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dB  power ratio  amplitude ratio  

100  10 000 000 000  100 000  
90  1 000 000 000  31 623  
80  100 000 000  10 000  
70  10 000 000  3 162  
60  1 000 000  1 000  
50  100 000  316  .2  
40  10 000  100  
30  1 000  31  .62  
20  100  10  
10  10  3  .162  
6  3  .981  1  .995 (~2) 
3  1  .995 (~2)  1  .413 
1  1  .259  1  .122 
0  1  1  
1  0  .794  0  .891 
3  0  .501 (~1/2)  0  .708 
6  0  .251  0  .501 (~1/2) 
10  0  .1  0  .316 2 
20  0  .01  0  .1 
30  0  .001  0  .031 62 
40  0  .000 1  0  .01 
50  0  .000 01  0  .003 162 
60  0  .000 001  0  .001 
70  0  .000 000 1  0  .000 316 2 
80  0  .000 000 01  0  .000 1 
90  0  .000 000 001  0  .000 031 62 
100  0  .000 000 000 1  0  .000 01 
An example scale showing power ratios x and amplitude ratios √x and dB equivalents 10 log_{10} x. It is easier to grasp and compare 2 or 3digit numbers than to compare up to 10 digits. 
dB  power ratio  amplitude ratio  

100  10 000 000 000  100 000  
90  1 000 000 000  31 623  
80  100 000 000  10 000  
70  10 000 000  3 162  
60  1 000 000  1 000  
50  100 000  316  .2  
40  10 000  100  
30  1 000  31  .62  
20  100  10  
10  10  3  .162  
6  3  .981  1  .995 (~2) 
3  1  .995 (~2)  1  .413 
1  1  .259  1  .122 
0  1  1  
1  0  .794  0  .891 
3  0  .501 (~1/2)  0  .708 
6  0  .251  0  .501 (~1/2) 
10  0  .1  0  .316 2 
20  0  .01  0  .1 
30  0  .001  0  .031 62 
40  0  .000 1  0  .01 
50  0  .000 01  0  .003 162 
60  0  .000 001  0  .001 
70  0  .000 000 1  0  .000 316 2 
80  0  .000 000 01  0  .000 1 
90  0  .000 000 001  0  .000 031 62 
100  0  .000 000 000 1  0  .000 01 
An example scale showing power ratios x and amplitude ratios √x and dB equivalents 10 log_{10} x. It is easier to grasp and compare 2 or 3digit numbers than to compare up to 10 digits. 
The decibel (dB) is a logarithmic unit used to express the ratio between two values of a physical quantity, often power or intensity. One of these quantities is often a reference value, and in this case the decibel can be used to express the absolute level of the physical quantity. The decibel is also commonly used as a measure of gain or attenuation, the ratio of input and output powers of a system, or of individual factors that contribute to such ratios. The number of decibels is ten times the logarithm to base 10 of the ratio of the two power quantities.^{[1]} A decibel is one tenth of a bel, a seldomused unit named in honor of Alexander Graham Bell.
The decibel is used for a wide variety of measurements in science and engineering, most prominently in acoustics, electronics, and control theory. In electronics, the gains of amplifiers, attenuation of signals, and signaltonoise ratios are often expressed in decibels. The decibel confers a number of advantages, such as the ability to conveniently represent very large or small numbers, and the ability to carry out multiplication of ratios by simple addition and subtraction. On the other hand, even some professionals find the decibel confusing and cumbersome.
A change in power by a factor of 10 is a 10 dB change in level. A change in power by a factor of two is approximately a 3 dB change. A change in voltage by a factor of 10 is equivalent to a change in power by a factor of 100 and is thus a 20 dB change. A change in voltage ratio by a factor of two is approximately a 6 dB change.
The decibel symbol is often qualified with a suffix that indicates which reference quantity or frequency weighting function has been used. For example, dBm indicates a reference level of one milliwatt, while dBu is referenced to approximately 0.775 volts RMS.^{[2]}
The definitions of the decibel and bel use base 10 logarithms. The neper, an alternative logarithmic ratio unit sometimes used, uses the natural logarithm (base e).^{[3]}
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 the average listener. Standard telephone cable was defined as "a cable having uniformly distributed resistance of 88 ohms per loop mile and uniformly distributed shunt capacitance of .054 microfarad per mile" (approximately 19 gauge).^{[4]}
The transmission unit (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 a reference power level.^{[5]} The definitions were conveniently chosen such that 1 TU approximately equaled 1 MSC (specifically, 1.056 TU = 1 MSC).^{[6]} In 1928, the Bell system renamed the TU the decibel.^{[7]} Along with the decibel, the Bell System defined the bel, the base10 logarithm of the power ratio, in honor of their founder and telecommunications pioneer Alexander Graham Bell.^{[8]} The bel is seldom used, as the decibel was the proposed working unit.^{[9]}
The naming and early definition of the decibel is described in the NBS Standard's Yearbook of 1931:^{[10]}
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 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.
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^{0.1} and any two amounts of power differ by N decibels when they are in the ratio of 10^{N(0.1)}. 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 expressing the efficiency of different parts of the circuit...
In April 2003, the International Committee for Weights and Measures (CIPM) considered a recommendation for the decibel's inclusion in the International System of Units (SI), but decided not to adopt the decibel as an SI unit.^{[11]} However, the decibel is recognized by other international bodies such as the International Electrotechnical Commission (IEC) and International Organization for Standardization (ISO).^{[12]} 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.^{[13]} The term field quantity is deprecated by ISO. Neither IEC nor ISO permit the use of modifiers such as dBA or dBV. Such units, though widely used, are not defined by international standards.
A decibel (dB) is one tenth of a bel (B), i.e., 1B = 10dB. The bel represents a ratio between two power quantities of 10:1, and a ratio between two field quantities of √10:1.^{[14]} A field quantity is a quantity such as voltage, current, sound pressure, electric field strength, velocity and charge density, the square of which in linear systems is proportional to power. A power quantity is a power or a quantity directly proportional to power, e.g., energy density, acoustic intensity and luminous intensity.
The calculation of the ratio in decibels varies depending on whether the quantity being measured is a power quantity or a field quantity.
Two signals that differ by one decibel have a power ratio of approximately 1.25892 (or ) and an amplitude ratio of 1.12202 (or ).^{[15]}^{[16]}
The bel is defined by ISO Standard 800003:2006 as (1/2) ln(10) nepers. Because the decibel is one tenth of a bel, it follows that 1 dB = (1/20) ln(10) Np. The same standard defines 1 Np as equal to 1.
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, the ratio of a power value P_{1} to another power value P_{0} is represented by L_{dB}, that ratio expressed in decibels,^{[17]} which is calculated using the formula:
The base10 logarithm of the ratio of the two power levels is the number of bels. The number of decibels is ten times the number of bels (equivalently, a decibel is onetenth of a bel). P_{1} and P_{0} must measure the same type of quantity, and have the same units before calculating the ratio. 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}:
When referring to measurements of field 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:
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.
The term rootpower quantity is introduced by ISO Standard 800001:2009 as a synonym of field quantity. The term field quantity is deprecated by that standard.
All of these examples yield dimensionless answers in dB because they are relative ratios expressed in decibels. Note that the unit "dBW" is often used to denote a ratio where the reference is 1 W, and similarly "dBm" for a 1 mW reference point.
Notice that , illustrating the consequence from the definitions above that has the same value, , 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.
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 decibel has the following properties:
According to several articles published in Electrical Engineering^{[18]} and the Journal of the Acoustical Society of America,^{[19]}^{[20]}^{[21]} the decibel suffers from the following disadvantages:
Hickling^{[20]} concludes "Decibels are a useless affectation, which is impeding the development of noise control as an engineering discipline".
Another disadvantage is that decibel units are not additive^{[22]} thus being "of unacceptable form for use in dimensional analysis".^{[23]}
The decibel is commonly used in acoustics as a unit of sound pressure level, for a reference pressure of 20 micropascals in air^{[24]} and 1 micropascal in water. The reference pressure in air is set at the typical threshold of perception of an average human and there are common comparisons used to illustrate different levels of sound pressure. Sound pressure is a field quantity, so the formula used to calculate sound pressure level is the field version:
The human ear has a large dynamic range in audio perception. The ratio of the sound intensity that causes permanent damage during short exposure to the quietest sound that the ear can hear is greater than or equal to 1 trillion (10^{12}).^{[25]} Such large measurement ranges are conveniently expressed in logarithmic units: the base10 logarithm of 10^{12} is 12, which is expressed as a sound pressure level of 120 dB re 20 micropascals. Since the human ear is not equally sensitive to all sound frequencies, noise levels at maximum human sensitivity—somewhere between 2 and 4 kHz—are factored more heavily into some measurements using frequency weighting. (See also Stevens' power law.)
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 denote signal gain or loss from a transmitter to a receiver through some medium (free space, waveguide, 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 level corresponding to 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 approximately 0.775 V_{RMS}. Chosen for historical reasons, the reference value 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 circuits.
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.^{[26]}
In spectrometry and optics, the blocking unit used to measure optical density is equivalent to −1 B.
In connection with video and digital 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, as in a CCD imager where response voltage is linear in intensity.^{[27]} Thus, a camera signaltonoise ratio or dynamic range of 40 dB represents a power ratio of 100:1 between signal power and noise power, not 10,000:1.^{[28]} Sometimes the 20 log ratio definition is applied to electron counts or photon counts directly, which are proportional to intensity without the need to consider whether the voltage response is linear.^{[29]}
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 "signaltonoise" (of the camera) would be specified in 20 log dBs, 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.
Photographers also often use an alternative base2 log unit, the fstop, and in software contexts these image level ratios, particularly dynamic range, are often loosely referred to by the number of bits needed to represent the quantity, such that 60 dB (digital photographic) is roughly equal to 10 fstops or 10 bits, since 10^{3} is nearly equal to 2^{10}.
Suffixes are commonly attached to the basic dB unit in order to indicate the reference level against which the decibel measurement is taken. For example, dBm indicates power measurement relative to 1 milliwatt.
In cases such as this, where the numerical value of the reference is explicitly and exactly stated, 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. 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 SI does not permit attaching qualifiers to units, whether as suffix or prefix, other than standard SI prefixes. Therefore, even though the decibel is accepted for use alongside SI units, the practice of attaching a suffix to the basic dB unit, forming compound units such as dBm, dBu, dBA, etc., is not.^{[30]}
Outside of documents adhering to SI units, the practice is very common as illustrated by the following examples. Please note there is no general rule, rather disciplinespecific practices. Sometimes the suffix is a unit symbol ("W","K","m"), sometimes it's a transliteration of a unit symbol ("uV" instead of μV for micro volt), sometimes it's an acronym for the units name ("sm" for m^{2}, "m" for mW), other times it's a mnemonic for the type of quantity being calculated ("i" for antenna gain w.r.t. an isotropic antenna, "λ" for anything normalized by the EM wavelength). Sometimes the suffix is connected with a dash (dBHz), most of the time it's not.
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.
dBV
dBu or dBv
dBmV
dBμV or dBuV
Probably the most common usage of "decibels" in reference to sound loudness is dB SPL, sound pressure level referenced to the nominal threshold of human hearing:^{[34]} The measures of pressure (a field quantity) use the factor of 20, and the measures of power (e.g. dB SIL and dB SWL) use the factor of 10.
dB SPL
An RMS sound pressure of one pascal corresponds to a level of 94 dB SPL.
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]}
dBTP
dBsm
dBi
dBd
dBiC
dBq
dBsm
dBm^{−1}
dBHz
dBov or dBO
dBr
dBrnC
dBK
dB/K
Apart from suffixes and reference levels as above, decibels can also be involved in ratios or fractions: "dB/m" means decibels per meter, "dB/mi" is decibels per mile, etc. Attenuation constants are commonly expressed in such units, in fields such as optical fiber communication, radio propagation path loss, etc. These quantities are to be manipulated obeying the rules of dimensional analysis, e.g., a 100meter run with a 3.5 dB/km fiber yields a loss of 0.35 dB = 3.5 dB/km × 0.1 km.

