# Decibel: Wikis

Note: Many of our articles have direct quotes from sources you can cite, within the Wikipedia article! This article doesn't yet, but we're working on it! See more info or our list of citable articles.

### Did you know ...

More interesting facts on Decibel

# Encyclopedia

Attenuation chart of an RG-6 Coaxial cable, measured in decibels per 100 feet of cable

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 seldom-used 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 base-10 logarithms. For a similar unit using natural logarithms to base e, see neper.

## History

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 base-10 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 base-10 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]

## Definitions

### Power

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, if L represents the ratio of a power value P1 to another power value P0, then LdB represents that ratio expressed in decibels and is calculated using the formula:

$L_\mathrm{dB} = 10 \log_{10} \bigg(\frac{P_1}{P_0}\bigg) \,$

P1 and P0 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 scale-invariant. Note that 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:

$P_1 = 10^\frac{L_\mathrm{dB}}{10} P_0 \,$.

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

$L_\mathrm{B} = \log_{10} \bigg(\frac{P_1}{P_0}\bigg) \,$
$P_1 = 10^{L_\mathrm{B}} P_0 \,$.

### Amplitude, voltage and current

When referring to measurements of 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:

$L_\mathrm{dB} = 10 \log_{10} \bigg(\frac{A_1^2}{A_0^2}\bigg) = 20 \log_{10} \bigg(\frac{A_1}{A_0}\bigg). \,$

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 $10 \log_{10} \frac{a^2}{b^2}$ and $20 \log_{10} \frac{a}{b}$ is of the standard properties of logarithms.

The formula may be rearranged to give

$A_1 = 10^\frac{L_\mathrm{dB}}{20} A_0 \,$

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:

$G_\mathrm{dB} =20 \log_{10} \left (\frac{V_1}{V_0} \right ) \quad \mathrm \quad$

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.

### Examples

Note that all of these examples yield dimensionless answers in dB because they are relative ratios expressed in decibels.

• To calculate the ratio of 1 kW (one kilowatt, or 1000 watts) to 1 W in decibels, use the formula
$G_\mathrm{dB} = 10 \log_{10} \bigg(\frac{1000~\mathrm{W}}{1~\mathrm{W}}\bigg) = 30~\mathrm{dB} \,$
• To calculate the ratio of $\sqrt(1000)~\mathrm{V} \approx 31.62~\mathrm{V}$ to $1~\mathrm{V}$ in decibels, use the formula
$G_\mathrm{dB} = 20 \log_{10} \bigg(\frac{31.62~\mathrm{V}}{1~\mathrm{V}}\bigg) = 30~\mathrm{dB} \,$

Notice that $({31.62\,\mathrm{V}}/{1\,\mathrm{V}})^2 \approx {1\,\mathrm{kW}}/{1\,\mathrm{W}}$, illustrating the consequence from the definitions above that GdB has the same value, $30~\mathrm{dB}$, regardless of whether it is obtained with the 10-log or 20-log rules; provided that in the specific system being considered power ratios are equal to amplitude ratios squared.

• To calculate the ratio of 1 mW (one milliwatt) to 10 W in decibels, use the formula
$G_\mathrm{dB} = 10 \log_{10} \bigg(\frac{0.001~\mathrm{W}}{10~\mathrm{W}}\bigg) = -40~\mathrm{dB} \,$
• To find the power ratio corresponding to a 3 dB change in level, use the formula
$G = 10^\frac{3}{10} \times 1\ = 1.99526... \approx 2 \,$
• An example illustrating the subtleties of the 20-log vs. 10-log rules is given by the so-called polarization ellipticity, the minor-to-major-axis ratio of the polarization ellipse. It is an amplitude ratio, thus when reported in decibels, it follows the 20-log rule, αdB = 20log10α = 10log10α2. A reader unfamiliar with the applicability of each 20- and 10-log rules might find αdB inconsistent, arguing that it redefines the original α as a power ratio rather than an amplitude ratio. The crux is that the subscript dB might imply either of two different mathematical operations, thus it can only be interpreted unambiguously given additional information about the nature of the quantity being reported (power ratio or amplitude ratio).

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 $\scriptstyle\sqrt{2}$, 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 ratio is 106/10, or about 3.9811, a relative error of about 0.5%.

## Merits

The use of the decibel has a number of merits:

• 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.

## Uses

### Acoustics

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 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 — for example, the higher harmonics of middle A (between 2 and 4 kHz) — are factored more heavily into some measurements using frequency weighting.

### Electronics

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 VRMS. 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.

### Optics

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.

### Video and digital imaging

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 signal-to-noise ratio of 60 dB represents a power ratio of 1000:1 between signal power and noise power, not 1,000,000:1.[8]

## Common reference levels and corresponding units

### Absolute and relative decibel measurements

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,

• 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 103/10 × 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.[9] However, outside of documents adhering to SI units, the practice is very common as illustrated by the following examples.

### Absolute measurements

#### Electric power

dBm or dBmW

dB(1 mW) — power measurement relative to 1 milliwatt. XdBm = XdBW + 30.

dBW

dB(1 W) — similar to dBm, except the reference level is 1 watt. 0 dBW = +30 dBm; −30 dBW = 0 dBm; XdBW = XdBm − 30.

#### Voltage

Since the decibel is defined with respect to power, not amplitude, conversions of voltage ratios to decibels must square the amplitude, as discussed above.

A schematic showing the relationship between dBu (the voltage source) and dBm (the power dissipated as heat by the 600 Ω resistor)

dBV

dB(1 VRMS) — voltage relative to 1 volt, regardless of impedance.[1]

dBu or dBv

dB(0.775 VRMS) — voltage relative to 0.775 volts.[1] Originally dBv, it was changed to dBu to avoid confusion with dBV.[10] 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). Reference voltage $V = \sqrt{600 \, \Omega \cdot 0.001\,\mathrm W}\, \approx 0.7746\,\mathrm V$

dBmV

dB(1 mVRMS) — 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 μVRMS) — voltage relative to 1 microvolt. Widely used in television and aerial amplifier specifications. 60 dBμV = 0 dBmV.

#### Acoustics

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 (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.[12]

dB(PA)

dB — relative to 1 Pa, often used in telecommunications.

dB SIL

dB sound intensity level — relative to 10−12 W/m2, 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). These measurements usually refer to noise and noisome effects on humans and animals, and are in widespread use in the industry with regard to noise control issues, regulations and environmental standards. Other variations that may be seen are dBA or dBA. According to ANSI standards, the preferred usage is to write LA = 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.[citation needed]

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

dBZ

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.[13]

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.[14]

#### Radio power, energy, and field strength

dBc

dBc — relative to carrier — in telecommunications, this indicates the relative levels of noise or sideband peak power, compared with the carrier power. Compare dBC, 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. When used in audio work the milliwatt is referenced to a 600 ohm load, with the resultant voltage being 0.775 volts. When used in the 2-way radio field, the dB is referenced to a 50 ohm load, with the resultant voltage being 0.224 volts. There are times when spec sheets may show the voltage & power level e.g. -120 dBm = 0.224 microvolts.

dBμV/m or dBuV/m

dB(μV/m) — electric field strength relative to 1 microvolt per meter.

dBf

dB(fW) — power relative to 1 femtowatt.

dBW

dB(W) — power relative to 1 watt.

dBk

dB(kW) — power relative to 1 kilowatt.

### Antenna measurements

dBi

dB(isotropic) — the forward gain of an antenna compared with the hypothetical isotropic antenna, which uniformly distributes energy in all directions. Linear polarization of the EM field is assumed unless noted otherwise.

dBd

dB(dipole) — the forward gain of an antenna compared with a half-wave dipole antenna. 0 dBd = 2.15 dBi

dBiC

dB(isotropic circular) — the forward gain of an antenna compared to a circularly polarized isotropic antenna. There is no fixed conversion rule between dBiC and dBi, as it depends on the receiving antenna and the field polarization.

dBq

dB(quarterwave) — the forward gain of an antenna compared to a quarter wavelength whip. Rarely used, except in some marketing material. 0 dBq = -0.85 dBi

### Other measurements

dBFS or dBfs

dB(full scale) — the amplitude of a signal (usually audio) compared with 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 always negative or zero, since they are less than the maximum or full-scale. Full-scale is typically defined as the power level of a full-scale sinusoid, though some systems will have extra headroom for peaks above the nominal full scale.

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. Also used in carrier-to-noise-density ratio (not to be confused with carrier-to-noise ratio, in dB).

dBov or dBO

dB(overload) — the amplitude of a signal (usually audio) compared with 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 from something else, which is made apparent in context. The difference of a filter's response to nominal levels, for instance.

dBrn

## References

1. ^ a b c Analog Devices : Virtual Design Center : Interactive Design Tools : Utilities : VRMS / dBm / dBu / dBV calculator
2. ^ Sound system engineering, p. 35, Carolyn Davis, 1997
3. ^ "Transmission Circuits for Telephonic Communication", Bell Labs, 1925
4. ^ 100 Years of Telephone Switching, p. 276, Robert J. Chapuis, Amos E. Joel, 2003
5. ^ Consultative Committee for Units, Meeting minutes, Section 3
6. ^ "Letter symbols to be used in electrical technology - Part 3: Logarithmic and related quantities, and their units", IEC 60027-3 Ed. 3.0, International Electrotechnical Commission, 19th July 2002.
7. ^ A. Thompson and B. N. Taylor, "Comments on Some Quantities and Their Units", The NIST Guide for the use of the International System of Units, National Institute of Standards and Technology, May 1996.
8. ^ Stephen J. Sangwine and Robin E. N. Horne (1998). The Colour Image Processing Handbook. Springer. p. 127. ISBN 9780412806209.
9. ^ Thompson, A. and Taylor, B. N. Guide for the Use of the International System of Units (SI) 2008 Edition, 2nd printing (November 2008), SP811 PDF
10. ^ What is the difference between dBv, dBu, dBV, dBm, dB SPL, and plain old dB? Why not just use regular voltage and power measurements? - rec.audio.pro Audio Professional FAQ
11. ^ Jay Rose (2002). Audio postproduction for digital video. Focal Press,. p. 25. ISBN 9781578201167.
12. ^ Morfey, C. L. (2001). Dictionary of Acoustics. Academic Press, San Diego.
13. ^ "Radar FAQ from WSI". Retrieved 2008-03-18.
14. ^ "Definition at Everything2". Retrieved 2008-08-06.

• 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. doi:10.1037/h0046162. PMID 13441853.

# Wiktionary

Up to date as of January 15, 2010
(Redirected to decibel article)

### Definition from Wiktionary, a free dictionary

Wikipedia has an article on:

Wikipedia

## English

### Noun

 Singular decibel Plural decibels

decibel (plural decibels)

1. a common measure of sound intensity that is 1 tenth of a bel on the logarithmic intensity scale. It is defined as dB = 10 * log10(P 1/P 2), where P1 and P2 are the relative powers of the sound.

decibel m. inv.

# Simple English

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.

## Examples and protection

Some examples of sounds are:

Sound Level Examples
200-250 DB Cannon at 12'
175-200 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.
30-35 DB Very quiet conversation, private office noise
20 DB Rustling leaves, whispering
10 DB Sound-proofed 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 10-15 minutes
120 3-5 minutes
[1]

## References

1. Pocket Ref, General Sciences, pages 322-323.