiC
dBq
dBFS or dBfs
dBHz
dBov or dBO
dBr

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Singular 
Plural 
decibel (plural decibels)
decibel m. inv.
A decibel or dB measures power or intensity. Most often, it is used to say how loud a sound is. At the moment, the decibel is not an SI unit. dB are units of sound mostly for consensus on hearing protection.
Some examples of sounds are:
Sound Level  Examples 

200250 DB  Cannon at 12' 
175200 DB  Saturn Rocket firing 
150 DB  Airplane at takeoff 
130 DB  Above this can damage the ear quickly, and pain is felt. 
120 DB  Diesel engine, ball mill 
100 DB  Lawn mower, factory 
90 DB  Band or symphony, above this can damage the ear if heard extensively. 
80 DB  Police or fire siren, electric shaver 
70 DB  Radio sound level, crowded neighborhood. 
50 DB  Can normally awaken a sleeping person. 
3035 DB  Very quiet conversation, private office noise 
20 DB  Rustling leaves, whispering 
10 DB  Soundproofed room, the minimum most human ears can hear. 
Hearing protection can also be used to shield from ear damage.
Decibels  Maximum Exposure Time 

90  8 hours 
92  6 hours 
95  4 hours 
97  3 hours 
100  2 hours 
102  90 minutes 
105  60 minutes 
110  30 minutes 
115  1015 minutes 
120  35 minutes 
