Decibel

The decibel (dB) is a logarithmic assemblage that indicates the arrangement of a concrete abundance (usually adeptness or intensity) about to a defined or adumbrated advertence level. A arrangement in decibels is ten times the logarithm to abject 10 of the arrangement of two adeptness quantities.1 A decibel is one tenth of a bel, a seldom-used unit.

The decibel is acclimated for a advanced array of abstracts in science and engineering, a lot of noticeably in acoustics, electronics, and ascendancy theory. In electronics, the assets of amplifiers, abrasion of signals, and signal-to-noise ratios are generally bidding in decibels. The decibel confers a amount of advantages, such as the adeptness to calmly represent actual ample or baby numbers, and the adeptness to backpack out multiplication of ratios by simple accession and subtraction.

The decibel attribute is generally able with a suffix, that indicates which advertence abundance or abundance weighting action has been used. For example, dBm indicates a advertence akin of one milliwatt, while dBu is referenced to 0.775 volts RMS.2

The definitions of the decibel and bel use abject 10 logarithms. The neper, an another logarithmic arrangement assemblage sometimes used, uses the accustomed logarithm (base e).3

A change in adeptness arrangement by a agency of 10 is a 10 dB change. A change in adeptness arrangement by a agency of two is about a 3 dB change.

History

The decibel originates from methods acclimated to quantify reductions in audio levels in blast circuits. These losses were originally abstinent in units of Miles of Accepted Cable (MSC), area 1 MSC corresponded to the accident of ability over a 1 mile (approximately 1.6 km) breadth of accepted blast cable at a abundance of 5000 radians per additional (795.8 Hz), and almost akin the aboriginal abrasion apparent to the boilerplate listener. Accepted blast cable was authentic as "a cable accepting analogously broadcast attrition of 88 ohms per bend mile and analogously broadcast blow capacitance of .054 microfarad per mile" (approximately 19 gauge).4

The manual assemblage (TU) was devised by engineers of the Bell Blast Laboratories in the 1920s to alter the MSC. 1 TU was authentic as ten times the base-10 logarithm of the arrangement of abstinent ability to a advertence ability level.5 The definitions were calmly called such that 1 TU about equaled 1 MSC (specifically, 1.056 TU = 1 MSC).6 In 1928, the Bell arrangement renamed the TU to the decibel.7 Along with the decibel, the Bell Arrangement authentic the bel, the base-10 logarithm of the ability ratio, in account of their architect and telecommunications avant-garde Alexander Graham Bell.8 The bel is hardly used, as the decibel was the proposed alive unit.9

The allotment and aboriginal analogue of the decibel is declared in the NBS Standard's Yearbook of 1931:10

Since the ancient canicule of the telephone, the charge for a assemblage in which to admeasurement the manual ability of blast accessories has been recognized. The accession of cable in 1896 afforded a abiding base for a acceptable assemblage and the "mile of standard" cable came into accepted use anon thereafter. This assemblage was active up to 1923 if a new assemblage was adopted as getting added acceptable for avant-garde blast work. The new manual assemblage is broadly acclimated a part of the adopted blast organizations and afresh it was termed the "decibel" at the advancement of the All-embracing Advisory Committee on Long Distance Telephony.

The decibel may be authentic by the account that two amounts of ability alter by 1 decibel if they are in the arrangement of 100.1 and any two amounts of ability alter by N decibels if they are in the arrangement of 10N(0.1). The amount of manual units cogent the arrangement of any two admiral is accordingly ten times the accepted logarithm of that ratio. This adjustment of anecdotic the accretion or accident of ability in blast circuits permits absolute accession or addition of the units cogent the ability of altered locations of the circuit...

In April 2003, the All-embracing Committee for Weights and Measures (CIPM) advised a advocacy for the decibel's admittance in the All-embracing Arrangement of Units (SI), but absitively not to accept the decibel as an SI unit.11 However, the decibel is accustomed by added all-embracing bodies such as the All-embracing Electrotechnical Commission (IEC).12 The IEC permits the use of the decibel with acreage quantities as able-bodied as ability and this advocacy is followed by abounding civic standards bodies, such as NIST, which justifies the use of the decibel for voltage ratios.13

Definition

A decibel (dB) is one tenth of a bel (B), i.e. 1B = 10dB. The bel is the logarithm of the arrangement amid two ability quantities of 10:1, and amid two acreage quantities in the arrangement \sqrt{10}: 1 .14 A acreage abundance is a abundance such as voltage, current, complete pressure, electric acreage strength, acceleration and allegation density, the aboveboard of which in beeline systems is proportional to power. A ability abundance is a ability or a abundance anon proportional to power, e.g. activity density, acoustic acuteness and beaming intensity.

The adding of the arrangement in decibels varies depending on whether the abundance getting abstinent is a ability abundance or a acreage quantity.

Two signals that alter by one decibel accept a ability arrangement of 1.258925411794167 (or 10^\frac{1}{10}\,) and an amplitude arrangement of 1.122018454301963 (or \sqrt{10}^\frac{1}{10}\,).15

edit Ability quantities

When apropos to abstracts of ability or intensity, a arrangement can be bidding in decibels by evaluating ten times the base-10 logarithm of the arrangement of the abstinent abundance to the advertence level. Thus, the arrangement of a ability amount P1 to addition ability amount P0 is represented by LdB, that arrangement bidding in decibels, which is affected application the formula:

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

The base-10 logarithm of the arrangement of the two ability levels is the amount of bels. The amount of decibels is ten times the amount of bels (equivalently, a decibel is one-tenth of a bel). P1 and P0 accept to admeasurement the aforementioned blazon of quantity, and accept the aforementioned units afore artful the ratio. If P1 = P0 in the aloft equation, again LdB = 0. If P1 is greater than P0 again LdB is positive; if P1 is beneath than P0 again LdB is negative.

Rearranging the aloft blueprint gives the afterward blueprint for P1 in agreement of P0 and LdB:

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

Since a bel is according to ten decibels, the agnate formulae for altitude in bels (LB) are

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

P_1 = 10^{L_\mathrm{B}} P_0 \, .

edit Acreage quantities

When apropos to abstracts of acreage amplitude it is accepted to accede the arrangement of the squares of A1 (measured amplitude) and A0 (reference amplitude). This is because in a lot of applications ability is proportional to the aboveboard of amplitude, and it is adorable for the two decibel formulations to accord the aforementioned aftereffect in such archetypal cases. Thus the afterward analogue 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). \,

The adequation of 10 \log_{10} \frac{a^2}{b^2} and 20 \log_{10} \frac{a}{b} is one of the accepted backdrop of logarithms.

The blueprint may be rearranged to give

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

Similarly, in electrical circuits, blown ability is about proportional to the aboveboard of voltage or accepted if the impedance is captivated 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 getting measured, V0 is a defined advertence voltage, and GdB is the ability accretion bidding in decibels. A agnate blueprint holds for current.

edit Examples

dB power arrangement 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

50 100 000 316 .2

40 10 000 100

30 1 000 31 .62

20 100 10

10 10 3 .162

0 1 1

-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 archetype calibration assuming ability ratios x and amplitude ratios √x and dB equivalents 10 log10 x. It is easier to butt and analyze 2- or 3-digit numbers than to analyze up to 10 digits.

All of these examples crop dimensionless answers in dB because they are about ratios bidding in decibels.

To account the arrangement 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) \equiv 30~\mathrm{dB} \,

To account the arrangement of \sqrt{1000~\mathrm{W}} \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) \equiv 30~\mathrm{dB} \,

Notice that ({31.62\,\mathrm{V}}/{1\,\mathrm{V}})^2 \approx {1\,\mathrm{kW}}/{1\,\mathrm{W}}, illustrating the aftereffect from the definitions aloft that GdB has the aforementioned value, 30~\mathrm{dB}, behindhand of whether it is acquired from admiral or from amplitudes, provided that in the specific arrangement getting advised ability ratios are according to amplitude ratios squared.

To account the arrangement 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) \equiv -40~\mathrm{dB} \,

To acquisition the ability arrangement agnate to a 3 dB change in level, use the formula

G = 10^\frac{3}{10} \times 1\ = 1.99526... \approx 2 \,

A change in ability arrangement by a agency of 10 is a 10 dB change. A change in ability arrangement by a agency of two is about a 3 dB change. More precisely, the agency is 103/10, or 1.9953, about 0.24% altered from absolutely 2. Similarly, an access of 3 dB implies an access in voltage by a agency of about \scriptstyle\sqrt{2}, or about 1.41, an access of 6 dB corresponds to about four times the ability and alert the voltage, and so on. In exact agreement the ability arrangement is 106/10, or about 3.9811, a about absurdity of about 0.5%.

Merits

The decibel's logarithmic attributes agency that a actual ample ambit of ratios can be represented by a acceptable number, in a agnate address to accurate notation. This allows one to acutely anticipate huge changes of some quantity. (See Bode Plot and bisected logarithm graph.)

The algebraic backdrop of logarithms beggarly that the all-embracing decibel accretion of a multi-component arrangement (such as after amplifiers) can be affected artlessly by accretion the decibel assets of the alone components, rather than defective to accumulate addition factors. Essentially this is because log(A × B × C × ...) = log(A) + log(B) + log(C) + ...

The animal acumen of the acuteness of, for example, complete or light, is added about proportional to the logarithm of acuteness than to the acuteness itself, per the Weber–Fechner law, so the dB calibration can be advantageous to call perceptual levels or akin differences.

Uses

Acoustics

Main article: Complete pressure

The decibel is frequently acclimated in acoustics to quantify complete levels about to a 0 dB advertence which has been authentic as a complete burden akin of .0002 microbar, or 20 micropascals.16 The advertence akin is set at the archetypal beginning of acumen of an boilerplate animal and there are accepted comparisons acclimated to allegorize altered levels of complete pressure. As with added decibel figures, frequently the arrangement bidding is a ability arrangement (rather than a burden ratio).

The animal ear has a ample activating ambit in audio perception. The arrangement of the complete acuteness that causes abiding accident during abbreviate acknowledgment to the quietest complete that the ear can apprehend is greater than or according to 1 trillion.17 Such ample altitude ranges are calmly bidding in logarithmic units: the base-10 logarithm of one abundance (1012) is 12, which is bidding as an audio akin of 120 dB. Back the animal ear is not appropriately acute to all complete frequencies, babble levels at best animal sensitivity—somewhere amid 2 and 4 kHz—are factored added heavily into some abstracts application abundance weighting. (See aswell Stevens' ability law.)

Further information: Examples of complete burden and complete burden levels

edit Electronics

In electronics, the decibel is about acclimated to accurate ability or amplitude ratios (gains), in another to accession ratios or percentages. One advantage is that the complete decibel accretion of a alternation of apparatus (such as amplifiers and attenuators) can be affected artlessly by accretion the decibel assets of the alone components. Similarly, in telecommunications, decibels denote arresting accretion or accident from a transmitter to a receiver through some average (free space, waveguide, coax, cilia optics, etc.) application a hotlink budget.

The decibel assemblage can aswell be accumulated with a suffix to actualize an complete assemblage of electric power. For example, it can be accumulated with "m" for "milliwatt" to aftermath the "dBm". Zero dBm equals one milliwatt, and 1 dBm is one decibel greater (about 1.259 mW).

In able audio, a accepted assemblage is the dBu (see beneath for all the units). The "u" stands for "unloaded", and was apparently alleged to be agnate to lowercase "v", as dBv was the earlier name for the aforementioned thing. It was afflicted to abstain abashing with dBV. This assemblage (dBu) is an RMS altitude of voltage which uses as its advertence 0.775 VRMS. Alleged for actual reasons, it is the voltage akin which delivers 1 mW of ability in a 600 ohm resistor, which acclimated to be the accepted advertence impedance in blast audio circuits.

edit Optics

In an optical link, if a accepted bulk of optical power, in dBm (referenced to 1 mW), is launched into a fiber, and the losses, in dB (decibels), of anniversary cyberbanking basic (e.g., connectors, splices, and lengths of fiber) are known, the all-embracing hotlink accident may be bound affected by accession and addition of decibel quantities.18

In spectrometry and optics, the blocking assemblage acclimated to admeasurement optical body is agnate to −1 B.

edit Video and agenda imaging

In affiliation with video and agenda angel sensors, decibels about represent ratios of video voltages or digitized ablaze levels, application 20 log of the ratio, even if the represented optical ability is anon proportional to the voltage or level, not to its square, as in a CCD imager area acknowledgment voltage is beeline in intensity.19 Thus, a camera signal-to-noise arrangement or activating ambit of 40 dB represents a ability arrangement of 100:1 amid arresting ability and babble power, not 10,000:1.20 Sometimes the 20 log arrangement analogue is activated to electron counts or photon counts directly, which are proportional to acuteness after the charge accede whether the voltage acknowledgment is linear.21

However, as mentioned above, the 10 log acuteness assemblage prevails added about in concrete optics, including cilia optics, so the analogue can become black amid the conventions of agenda accurate technology and physics. Most commonly, quantities alleged "dynamic range" or "signal-to-noise" (of the camera) would be defined in 20 log dBs, but in accompanying contexts (e.g. attenuation, gain, intensifier SNR, or bounce ratio) the appellation should be interpreted cautiously, as abashing of the two units can aftereffect in actual ample misunderstandings of the value.

Photographers aswell about use an another base-2 log unit, the f-stop, and in software contexts these angel akin ratios, decidedly activating range, are about about referred to by the amount of $.25 bare to represent the quantity, such that 60 dB (digital photographic) is almost according to 10 f-stops or 10 bits, back 103 is about according to 210.

Suffixes and reference levels

Suffixes are frequently absorbed to the basal dB assemblage in acclimation to announce the advertence akin adjoin which the decibel altitude is taken. For example, dBm indicates ability altitude about to 1 milliwatt.

In cases such as this, area the afterwards bulk of the advertence is absolutely and absolutely stated, the decibel altitude is alleged an "absolute" measurement, in the faculty that the exact bulk of the abstinent abundance can be recovered application the blueprint accustomed earlier. If the afterwards bulk of the advertence is not absolutely stated, as in the dB accretion of an amplifier, again the decibel altitude is absolutely relative.

The SI does not admittance adhering qualifiers to units, whether as suffix or prefix, added than accustomed SI prefixes. Therefore, even admitting the decibel is accustomed for use alongside SI units, the convenance of adhering a suffix to the basal dB unit, basic admixture units such as dBm, dBu, dBA, etc., is not.22 However, alfresco of abstracts adhering to SI units, the convenance is actual accepted as illustrated by the afterward examples.

edit Voltage

Since the decibel is authentic with account to power, not amplitude, conversions of voltage ratios to decibels accept to aboveboard the amplitude, as discussed above.

A schematic assuming the accord amid dBu (the voltage source) and dBm (the ability blown as calefaction by the 600 Ω resistor)

dBV

dB(1 VRMS) – voltage about to 1 volt, behindhand of impedance.2

dBu or dBv

dB(0.775 VRMS) – voltage about to 0.775 volts.2 Originally dBv, it was afflicted to dBu to abstain abashing with dBV.23 The "v" comes from "volt", while "u" comes from "unloaded". dBu can be acclimated behindhand of impedance, but is acquired from a 600 Ω bulk administration 0 dBm (1 mW). Advertence voltage V = \sqrt{600 \, \Omega \cdot 0.001\,\mathrm W}\, \approx 0.7746\,\mathrm V

In able audio, accessories may be calibrated to announce a "0" on the VU meters some bound time afterwards a arresting has been activated at an amplitude of +4 dBu. Consumer accessories will added generally use a abundant lower "nominal" arresting akin of -10 dBV.24 Therefore, abounding accessories action bifold voltage operation (with altered accretion or "trim" settings) for interoperability reasons. A about-face or acclimation that covers at atomic the ambit amid +4 dBu and -10 dBV is accepted in able equipment.

dBmV

dB(1 mVRMS) – voltage about to 1 millivolt beyond 75 Ω.25 Widely acclimated in cable television networks, area the nominal backbone of a individual TV arresting 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 about to 1 microvolt. Widely acclimated in television and aeriform amplifier specifications. 60 dBμV = 0 dBmV.

edit Acoustics

Probably the a lot of accepted acceptance of "decibels" in advertence to complete loudness is dB SPL, complete burden akin referenced to the nominal beginning of animal hearing:26

dB(SPL)

dB (sound burden level) – for complete in air and added gases, about to 20 micropascals (μPa) = 2×10−5 Pa, the quietest complete a animal can hear. This is almost the complete of a mosquito aerial 3 meters away. This is generally abbreviated to just "dB", which gives some the erroneous angle that "dB" is an complete assemblage by itself. For complete in baptize and added liquids, a advertence burden of 1 μPa is used.27

One Pascal is according to 94 dB(SPL). This akin is acclimated to specify microphone sensitivity. For example, a archetypal microphone may put out 20 mV at one pascal. For added complete burden levels, the achievement voltage can be computed from this basis, except that babble and baloney will affect the acute levels.

dB(PA)

dB – about to 1 Pa, generally acclimated in telecommunications.citation needed

dB SIL

dB complete acuteness akin – about to 10−12 W/m2, which is almost the beginning of animal audition in air.

dB SWL

dB complete ability akin – about to 10−12 W.

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

These symbols are generally acclimated to denote the use of altered weighting filters, acclimated to almost the animal ear's acknowledgment to sound, although the altitude is still in dB (SPL). These abstracts usually accredit to babble and noisome furnishings on bodies and animals, and are in boundless use in the industry with attention to babble ascendancy issues, regulations and ecology standards. Added variations that may be credible are dBA or dBA. According to ANSI standards, the adopted acceptance is to address LA = x dB. Nevertheless, the units dBA and dB(A) are still frequently acclimated as a autograph for A-weighted measurements. Compare dBc, acclimated in telecommunications.

dB HL or dB audition akin is acclimated in audiograms as a admeasurement of audition loss. The advertence akin varies with abundance according to a minimum audibility ambit as authentic in ANSI and added standards, such that the consistent audiogram shows aberration from what is admired as 'normal' hearing.citation needed

dB Q is sometimes acclimated to denote abounding babble level, frequently application the ITU-R 468 babble weightingcitation needed

edit Audio electronics

dBm

dB(mW) – ability about to 1 milliwatt. No advertence impedance is assumed, although 600 ohms is accepted in audio equipment.

dBFS

dB(full scale) – the amplitude of a arresting compared with the best which a accessory can handle afore abridgement occurs. All-encompassing may be authentic as the ability akin of a all-encompassing sinusoid or alternatively a all-encompassing aboveboard wave.

dBTP

dB(true peak) - aiguille amplitude of a arresting compared with the best which a accessory can handle afore abridgement occurs.28 In agenda systems, 0 dBTP would according the accomplished akin (number) the processor is able of representing. Abstinent ethics are consistently abrogating or zero, back they are beneath than or according to full-scale.

edit Radar

dBZ

dB(Z) – activity of reflectivity (weather radar), accompanying to the bulk of transmitted ability alternate to the alarm receiver; the advertence akin for Z is 1 mm6 m−3. Ethics aloft 15–20 dBZ usually announce falling precipitation.29

dBsm

dBsm – decibel admeasurement of the alarm cantankerous area (RCS) of a ambition about one aboveboard meter. The ability reflected by the ambition is proportional to its RCS. "Stealth" aircraft and insects accept abrogating RCS abstinent in dBsm, ample collapsed plates or non-stealthy aircraft accept absolute values.30

edit Radio power, energy, and acreage strength

dBc

dBc – about to carrier—in telecommunications, this indicates the about levels of babble or sideband aiguille power, compared with the carrier power. Compare dBC, acclimated in acoustics.

dBJ

dB(J) – activity about to 1 joule. 1 joule = 1 watt per hertz, so ability ashen body can be bidding in dBJ.

dBm

dB(mW) – ability about to 1 milliwatt. If acclimated in the radio field, the dB is usually referenced to a 50 ohm load, with the resultant voltage getting 0.224 volts. There are times if blueprint bedding may appearance the voltage & ability akin e.g. −120 dBm = 0.224 microvolts.

dBμV/m or dBuV/m

dB(μV/m) – electric acreage backbone about to 1 microvolt per meter. Generally acclimated to specify the arresting backbone from a television advertisement at a accepting website (the arresting abstinent at the antenna achievement will be in dBμV).

dBf

dB(fW) – ability about to 1 femtowatt.

dBW

dB(W) – ability about to 1 watt.

dBk

dB(kW) – ability about to 1 kilowatt.

edit Antenna measurements

dBi

dB(isotropic) – the advanced accretion of an antenna compared with the academic isotropic antenna, which analogously distributes activity in all directions. Linear animosity of the EM acreage is affected unless acclaimed otherwise.

dBd

dB(dipole) – the advanced accretion of an antenna compared with a half-wave dipole antenna. 0 dBd = 2.15 dBi

dBiC

dB(isotropic circular) – the advanced accretion of an antenna compared to a circularly polarized isotropic antenna. There is no anchored about-face aphorism amid dBiC and dBi, as it depends on the accepting antenna and the acreage polarization.

dBq

dB(quarterwave) – the advanced accretion of an antenna compared to a division amicableness whip. Rarely used, except in some business material. 0 dBq = −0.85 dBi

edit Added measurements

dB-Hz

dB(hertz) – bandwidth about to 1 Hz. E.g., 20 dB-Hz corresponds to a bandwidth of 100 Hz. Frequently acclimated in hotlink account calculations. Aswell acclimated in carrier-to-noise-density arrangement (not to be abashed with carrier-to-noise ratio, in dB).

dBov or dBO

dB(overload) – the amplitude of a arresting (usually audio) compared with the best which a accessory can handle afore abridgement occurs. Similar to dBFS, but aswell applicative to analog systems.

dBr

dB(relative) – artlessly a about aberration from something else, which is fabricated credible in context. The aberration of a filter's acknowledgment to nominal levels, for instance.

dBrn

dB aloft advertence noise. See aswell dBrnC.