1.a logarithmic unit of sound intensity; 10 times the logarithm of the ratio of the sound intensity to some reference intensity
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DeciBel Research Inc. • Decibel (KDE) • Decibel (disambiguation) • Decibel (magazine) • Decibel Audio Player • Decibel Festival • Decibel scale • Decibel watt • Doctor Decibel • Miss Decibel • Miss Decibel (song)
unité de mesure physique (fr)[Classe...]
unité de puissance sonore (fr)[Classe]
|dB||power ratio||amplitude ratio|
|100||10 000 000 000||100 000|
|90||1 000 000 000||31 620|
|80||100 000 000||10 000|
|70||10 000 000||3 162|
|60||1 000 000||1 000|
|-50||0||.000 01||0||.003 162|
|-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 log10 x. It is easier to grasp and compare 2- or 3-digit numbers than to compare up to 10 digits.|
The decibel (dB) is a logarithmic unit that indicates the ratio of a physical quantity (usually power or intensity) relative to a specified or implied reference level. A ratio in decibels is ten times the logarithm to base 10 of the ratio of two power quantities. A decibel is one tenth of a bel, a seldom-used unit.
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 signal-to-noise 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.
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.
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.
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).
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 base-10 logarithm of the ratio of measured power to a reference power level. The definitions were conveniently chosen such that 1 TU approximately equaled 1 MSC (specifically, 1.056 TU = 1 MSC). In 1928, the Bell system renamed the TU the decibel. Along with the decibel, the Bell System defined the bel, the base-10 logarithm of the power ratio, in honor of their founder and telecommunications pioneer Alexander Graham Bell. The bel is seldom used, as the decibel was the proposed working unit.
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 100.1 and any two amounts of power differ by N decibels when they are in the ratio of 10N(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. However, the decibel is recognized by other international bodies such as the International Electrotechnical Commission (IEC). 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.
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 . 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 1.25892 (or ) and an amplitude ratio of 1.12202 (or ).
When referring to measurements of power or intensity, a ratio can be expressed in decibels by evaluating ten times the base-10 logarithm of the ratio of the measured quantity to the reference level. Thus, the ratio of a power value P1 to another power value P0 is represented by LdB, that ratio expressed in decibels, which is calculated using the formula:
The base-10 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 one-tenth of a bel). P1 and P0 must measure the same type of quantity, and have the same units before calculating the ratio. If P1 = P0 in the above equation, then LdB = 0. If P1 is greater than P0 then LdB is positive; if P1 is less than P0 then LdB is negative.
Rearranging the above equation gives the following formula for P1 in terms of P0 and LdB:
Since a bel is equal to ten decibels, the corresponding formulae for measurement in bels (LB) are
When referring to measurements of field amplitude, it is usual to consider the ratio of the squares of A1 (measured amplitude) and A0 (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 equivalence of and is one 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 V1 is the voltage being measured, V0 is a specified reference voltage, and GdB is the power gain expressed in decibels. A similar formula holds for current.
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 103/10, 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 106/10, 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 a 0 dB reference which has been defined as a sound pressure level of .0002 microbar, or 20 micropascals. The reference level is set at the typical threshold of perception of an average human and there are common comparisons used to illustrate different levels of sound pressure. As 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 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. Such large measurement ranges are conveniently expressed in logarithmic units: the base-10 logarithm of one trillion (1012) 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—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 equals 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 VRMS. 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 audio 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.
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. Thus, a camera signal-to-noise ratio or dynamic range of 40 dB represents a power ratio of 100:1 between signal power and noise power, not 10,000:1. 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.
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 "signal-to-noise" (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 base-2 log unit, the f-stop, 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 f-stops or 10 bits, since 103 is nearly equal to 210.
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. However, outside of documents adhering to SI units, the practice is very common as illustrated by the following examples.
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.
dBu or dBv
In professional audio, 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 +4 dBu. Consumer equipment will more often use a much lower "nominal" signal level of -10 dBV. 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 +4 dBu and -10 dBV is common in professional equipment.
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: 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.
One Pascal is equal to 94 dB(SPL). This level is used to specify microphone sensitivity. For example, a typical microphone may put out 20 mV at one pascal. For other sound pressure levels, the output voltage can be computed from this basis, except that noise and distortion will affect the extreme levels.
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.
dBμV/m or dBuV/m
dBov or dBO
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