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decibel, abbr. dB, unit used to measure the loudness of sound. It is one tenth of a bel (named for A. G. Bell), but the larger unit is rarely used. The decibel is a measure of sound intensity as a function of power ratio, with the difference in decibels between two sounds being given by dB=10 log_{10}(P_{1}/P_{2}), where P_{1} and P_{2} are the power levels of the two sounds. The faintest audible sound, corresponding to a sound pressure of about 0.0002 dyne per sq cm, is arbitrarily assigned a value of 0 dB. The loudest sounds that can be tolerated by the human ear are about 120 dB. The level of normal conversation is about 50 to 60 dB. The decibel is also used to measure certain other quantities, such as power loss in telephone lines.

The Columbia Electronic Encyclopedia Copyright © 2004.

Licensed from Columbia University Press

Licensed from Columbia University Press

Unit for measuring the relative intensities of sounds or the relative amounts of acoustic or electric power. Because it requires about a tenfold increase in power for a sound to register twice as loud to the human ear, a logarithmic scale is useful for comparing sound intensity. Thus, the threshold of human hearing (absolute silence) is assigned the value of 0 dB and each increase of 10 dB corresponds to a tenfold increase in intensity and a doubling in loudness. The “threshold of pain” for intensity varies from 120 to 130 dB among different individuals. A related unit is the bel = 10 dB.

Learn more about decibel (dB) with a free trial on Britannica.com.

Encyclopedia Britannica, 2008. Encyclopedia Britannica Online.

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 (B).

The decibel is useful for a wide variety of measurements in science and engineering (e.g., acoustics and electronics) 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, for example, 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 0.7746 volts. The definitions of the decibel and bel use base-10 logarithms. For a similar unit using natural logarithms to base e, see neper.

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.

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Naturally, P_{1} and P_{0} must have the same dimension (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. 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}:

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Since a bel is equal to ten decibels, the corresponding formulae for measurement in bels (L_{B}) are

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The formula may be rearranged to give

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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:

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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.

- To calculate the ratio of 1 kW (one kilowatt, or 1000 watts) to 1 W in decibels, use the formula

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- To calculate the ratio of 1 mW (one milliwatt) to 10 W in decibels, use the formula

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- To find the power ratio corresponding to a 3 dB change in level, use the formula

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It is seen that there is a 10 dB increase (decrease) for each factor 10 increase (decrease) in the ratio of the two power levels, and approximately a 3 dB increase (decrease) for every factor 2 increase (decrease). In exact terms, 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 √2, 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 factor is 10^{6/10}, or about 3.9811, a relative error of about 0.5%.)

- The decibel's logarithmic nature means that a very large range of ratios can be represented by a convenient number, in a similar manner to scientific notation. This allows one to clearly visualize huge changes of some quantity. (See Bode Plot and half logarithm graph.)
- The mathematical properties of logarithms mean that the overall decibel gain of a multi-component system (such as consecutive amplifiers) can be calculated simply by summing the decibel gains of the individual components, rather than needing to multiply amplification factors. Essentially this is because log(A × B × C × ...) = log(A) + log(B) + log(C) + ...
- The human perception of, for example, sound or light, is, roughly speaking, such that a doubling of actual intensity causes perceived intensity to always increase by the same amount, irrespective of the original level. The decibel's logarithmic scale, in which a doubling of power or intensity always causes an increase of approximately 3 dB, corresponds to this perception.

A reason for using the decibel is that the ear is capable of detecting a very large range of sound pressures. 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 — for example, the higher harmonics of middle A (between 2 and 4 kHz) — are factored more heavily into sound descriptions using a process called frequency weighting.

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 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 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.

- 0 dBm means no change from 1 mW. Thus, 0 dBm is the power level corresponding to a power of exactly 1 mW.
- 3 dBm means 3 dB greater than 0 dBm. Thus, 3 dBm is the power level corresponding to 10
^{3/10}× 1 mW, or approximately 2 mW. - −6 dBm means 6 dB less than 0 dBm. Thus, −6 dBm is the power level corresponding to 10
^{−6/10}× 1 mW, or approximately 250 μW (0.25 mW).

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. However, outside of documents adhering to SI units, the practice is very common as illustrated by the following examples.

- dB(1 mW) — power measurement relative to 1 milliwatt. X
_{dBm}= X_{dBW}+ 30.

- dB(1 W) — similar to dBm, except the reference level is 1 watt. 0 dBW = +30 dBm; −30 dBW = 0 dBm; X
_{dBW}= X_{dBm}− 30.

dBV

- dB(1 V
_{RMS}) — voltage relative to 1 volt, regardless of impedance.

dBu or dBv

- dB(0.775 V
_{RMS}) — voltage relative to 0.775 volts. Originally dBv, it was changed to dBu to avoid confusion with dBV. The "v" comes from "volt", while "u" comes from "unloaded". dBu can be used regardless of impedance, but is derived from a 600 Ω load dissipating 0 dBm (1 mW). Compare ambiguous use of dBu in radio engineering.

dBmV

- dB(1 mV
_{RMS}) — voltage relative to 1 millivolt, regardless of impedance. Widely used in cable television 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 ~13 nW.

dBμV or dBuV

- dB(1 μV
_{RMS}) — voltage relative to 1 microvolt. Widely used in television and aerial amplifier specifications. 60 dBμV = 0 dBmV.

- dB (Sound Pressure Level) — for sound in air and other gases, relative to 20 micropascals (μPa) = 2×10
^{−5}Pa, the quietest sound a human can hear. This is roughly the sound of a mosquito flying 3 metres away. This is often abbreviated to just "dB", which gives some the erroneous notion that "dB" is an absolute unit by itself. For sound in water and other liquids, a reference pressure of 1 μPa is used.

dB SIL

- dB Sound Intensity Level — relative to 10
^{−12}W/m^{2}, which is roughly the threshold of human hearing in air.

dB SWL

- dB Sound Power Level — relative to 10
^{−12}W.

dB(A), dB(B), and dB(C)

- These symbols are often used to denote the use of different weighting filters, used to approximate the human ear's response to sound, although the measurement is still in dB (SPL). Other variations that may be seen are dB
_{A}or dBA. According to ANSI standards, the preferred usage is to write L_{A}= x dB. Nevertheless, the units dBA and dB(A) are still commonly used as a shorthand for A-weighted measurements. Compare dBc, used in telecommunications.

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.

dB Q is sometimes used to denote weighted noise level, commonly using the ITU-R 468 noise weighting

- dB(Z) - energy of reflectivity (weather radar), or the amount of transmitted power returned to the radar receiver. Values above 15-20 dBZ usually indicate falling precipitation.

dBsm

- dBsm - decibel (referenced to one)square meter, measure of reflected energy from a target compared to the RCS of a smooth perfectly conducting sphere at least several wavelengths in size with a cross-sectional area of 1 square meter. "Stealth" aircraft and insects have negative values of dBsm, large flat plates or non-stealthy aircraft have positive values.

- dBc — power relative to the power of the main carrier frequency; typically used to describe spurs, noise, channel crosstalk, and intermodal signals which may interfere with the carrier. Compare dB(C), used in acoustics.

dBJ

- dB(J) — energy relative to 1 joule. 1 joule = 1 watt per hertz, so power spectral density can be expressed in dBJ.

dBm

- dB(mW) — power relative to 1 milliwatt.

dBμ or dBu

- dB(μV/m) — electric field strength relative to 1 microvolt per meter. Compare the ambiguous use of dBu as a unit of voltage level.

dBf

- dB(fW) — power relative to 1 femtowatt.

dBW

- dB(W) — power relative to 1 watt.

dBk

- dB(kW) — power relative to 1 kilowatt.

- dB(dipole) — the forward gain of an antenna compared to a half-wave dipole antenna.

dBFS or dBfs

- dB(full scale) — the amplitude of a signal (usually audio) compared to the maximum which a device can handle before clipping occurs. In digital systems, 0 dBFS (peak) would equal the highest level (number) the processor is capable of representing. Measured values are usually negative, since they should be less than the maximum.

dB-Hz

- dB(hertz) — bandwidth relative to 1 Hz. E.g., 20 dB-Hz corresponds to a bandwidth of 100 Hz. Commonly used in link budget calculations.

dBi

- dB(isotropic) — the forward gain of an antenna compared to the hypothetical isotropic antenna, which uniformly distributes energy in all directions.

dBiC

- dB(isometric circular) — power measurement relative to a circularly polarized isometric antenna.

dBov or dBO

- dB(overload) — the amplitude of a signal (usually audio) compared to the maximum which a device can handle before clipping occurs. Similar to dBFS, but also applicable to analog systems.

dBr

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

- dB above reference noise. See also dBrnC.

- dB relative to carrier — in telecommunications, this indicates the relative levels of noise or sideband peak power, compared to the carrier power. Compare dBC, used in acoustics.

- Cent in music
- dB drag racing
- Equal-loudness contour
- ITU-R 468 noise weighting
- Neper
- Noise (environmental)
- Richter magnitude scale
- Signal noise
- Weighting filter — discussion of dBA

- Martin, W.H. (1929). "DeciBel--The New Name for the Transmission Unit".
*Bell System Technical Journal*January - STEVENS SS (1957). "On the psychophysical law".
*Psychol Rev*64 (3): 153–81.

- What is a decibel? With sound files and animations
- Conversion of dBu to volts, dBV to volts, and volts to dBu, and dBV
- Working with decibels - a tutorial
- Conversion of sound level units: dBSPL or dBA to sound pressure p and sound intensity J
- Conversion of voltage V to dB, dBu, dBV, and dBm
- OSHA Regulations on Occupational Noise Exposure
- V
_{peak}, V_{RMS}, Power, dBm, dBu, dBV online converter at Analog Devices - Use of the decibel with respect to aerials and aerial systems

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Last updated on Thursday October 09, 2008 at 03:38:02 PDT (GMT -0700)

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