A unit used to express relative difference in power or intensity, usually between two acoustic or electric signals, equal to ten times the common logarithm of the ratio of the two levels.
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A unit used to express relative difference in power or intensity, usually between two acoustic or electric signals, equal to ten times the common logarithm of the ratio of the two levels.
A logarithmic unit used to express the magnitude of a change in level of power, voltage, current, or sound intensity. A decibel (dB) is 1/10 bel.
In acoustics a step of 1 bel is too large for most uses. It is therefore the practice to express sound intensity in decibels. The level of a sound of intensity I in decibels relative to a reference intensity IR is given by notation (1). Because sound intensity
1. 
is proportional to the square of sound pressure P, the level in decibels is given by Eq. (2).
2. 
The reference pressure is usually taken as 0.0002 dyne/cm2 or 0.0002 microbar. (The pressure of the Earth's atmosphere at sea level is approximately 1 bar.) See also Sound pressure.
The neper is similar to the decibel but is based upon natural (napierian) logarithms. One neper is equal to 8.686 dB. See also Neper; Volume unit (vu).
Unit measurement of the intensity of sound; abbreviated db.
A logarithmic ratio unit that indicates by what proportion one intensity level differs from another.
electrics, acoustics, etc. Symbol dB. A comparative measure of power levels, applied to electric signals, sound, etc., introduced in 1924 as the transmission unit
[Hartley R. V. L. Elect. Comm. Vol. 3, 34-42 (1924)] measured, for powers P1 and P2, as
= 10 log10 P1/P2which means that an increment of 1 unit represents a multiplication of power ratio by 100.1, an increase of nearly 26%. The name decibel was in regular use by 1929
= log10 P1/P2.Either provides thereby a geometric scale.
10 log10 P1/P2 = 10 log10 (A1/A2)2 = 20 log10 A1/A2where A1 and A2 are the respective amplitudes. (This holds exactly only for a pure harmonic signal of a single frequency, but is sufficiently close to true for electrical signals generally to be applied collectively to their mixture of frequencies.)
10 log10 p1/p2is used for any comparable variables p1 and p2 (without consideration of the power-to-amplitude factor, which is notable for deciboyle since amplitude is electrical pressure). The boyle scheme uses the torr or mm of mercury as its unit, but the characteristic atmospheric pressure of 1 bar (100 kPa, 750.062~ torr) as its reference.
10 log (p/750.062~) = 10 log p - 10 log 750.062~ = (10 log p) - 28.751~.
A unit used for expressing the difference in level between sounds of different intensities; as it is a logarithmic unit, it corresponds well to the listener's experience of volume.
For more information on decibel (dB), visit Britannica.com.
A unit of measurement of the volume of sounds.
A unit used to express the ratio of two powers, usually electric or acoustic powers, equal to one-tenth of a bel; one decibel equals approximately the smallest difference in acoustic power the human ear can detect. Abbreviated dB or db. See also bel.
The sharp increase in decibel level indicated that the music was becoming too loud.
The decibel (dB) is a logarithmic unit of measurement that expresses the
magnitude of a physical quantity (usually power) relative to a specified or implied
reference level. Its logarithmic nature allows very large or very small ratios to be
represented by a convenient number, in a similar manner to scientific notation.
Being essentially a ratio, it is a dimensionless unit. Decibels are useful for a
wide variety of measurements in acoustics, physics,
electronics and other disciplines.
The idea of decibel is to linearize a physical value which is exponential but perceived as linear (in fact as a logarithm of the original) by human. This concerns a lot of common stuff, such as intensity of light, level of noise, frequency of sound.
The decibel is not an SI unit, although the International Committee for Weights and Measures (CIPM) has recommended its inclusion in the SI system.[citation needed] Following the SI convention, the d is lowercase, as it represents the SI prefix deci-, and the B is capitalized, as it is an abbreviation of a name-derived unit, the bel (see below). The full name decibel follows the usual English capitalization rules for a common noun. The decibel symbol is often qualified with a suffix, which indicates which reference quantity has been assumed. For example, "dBm" indicates that the reference quantity is one milliwatt. The practice of attaching a suffix in this way, though not permitted by SI,[1] is widely followed.
A decibel is one tenth of a bel (B). Devised by engineers of the Bell Telephone Laboratory to quantify the reduction in audio level over a 1 mile (approximately 1.6 km) length of standard telephone cable, the bel was originally called the transmission unit or TU, but was renamed in 1923 or 1924 in honor of the Bell System's founder and telecommunications pioneer Alexander Graham Bell. In many situations, however, the bel proved inconveniently large, so the decibel has become more common.
The definitions of the decibel and bel use base-10 logarithms. For a similar unit using natural logarithms to base e, see neper.
An increase of 3 dB corresponds to an approximate doubling of power. (In exact terms, the factor is 103/10, or 1.9953, about 0.24% different from exactly 2.) Since in many electrical applications power is proportional to the square of voltage, an increase of 3 dB implies an increase in voltage by a factor of approximately √2, or about 1.41. Similarly, an increase of 6 dB corresponds to approximately four times the power and twice the voltage, and so on. (In exact terms the power factor is 106/10, or about 3.9811, a relative error of about 0.5%.) See the formulas below for further details.
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, XdB is calculated using the formula:

where X is the actual value of the quantity being measured, X0 is a specified or implied reference level, and then XdB is the quantity expressed in units of decibels, relative to X0. Which reference is used depends on convention and context (see later in this article). X and X0 must have the same dimensions (that is, must measure the same type of quantity), and must as necessary be converted to the same units before calculating the ratio of their numerical values. The reference level itself is always at 0 dB, as shown by setting X = X0 in the above equation. If X is greater than X0 then XdB is positive; if X is less than X0 then XdB is negative.
Rearranging the above equation gives the following formula for X in terms of X0 and XdB:

Since a bel is equal to ten decibels, the corresponding formulae for measurement in bels (XB) are


When referring to measurements of amplitude it is usual to consider the ratio of the squares of X (measured amplitude) and X0 (reference amplitude). This is because in most applications power is proportional to the square of amplitude. 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 is the voltage being measured, V0 is a specified reference voltage, and VdB is the voltage gain expressed in decibels. A similar formula holds for current.
These examples assume that X in the formulas above measures power relative to 1 W (one watt); i.e. X0 = 1 W.



It will be seen that there is a 10 dB increase (decrease) for each factor 10 increase (decrease) in the ratio of X to
X0, and approximately a 3 dB increase (decrease) for every factor 2 increase (decrease).
The use of decibels 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 human perception; see sound pressure.
A reason for using the decibel is that the ear is capable of detecting a very large range of sound pressures (see Examples of sound pressure and sound pressure levels). The ratio of the sound pressure that causes permanent damage from short exposure to the limit that (undamaged) ears can hear is above a million. Because the power in a sound wave is proportional to the square of the pressure, the ratio of the maximum power to the minimum power is above one (short scale) trillion. To deal with such a range, logarithmic units are useful: the log of a trillion is 12, so this ratio represents a difference of 120 dB. Since the human ear is not equally sensitive to all the frequencies of sound within the entire spectrum, noise levels at maximum human sensitivity — middle A and its higher harmonics (between 2 and 4 kHz) — are factored more heavily into sound descriptions using a process called frequency weighting.
The decibel is used rather than arithmetic ratios or percentages because when certain types of circuits, such as amplifiers and attenuators, are connected in series, expressions of power level in decibels may be arithmetically added and subtracted. It is also common in disciplines such as audio, in which the properties of the signal are best expressed in logarithms due to the response of the human ear.
In radio electronics and telecommunications, the decibel is used to describe the ratio between two measurements of electric power. It 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 one milliwatt, and 1 dBm is one decibel greater than 0 dBm, or about 1.259 mW.
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.
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 VRMS. Chosen for historical reasons, it is the voltage level at which you get 1 mW of power in a 600 ohm resistor, which used to be the standard reference impedance in almost all professional low impedance 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 fibre, and the losses, in dB (decibels), of each electronic component (e.g., connectors, splices, and lengths of fibre) are known, the overall link loss may be quickly calculated by simple 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.
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 formulas 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.[2] However, the practice is very common, as illustrated by the following examples.
dBm or dBmW
Note that the decibel has a different definition when applied to voltage (as contrasted with power). See the "Definitions" section above.
dBu or dBv
dBV
dBmV
dB(SPL)
dB SIL
dB SWL
dB(A), dB(B), and dB(C)
dBJ
dBm
dBμ or dBu
dBf
dBW
dBk
dBd
dBFS or dBfs
dB-Hz
dBi
dBiC
dBov or dBO
dBr
Decibels are handy for mental calculation, because adding them is easier than multiplying ratios. First, however, one has to be able to convert easily between ratios and decibels. The most obvious way is to memorize the logs of small primes, but there are a few other tricks that can help.
The values of coins and banknotes are round numbers. The rules are:
Now 6.25 and 6.4 are approximately equal to 6.3, so we don't care. Thus the round numbers between 1 and 10 are these:
Ratio 1 1.25 1.6 2 2.5 3.2 4 5 6.3 8 10 dB 0 1 2 3 4 5 6 7 8 9 10
This useful approximate table of logarithms is easily reconstructed or memorized.
To one decimal place of precision, 4.x is 6.x in dB (energy).
Examples:
To one decimal place of precision, x → (½ • x + 5.0 dB) for 7.0 ≤ x ≤ 10.
Examples:
A level difference of ±3 dB is roughly double/half power (equal to a ratio of 1.995). That is why it is commonly used as a marking on sound equipment and the like.
Another common sequence is 1, 2, 5, 10, 20, 50 ... . These preferred numbers are very close to being equally spaced in terms of their logarithms. The actual values would be 1, 2.15, 4.64, 10 ... .
The conversion for decibels is often simplified to: "+3 dB means two times the power and 1.414 times the voltage", and "+6 dB means four times the power and two times the voltage ".
While this is accurate for many situations, it is not exact. As stated above, decibels are defined so that +10 dB means "ten times the power". From this, we calculate that +3 dB actually multiplies the power by 103/10. This is a power ratio of 1.9953 or about 0.25% different from the "times 2" power ratio that is sometimes assumed. A level difference of +6 dB is 3.9811, about 0.5% different from 4.
To contrive a more serious example, consider converting a large decibel figure into its linear ratio, for example 120 dB. The power ratio is correctly calculated as a ratio of 1012 or one trillion. But if we use the assumption that 3 dB means "times 2", we would calculate a power ratio of 2120/3 = 240 = 1.0995 × 1012, giving a 10% error.
In digital audio linear pulse-code modulation, the first bit (least significant bit, or LSB) produces residual quantization noise (bearing little resemblance to the source signal) and each subsequent bit offered by the system doubles the (voltage) resolution, corresponding to a 6 dB (power) ratio. So for instance, a 16-bit (linear) audio format offers 15 bits beyond the first, for a dynamic range (between quantization noise and clipping) of (15 × 6) = 90 dB, meaning that the maximum signal (see 0 dBFS, above) is 90 dB above the theoretical peak(s) of quantization noise. The negative impacts of quantization noise can be reduced by implementing dither.
As is clear from the above description, the dB level is a logarithmic way of expressing not only power ratios, but also voltage ratios The following tables are cheat-sheets that provide values for various dB power ratios and also "voltage" ratios.
| dB level | power ratio |
dB level | voltage ratio |
|
|---|---|---|---|---|
| −30 dB | 1/1000 = 0.001 | −30 dB | = 0.03162 |
|
| −20 dB | 1/100 = 0.01 | −20 dB | = 0.1 |
|
| −10 dB | 1/10 = 0.1 | −10 dB | = 0.3162 |
|
| −3 dB | 1/2 = 0.5 (approx.) | −3 dB | = 0.7071 |
|
| 3 dB | 2 (approx.) | 3 dB | = 1.414 |
|
| 10 dB | 10 | 10 dB | = 3.162 |
|
| 20 dB | 100 | 20 dB | = 10 |
|
| 30 dB | 1000 | 30 dB | = 31.62 |
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Français (French)
n. - décibel
Ελληνική (Greek)
n. - (φυσ.) ντεσιμπέλ (μονάδα μέτρησης της έντασης ήχου)
Português (Portuguese)
n. - decibel (m)
Español (Spanish)
n. - decibel, decibelio
Svenska (Swedish)
n. - decibel
中文(简体) (Chinese (Simplified))
分贝
中文(繁體) (Chinese (Traditional))
n. - 分貝
한국어 (Korean)
n. - 데시벨(전력, 음향의 측정 단위)
العربيه (Arabic)
(الاسم) وحدة قياس, شدة الصوت
עברית (Hebrew)
n. - יחידה לעוצמת קול, דציבל
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