Decibel

The decibel (symbol: dB) is a relative unit of measurement equal to one tenth of a bel (B). It expresses the ratio of two values of a power or root-power quantity on a logarithmic scale. Two signals whose levels differ by one decibel have a power ratio of 101/10 (approximately 1.26) or root-power ratio of 101/20 (approximately 1.12).

The strict original usage above only expresses a relative change. However, the word decibel has since also been used for expressing an absolute value that is relative to some fixed reference value, in which case the dB symbol is often suffixed with letter codes that indicate the reference value. For example, for the reference value of 1volt, a common suffix is "V" (e.g., "20dBV").

As it originated from a need to express power ratios, two principal types of scaling of the decibel are used to provide consistency depending on whether the scaling refers to ratios of power quantities or root-power quantities. When expressing a power ratio, the corresponding change in decibels is defined as ten times the logarithm with base 10 of that ratio. That is, a change in power by a factor of 10 corresponds to a 10dB change in level. When expressing root-power ratios, a change in amplitude by a factor of 10 corresponds to a 20dB change in level. The decibel scales differ by a factor of two, so that the related power and root-power levels change by the same value in linear systems, where power is proportional to the square of amplitude.

The definition of the decibel originated in the measurement of transmission loss and power in telephony of the early 20th century in the Bell System in the United States. The bel was named in honor of Alexander Graham Bell, but the bel is seldom used. Instead, the decibel is used for a wide variety of measurements in science and engineering, most prominently for sound power in acoustics, in electronics and control theory. In electronics, the gains of amplifiers, attenuation of signals, and signal-to-noise ratios are often expressed in decibels.

History

The decibel originates from methods used to quantify signal loss in telegraph and telephone circuits. Until the mid-1920s, the unit for loss was miles of standard cable (MSC). 1MSC corresponded to the loss of power over one mile (approximately 1.6km) of standard telephone cable at a frequency of 5000radians per second (795.8Hz), and matched closely the smallest attenuation detectable to a listener. A standard telephone cable was "a cable having uniformly distributed resistance of 88ohms per loop-mile and uniformly distributed shunt capacitance of 0.054microfarads per mile" (approximately corresponding to 19gauge wire).

In 1924, Bell Telephone Laboratories received a favorable response to a new unit definition among members of the International Advisory Committee on Long Distance Telephony in Europe and replaced the MSC with the Transmission Unit (TU). 1TU was defined such that the number of TUs was ten times the base-10 logarithm of the ratio of measured power to a reference power. The definition was conveniently chosen such that 1TU approximated 1MSC; specifically, 1.056MSC was 1TU. In 1928, the Bell system renamed the TU as the decibel, being one tenth of a newly defined unit for the base-10 logarithm of the power ratio. It was named the bel, in honor of the telecommunications pioneer Alexander Graham Bell. The bel is seldom used, as the decibel was the proposed working unit.

The naming and early definition of the decibel is described in the NBS Standard's Yearbook of 1931:

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...

The word decibel was soon misused to refer to absolute quantities and to ratios other than power. Some proposals attempted to address the resulting confusion. In 1954, J. W. Horton considered that 100.1 be treated as an elementary ratio and proposed the word logit as "a standard ratio which has the numerical value 100.1 and which combines by multiplication with similar ratios of the same value", so one would describe a 100.1 ratio of units of mass as "a mass logit". This contrasts with the word unit which would be reserved for magnitudes which combine by addition and reserves the word decibel specifically for unit transmission loss. The decilog was another proposal (by N. B. Saunders in 1943, A. G. Fox in 1951, and E. I. Green in 1954) to express a division of the logarithmic scale corresponding to a ratio of 100.1.

In April2003, the International Committee for Weights and Measures (CIPM) considered a recommendation for the inclusion of the decibel in the International System of Units (SI), but decided against the proposal. However, the decibel is recognized by other international bodies such as the International Electrotechnical Commission (IEC) and International Organization for Standardization (ISO). The IEC permits the use of the decibel with root-power 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. In spite of their widespread use, suffixes (such as in dBA or dBV) are not recognized by the IEC or ISO.

Definition

The IEC Standard 60027-3:2002 defines the following quantities. The decibel (dB) is one-tenth of a bel: 1dB= 0.1B. The bel (B) is ⁠1/2⁠ln(10) nepers: 1B= ⁠1/2⁠ln(10)Np. The neper is the change in the level of a root-power quantity when the root-power quantity changes by a factor of e, that is 1 Np = ln(e) = 1, thereby relating all of the units as nondimensional natural log of root-power-quantity ratios, 1dB= 0.11513...Np= 0.11513.... Finally, the level of a quantity is the logarithm of the ratio of the value of that quantity to a reference value of the same kind of quantity.

Therefore, the bel represents the logarithm of a ratio between two power quantities of 10:1, or the logarithm of a ratio between two root-power quantities of √10:1.

Two signals whose levels differ by one decibel have a power ratio of 101/10, which is approximately 1.25893, and an amplitude (root-power quantity) ratio of 101/20 (1.12202).

The bel is rarely used either without a prefix or with SI unit prefixes other than deci; it is customary, for example, to use hundredths of a decibel rather than millibels. Thus, five one-thousandths of a bel would normally be written 0.05dB, and not 5mB.

The method of expressing a ratio as a level in decibels depends on whether the measured property is a power quantity or a root-power quantity; see Power, root-power, and field quantities for details.

Power quantities

When referring to measurements of power quantities, a ratio can be expressed as a level in decibels by evaluating ten times the base-10 logarithm of the ratio of the measured quantity to reference value. Thus, the ratio of P (measured power) to P0 (reference power) is represented by LP, that ratio expressed in decibels, which is calculated using the formula:

L P = 1 2 ln ( P P 0 ) Np = 10 log 10 ( P P 0 ) dB {\displaystyle L_{P}={\frac {1}{2}}\ln \!\left({\frac {P}{P_{0}}}\right)\,{\text{Np}}=10\log _{10}\!\left({\frac {P}{P_{0}}}\right)\,{\text{dB}}}

The base-10 logarithm of the ratio of the two power quantities 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). P and P0 must measure the same type of quantity, and have the same units before calculating the ratio. If P = P0 in the above equation, then LP= 0. If P is greater than P0 then LP is positive; if P is less than P0 then LP is negative.

Rearranging the above equation gives the following formula for P in terms of P0 and LP:

P = 10 L P 10 dB P 0 {\displaystyle P=10^{\frac {L_{P}}{10\,{\text{dB}}}}P_{0}}

Root-power (field) quantities

When referring to measurements of root-power quantities, it is usual to consider the ratio of the squares of F (measured) and F0 (reference). This is because the definitions were originally formulated to give the same value for relative ratios for both power and root-power quantities. Thus, the following definition is used:

L F = ln ( F F 0 ) Np = 10 log 10 ( F 2 F 0 2 ) dB = 20 log 10 ⁡ ( F F 0 ) dB {\displaystyle L_{F}=\ln \!\left({\frac {F}{F_{0}}}\right)\,{\text{Np}}=10\log _{10}\!\left({\frac {F^{2}}{F_{0}^{2}}}\right)\,{\text{dB}}=20\log _{10}\left({\frac {F}{F_{0}}}\right)\,{\text{dB}}}

The formula may be rearranged to give

F = 10 L F 20 dB F 0 {\displaystyle F=10^{\frac {L_{F}}{20\,{\text{dB}}}}F_{0}}

Similarly, in electrical circuits, dissipated power is typically proportional to the square of voltage or current when the impedance is constant. Taking voltage as an example, this leads to the equation for power gain level LG:

L G = 20 log 10 ( V out V in ) dB {\displaystyle L_{G}=20\log _{10}\!\left({\frac {V_{\text{out}}}{V_{\text{in}}}}\right)\,{\text{dB}}}

where Vout is the root-mean-square (rms) output voltage, Vin is the rms input voltage. A similar formula holds for current.

The term root-power quantity is introduced by ISO Standard 80000-1:2009 as a substitute of field quantity. The term field quantity is deprecated by that standard and root-power is used throughout this article.

Relationship between power and root-power levels

Although power and root-power quantities are different quantities, their respective levels are historically expressed in the same units, typically decibels. A factor of 2 is introduced to make changes in the respective levels match under restricted conditions such as when the medium is linear and the same waveform is under consideration with changes in amplitude, or the medium impedance is linear and independent of both frequency and time. This relies on the relationship

P ( t ) P 0 = ( F ( t ) F 0 ) 2 {\displaystyle {\frac {P(t)}{P_{0}}}=\left({\frac {F(t)}{F_{0}}}\right)^{2}}

holding. In a nonlinear system, this relationship does not hold by the definition of linearity. However, even in a linear system in which the power quantity is the product of two linearly related quantities (e.g. voltage and current), if the impedance is frequency- or time-dependent, this relationship does not hold in general, for example if the energy spectrum of the waveform changes.

For differences in level, the required relationship is relaxed from that above to one of proportionality (i.e., the reference quantities P0 and F0 need not be related), or equivalently,

P 2 P 1 = ( F 2 F 1 ) 2 {\displaystyle {\frac {P_{2}}{P_{1}}}=\left({\frac {F_{2}}{F_{1}}}\right)^{2}}

must hold to allow the power level difference to be equal to the root-power level difference from power P1 and F1 to P2 and F2. An example might be an amplifier with unity voltage gain independent of load and frequency driving a load with a frequency-dependent impedance: the relative voltage gain of the amplifier is always 0dB, but the power gain depends on the changing spectral composition of the waveform being amplified. Frequency-dependent impedances may be analyzed by considering the quantities power spectral density and the associated root-power quantities via the Fourier transform, which allows elimination of the frequency dependence in the analysis by analyzing the system at each frequency independently.

Conversions

Since logarithm differences expressed in these units often represent power ratios and root-power ratios, values for both are shown below. The bel is traditionally used as a unit of logarithmic power ratio, while the neper is used for logarithmic root-power (amplitude) ratio.

Examples

• Calculating the ratio in decibels of 1 kW (one kilowatt, or 1000 watts) to 1 W yields: L G = 10 log 10 ⁡ ( 1 000 W 1 W ) dB = 30 dB {\displaystyle L_{G}=10\log _{10}\left({\frac {1\,000\,{\text{W}}}{1\,{\text{W}}}}\right)\,{\text{dB}}=30\,{\text{dB}}}
• The ratio in decibels of √1000 V ≈ 31.62 V to 1 V is: L G = 20 log 10 ⁡ ( 31.62 V 1 V ) dB = 30 dB {\displaystyle L_{G}=20\log _{10}\left({\frac {31.62\,{\text{V}}}{1\,{\text{V}}}}\right)\,{\text{dB}}=30\,{\text{dB}}}

(31.62 V / 1 V)2 ≈ 1 kW / 1 W, illustrating the consequence from the definitions above that LG has the same value, 30dB, 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.

• The ratio in decibels of 10 W to 1 mW (one milliwatt) is obtained with the formula: L G = 10 log 10 ⁡ ( 10 W 0.001 W ) dB = 40 dB {\displaystyle L_{G}=10\log _{10}\left({\frac {10{\text{W}}}{0.001{\text{W}}}}\right)\,{\text{dB}}=40\,{\text{dB}}}
• The power ratio corresponding to a 3 dB change in level is given by: G = 10 3 10 × 1 = 1.995 26 … ≈ 2 {\displaystyle G=10^{\frac {3}{10}}\times 1=1.995\,26\ldots \approx 2}

A change in power ratio by a factor of 10 corresponds to a change in level of 10 dB. A change in power ratio by a factor of 2 or ⁠1/2⁠ is approximately a change of 3dB. More precisely, the change is ±3.0103dB, but this is almost universally rounded to 3dB in technical writing.[citation needed] This implies an increase in voltage by a factor of √2 ≈ 1.4142. Likewise, a doubling or halving of the voltage, corresponding to a quadrupling or quartering of the power, is commonly described as 6dB rather than ±6.0206dB.

Should it be necessary to make the distinction, the number of decibels is written with additional significant figures. 3.000dB corresponds to a power ratio of 103/10, or 1.9953, about 0.24% different from exactly 2, and a voltage ratio of 1.4125, about 0.12% different from exactly √2. Similarly, an increase of 6.000dB corresponds to a power ratio of 106/10 ≈ 3.9811, about 0.5% different from 4.

Properties

The decibel is useful for representing large ratios and for simplifying representation of multiplicative effects, such as attenuation from multiple sources along a signal chain. Its application in systems with additive effects is less intuitive, such as in the combined sound pressure level of two machines operating together. Care is also necessary with decibels directly in fractions and with the units of multiplicative operations.

Reporting large ratios

The logarithmic scale nature of the decibel means that a very large range of ratios can be represented by a convenient number. For example, 50dB is easier to say than "the two powers bear a 100,000 to 1 ratio" or that "one power is 105 the other". Decibels express huge changes of a quantity with few digits of dB.

Representation of multiplication operations

Level values in decibels can be added instead of multiplying the underlying power values, which means that the overall gain of a multi-component system, such as a series of amplifier stages, can be calculated by summing the gains in decibels of the individual components, rather than multiply the amplification factors; that is, log(A × B × C)= log(A) + log(B) + log(C). Practically, this means that, armed only with the knowledge that 1dB is a power gain of approximately 26%, 3dB is approximately 2× power gain, and 10dB is 10× power gain, it is possible to determine the power ratio of a system from the gain in dB with only simple addition and multiplication. For example:

• A system consists of 3 amplifiers in series, with gains (ratio of power out to in) of 10dB, 8dB, and 7dB respectively, for a total gain of 25dB. Broken into combinations of 10, 3, and 1dB, this is: 25dB= 10dB+ 10dB+ 3dB+ 1dB+ 1dB With an input of 1watt, the output is approximately 1W× 10× 10× 2× 1.26× 1.26≈ 317.5W Calculated precisely, the output is 1W× 1025/10≈ 316.2W. The approximate value has an error of only +0.4% with respect to the actual value, which is negligible given the precision of the values supplied and the accuracy of most measurement instrumentation.

However, according to its critics, the decibel creates confusion, obscures reasoning, is more related to the era of slide rules than to modern digital processing, and is cumbersome and difficult to interpret. Quantities in decibels are not necessarily additive, thus being "of unacceptable form for use in dimensional analysis". Thus, units require special care in decibel operations. Take, for example, carrier-to-noise-density ratio C/N0 (in hertz), involving carrier power C (in W) and noise power spectral density N0 (in W/Hz). Expressed in decibels, this ratio would be a subtraction (C/N0)dB = CdB − N0dB. However, the linear-scale units still simplify in the implied fraction, so that the results would be expressed in dB-Hz.

Representation of addition operations

According to Mitschke, "The advantage of using a logarithmic measure is that in a transmission chain, there are many elements concatenated, and each has its own gain or attenuation. To obtain the total, addition of decibel values is much more convenient than multiplication of the individual factors." However, for the same reason that humans excel at additive operation over multiplication, decibels are awkward in inherently additive operations:

if two machines each individually produce a sound pressure level of, say, 90dB at a certain point, then when both are operating together we should expect the combined sound pressure level to increase to 93dB, but certainly not to 180dB!; suppose that the noise from a machine is measured (including the contribution of background noise) and found to be 87dBA but when the machine is switched off the background noise alone is measured as 83dBA. [...] the machine noise [level (alone)] may be obtained by 'subtracting' the 83dBA background noise from the combined level of 87dBA; i.e., 84.8dBA.; in order to find a representative value of the sound level in a room a number of measurements are taken at different positions within the room, and an average value is calculated. [...] Compare the logarithmic and arithmetic averages of [...] 70dB and 90dB: logarithmic average = 87dB; arithmetic average = 80dB.

Addition on a logarithmic scale is called logarithmic addition, and can be defined by taking exponentials to convert to a linear scale, adding there, and then taking logarithms to return. For example, where operations on decibels are logarithmic addition or subtraction and logarithmic multiplication or division, while operations on the linear scale are the usual operations:

87 dBA ⊖ 83 dBA = 10 ⋅ log 10 ⁡ ( 10 87 / 10 − 10 83 / 10 ) dBA ≈ 84.8 dBA {\displaystyle 87\,{\text{dBA}}\ominus 83\,{\text{dBA}}=10\cdot \log _{10}{\bigl (}10^{87/10}-10^{83/10}{\bigr )}\,{\text{dBA}}\approx 84.8\,{\text{dBA}}}

M lm ( 70 , 90 ) = ( 70 dBA + 90 dBA ) / 2 = 10 ⋅ log 10 ⁡ ( ( 10 70 / 10 + 10 90 / 10 ) / 2 ) dBA = 10 ⋅ ( log 10 ⁡ ( 10 70 / 10 + 10 90 / 10 ) − log 10 ⁡ 2 ) dBA ≈ 87 dBA {\displaystyle {\begin{aligned}M_{\text{lm}}(70,90)&=\left(70\,{\text{dBA}}+90\,{\text{dBA}}\right)/2\\&=10\cdot \log _{10}\left({\bigl (}10^{70/10}+10^{90/10}{\bigr )}/2\right)\,{\text{dBA}}\\&=10\cdot \left(\log _{10}{\bigl (}10^{70/10}+10^{90/10}{\bigr )}-\log _{10}2\right)\,{\text{dBA}}\approx 87\,{\text{dBA}}\end{aligned}}}

The logarithmic mean is obtained from the logarithmic sum by subtracting 10 log 10 ⁡ 2 {\displaystyle 10\log _{10}2}, since logarithmic division is linear subtraction.

Fractions

Attenuation constants, in topics such as optical fiber communication and radio propagation path loss, are often expressed as a fraction or ratio to distance of transmission. In this case, dB/m represents decibel per meter, dB/mi represents decibel per mile, for example. These quantities are to be manipulated obeying the rules of dimensional analysis, e.g., a 100-meter run with a 3.5 dB/km fiber yields a loss of 0.35 dB = 3.5 dB/km × 0.1km.

Uses

Perception

The human perception of the intensity of sound and light more nearly approximates the logarithm of intensity rather than a linear relationship (see Weber–Fechner law), making the dB scale a useful measure.

Acoustics

The decibel is commonly used in acoustics as a unit of sound power level or sound pressure level. The reference pressure for sound in air 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 sound pressure is a root-power quantity, the appropriate version of the unit definition is used:

L p = 20 log 10 ( p rms p ref ) dB , {\displaystyle L_{p}=20\log _{10}\!\left({\frac {p_{\text{rms}}}{p_{\text{ref}}}}\right)\,{\text{dB}},}

where prms is the root mean square of the measured sound pressure and pref is the standard reference sound pressure of 20 micropascals in air or 1 micropascal in water.

Use of the decibel in underwater acoustics leads to confusion, in part because of this difference in reference value.

Sound intensity is proportional to the square of sound pressure. Therefore, the sound intensity level can also be defined as:

L p = 10 log 10 ( I I ref ) dB , {\displaystyle L_{p}=10\log _{10}\!\left({\frac {I}{I_{\text{ref}}}}\right)\,{\text{dB}},}

The human ear has a large dynamic range in sound reception. The ratio of the sound intensity that causes permanent damage during short exposure to that of the quietest sound that the ear can hear is equal to or greater than 1trillion (1012). Such large measurement ranges are conveniently expressed in logarithmic scale: the base-10 logarithm of 1012 is 12, which is expressed as a sound intensity level of 120dB re 1 pW/m2. The reference values of I and p in air have been chosen such that this corresponds approximately to a sound pressure level of 120dB re 20μPa.

The original choice of the decibel over the bel as a log unit of change of intensity is because a single change in a property of sound which is below the just-noticeable difference (JND) does not affect perception of the sound. For amplitude, the JND for humans is around 1dB.

Since the human ear is not equally sensitive to all sound frequencies, the acoustic power spectrum is modified by frequency weighting (A-weighting being the most common standard) to get the weighted acoustic power before converting to a sound level or noise level in decibels.

Telephony

The decibel is used in telephony and audio. Similarly to the use in acoustics, a frequency weighted power is often used. For audio noise measurements in electrical circuits, the weightings are called psophometric weightings.

Electronics

In electronics, the decibel is often used to express power or amplitude ratios (as for 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, coaxial cable, fiber optics, etc.) using a link budget.

The decibel unit can also be combined with a reference level, often indicated via a suffix, to create an absolute unit of electric power. For example, dBW uses a 1W reference, while dBm uses a 1 mW reference (m being short for milliwatt). A power level of 0dBm corresponds to one milliwatt, and 1dBm is one decibel greater (about 1.259mW).

In professional audio specifications, a popular unit is the dBu. This is relative to the root mean square voltage which delivers 1mW (0dBm) into a 600-ohm resistor, or √1mW × 600Ω≈ 0.775VRMS. When used in a 600-ohm circuit (historically, the standard reference impedance in telephone circuits), dBu and dBm are identical.

Optics

In an optical link, if a known amount of optical power, in dBm (referenced to 1mW), is launched into a fiber, and the losses, in dB (decibels), of each 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 −1B.

Video and digital imaging

In connection with video and digital image sensors, decibels generally represent ratios of video voltages or digitized light intensities, using 20log of the ratio, even when the represented intensity (optical power) is directly proportional to the voltage generated by the sensor, 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 quoted as 40dB represents a ratio of 100:1 between optical signal intensity and optical-equivalent dark-noise intensity, not a 10,000:1 intensity (power) ratio as 40dB might suggest. Sometimes the 20log ratio definition is applied to electron counts or photon counts directly, which are proportional to sensor signal amplitude without the need to consider whether the voltage response to intensity is linear.

However, as mentioned above, the 10log 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 dB, 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 typically use a base-2 log unit, the stop, to describe light intensity ratios or dynamic range.

Suffixes and reference values

Suffixes are commonly attached to the basic dB unit in order to indicate the reference value by which the ratio is calculated. For example, dBm indicates power measurement relative to 1milliwatt.

In cases where the unit value of the reference is stated, the decibel value is known as "absolute". If the unit value of the reference is not explicitly stated, as in the dB gain of an amplifier, then the decibel value is considered relative.

This form of attaching suffixes to dB is widespread in practice, albeit being against the rules promulgated by standards bodies (ISO and IEC), given the "unacceptability of attaching information to units" and the "unacceptability of mixing information with units". The IEC 60027-3 standard recommends the following format: Lx (re xref) or as Lx/xref, where x is the quantity symbol and xref is the value of the reference quantity, e.g., LE (re 1μV/m)= 20dB or LE/(1 μV/m)= 20dB for the electric field strength E relative to 1 μV/m reference value. If the measurement result 20dB is presented separately, it can be specified using the information in parentheses, which is then part of the surrounding text and not a part of the unit: 20dB (re 1 μV/m) or 20dB (1 μV/m).

Outside of documents adhering to SI units, the practice is very common as illustrated by the following examples. There is no general rule, with various discipline-specific practices. Sometimes the suffix is a unit symbol ("W","K","m"), sometimes it is a transliteration of a unit symbol ("uV" instead of μV for microvolt), sometimes it is an acronym for the unit's name ("sm" for square meter, "m" for milliwatt), other times it is a mnemonic for the type of quantity being calculated ("i" for antenna gain with respect to an isotropic antenna, "λ" for anything normalized by the EM wavelength), or otherwise a general attribute or identifier about the nature of the quantity ("A" for A-weighted sound pressure level). The suffix is often connected with a hyphen, as in "dB‑Hz", or with a space, as in "dBHL", or enclosed in parentheses, as in "dB(HL)", or with no intervening character, as in "dBm" (which is non-compliant with international standards).

List of suffixes

Voltage

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.

dBV

dB(VRMS)– voltage relative to 1volt, regardless of impedance. This is used to measure microphone sensitivity, and also to specify the consumer line-level of −10 dBV, in order to reduce manufacturing costs relative to equipment using the much larger +4 dBu line-level standard.

dBu or dBv

Schematic of a 0dBu voltage source dissipating 0dBm of power as heat in a 600Ω resistor 0 dBu is defined as the RMS voltage that would dissipate 0dBm (1mW) in a 600Ω load. Per Ohm's law, this voltage equals:resistance ⋅ power = 600 Ω ⋅ 0.001 W = 0.6 V R M S ≈ 0.7746 V R M S . {\displaystyle {\sqrt {{\text{resistance}}\cdot {\text{power}}}}={\sqrt {600\ {\mathsf {\Omega }}\ \cdot \ 0.001\ {\mathsf {W}}\;}}={\sqrt {0.6}}\ {\mathsf {V_{RMS}}}\approx 0.7746\ {\mathsf {V_{RMS}}}\,.}Therefore, 1VRMS corresponds to: 20 ⋅ log 10 ⁡ ( 1 V R M S 0.6 V R M S ) ≈ 2.218 d B u . {\displaystyle 20\cdot \log _{10}\left({\frac {1\ {\mathsf {V_{RMS}}}}{{\sqrt {0.6}}\ {\mathsf {V_{RMS}}}}}\right)\approx 2.218\ {\mathsf {dB_{u}}}~.}Originally called dBv, it was changed to dBu to avoid confusion with dBV. According to Rupert Neve, the u originated from the volume unit displayed on a VU meter. The u has also been interpreted as unloaded.

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 typically uses a lower "nominal" signal level of −10 dBV. Therefore, many devices offer dual voltage operation (with different gain or "trim" settings) for compatibility. A switch or adjustment that covers at least the range between +4 dBu and −10 dBV is common in professional equipment.

dBmV

dBmV: dB(mVRMS) – root mean square voltage relative to 1millivolt across 75Ω. Widely used in cable television networks, where the nominal strength of a single TV signal at the receiver terminals is about 0dBmV. CableTV uses 75Ω coaxial cable, so 0dBmV corresponds to −78.75dBW, −48.75dBm or approximately 13nW.

dBmV0s

Defined by Recommendation ITU-R V.574.

dBμV or dBuV

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

Acoustics

Probably the most common usage of "decibels" in reference to sound level is dBSPL, sound pressure level referenced to the nominal threshold of human hearing: The measures of pressure (a root-power quantity) use the factor of 20, and the measures of power (e.g. dBSIL and dBSWL) use the factor of 10.

dBSPL

dBSPL (sound pressure level) – for sound in air and other gases, relative to 20micropascals (μPa), or 2×10−5Pa, a level of 0dBSPL is approximately the quietest sound a human can hear. For sound in water and other liquids, a reference pressure of 1μPa is used. An RMS sound pressure of one pascal corresponds to a level of 94dBSPL.

dBSIL

dB sound intensity level – relative to 10−12W/m2, which is roughly the threshold of human hearing in air.

dBSWL

dB sound power level – relative to 10−12W.

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 its effects on humans and other animals, and they are widely used in industry while discussing noise control issues, regulations and environmental standards. Other variations that may be seen are dBA or dB(A). According to standards from the International Electro-technical Committee (IEC 61672-2013) and the American National Standards Institute, ANSI S1.4, the preferred usage is to write LA = xdB. Nevertheless, the units dB(A) are still commonly used as a shorthand for A‑weighted measurements. Compare dBc, used in telecommunications.

dBHL

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]

dBQ

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

dBpp

relative to the peak to peak sound pressure.

dB(G)

G‑weighted spectrum

Audio electronics

See also dBV and dBu above.

dBm

dBmW – power relative to 1milliwatt. In audio and telephony, dBm is typically referenced relative to a 600Ω impedance, which corresponds to a voltage level of 0.775volts or 775millivolts.

dBm0

Power in dBm (described above) measured at a zero transmission level point.

dBFS

dB(full scale) – the amplitude of a signal compared with the maximum which a device can handle before clipping occurs. Full-scale may be defined as the power level of a full-scale sinusoid or alternatively a full-scale square wave. A signal measured with reference to a full-scale sine-wave appears 3dB weaker when referenced to a full-scale square wave, thus: 0dBFS(fullscale sine wave) = −3dBFS (fullscale square wave).

dBVU

dB volume unit

dBTP

dB(true peak) – peak amplitude of a signal compared with the maximum which a device can handle before clipping occurs. In digital systems, 0dBTP would equal the highest level (number) the processor is capable of representing. Measured values are always negative or zero, since they are less than or equal to full-scale.

Radar

dBZ

dBZ – decibel relative to Z= 1mm6⋅m−3: energy of reflectivity (weather radar), related to the amount of transmitted power returned to the radar receiver. Values above 20dBZ usually indicate falling precipitation.

dBsm

dB(m2) – decibel relative to one square meter: measure of the radar cross section (RCS) of a target. The power reflected by the target is proportional to its RCS. "Stealth" aircraft and insects have negative RCS measured in dBsm, large flat plates or non-stealthy aircraft have positive values.

Radio power, energy, and field strength

dBc

relative to carrier – in telecommunications, this indicates the relative levels of noise or sideband power, compared with the carrier power. Compare dB(C), used in acoustics.

dBpp

relative to the maximum value of the peak power.

dBJ

energy relative to 1joule. 1joule= 1watt second= 1watt per hertz, so power spectral density can be expressed in dBJ.

dBmJ

energy relative to 1millijoule, or 1 milliwatt per hertz.

dBm

dB(mW) – power relative to 1milliwatt. Usually referenced to a 50Ω load, so 0dBm corresponds to 0.224volts. 0dBm= -30dBW.

dBm/Hz

dB(mW/Hz) - power spectral density relative to 1 milliwatt per hertz, equivalent to dBmJ.

dBμV/m, dBuV/m, or dBμ

dB(μV/m) – electric field strength relative to 1microvolt per meter. Related to power flux density through the impedance of free space (η0= 376.73Ω), so 0dBμV/m corresponds to (1μV/m)2/η0= 2.65x10-15 W/m2= -145.76dBW/m2= -115.76 dBm/m2.

dBf

dB(fW) – power relative to 1femtowatt.

dBW

dB(W) – power relative to 1watt. 1dBW= +30dBm.

dBW/Hz

dB(W/Hz) - power spectral density relative to 1 watt per hertz. Equivalent to dBJ.

dBW/m2

dB(W/m2) - power flux density (of electromagnetic radiation) relative to 1W per square meter.

dBk

dB(kW) – power relative to 1kilowatt, 0dBk = +30dBW = +60dBm. Not to be confused with dBK, temperature relative to 1 Kelvin.

dBe

dB electrical.

dBo

dB optical. A change of 1dBo in optical power can result in a change of up to 2dBe in electrical signal power in a system that is thermal noise limited.

Antenna measurements

dBi

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

dBd

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

dBiC

dB(isotropic circular) – the gain of an antenna compared to the gain of a theoretical 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 gain of an antenna compared to the gain of a quarter wavelength whip. Rarely used, except in some marketing material; 0 dBq= −0.85 dBi

dBsm

dB(m2) – decibels relative to one square meter: A measure of the effective area for capturing signals of the antenna.

dBm−1

dB(m−1) – decibels relative to reciprocal of meter: measure of the antenna factor.

Other measurements

dBHz

dB(Hz) – bandwidth relative to one hertz; e.g., 20dBHz corresponds to a bandwidth of 100Hz. 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 dB FS, but also applicable to analog systems. According to ITU-T Rec. G.100.1 the level in dB ov of a digital system is defined as: L o v = 10 log 10 ⁡ ( P P m a x ) [ d B o v ] , {\displaystyle L_{\mathsf {ov}}=10\log _{10}\left({\frac {P}{\ P_{\mathsf {max}}\ }}\right)\ [{\mathsf {dB_{ov}}}],} with the maximum signal power P m a x = 1.0 {\displaystyle P_{\mathsf {max}}=1.0}, for a rectangular signal with the maximum amplitude x o v e r {\displaystyle x_{\mathsf {over}}}. The level of a tone with a digital amplitude (peak value) of x o v e r {\displaystyle x_{\mathsf {over}}} is therefore L o v = − 3.01 d B o v {\displaystyle L_{\mathsf {ov}}=-3.01\ {\mathsf {dB_{ov}}}}.

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

dB above reference noise. See also dBrnC

dBrnC

dB(rnC) represents an audio level measurement, typically in a telephone circuit, relative to a −90dBm reference level, with the measurement of this level frequency-weighted by a standard C-message weighting filter. The C-message weighting filter was chiefly used in North America. The psophometric filter is used for this purpose on international circuits.

dBK

dB(K) – decibels relative to 1K; used to express noise temperature.

dBK−1 or dB/K

dB(K−1) – decibels relative to 1K−1. — not decibels per kelvin: Used for the ⁠G/T⁠ (G/T) factor, a figure of merit used in satellite communications, relating the antenna gain G to the receiver system noise equivalent temperature T.

List of suffixes in alphabetical order

Unpunctuated suffixes

dBA

see dB(A).

dBa

see dBrn adjusted.

dBB

see dB(B).

dBc

relative to carrier – in telecommunications, this indicates the relative levels of noise or sideband power, compared with the carrier power.

dBC

see dB(C).

dBD

see dB(D).

dBd

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

dBe

dB electrical.

dBf

dB(fW) – power relative to 1femtowatt.

dBFS

dB(full scale) – the amplitude of a signal compared with the maximum which a device can handle before clipping occurs. Full-scale may be defined as the power level of a full-scale sinusoid or alternatively a full-scale square wave. A signal measured with reference to a full-scale sine-wave appears 3dB weaker when referenced to a full-scale square wave, thus: 0dBFS (fullscale sine wave)= −3dBFS (full-scale square wave).

dBG

G-weighted spectrum

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.

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.

dBJ

energy relative to 1joule: 1joule= 1watt-second= 1watt per hertz, so power spectral density can be expressed in dBJ.

dBk

dB(kW) – power relative to 1kilowatt.

dBK

dB(K) – decibels relative to kelvin: Used to express noise temperature.

dBm

dB(mW) – power relative to 1milliwatt.

dBm2 or dBsm

dB(m2) – decibel relative to one square meter

dBm0

Power in dBm measured at a zero transmission level point.

dBm0s

Defined by Recommendation ITU-R V.574.

dBmV

dB(mVRMS) – voltage relative to 1millivolt across 75Ω.

dBo

dB optical. A change of 1dBo in optical power can result in a change of up to 2dBe in electrical signal power in system that is thermal noise limited.

dBO

see dBov

dBov or dBO

dB(overload) – the amplitude of a signal (usually audio) compared with the maximum which a device can handle before clipping occurs.

dBpp

relative to the peak to peak sound pressure.

dBpp

relative to the maximum value of the peak electrical power.

dBq

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

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

dB above reference noise. See also dBrnC

dBrnC

represents an audio level measurement, typically in a telephone circuit, relative to the circuit noise level, with the measurement of this level frequency-weighted by a standard C-message weighting filter. The C-message weighting filter was chiefly used in North America.

dBsm

see dBm2

dBTP

dB(true peak) – peak amplitude of a signal compared with the maximum which a device can handle before clipping occurs.

dBu or dBv

RMS voltage relative to 0.6 V ≈ 0.7746 V ≈ − 2.218 d B V . {\displaystyle \ {\sqrt {0.6\ }}\ {\mathsf {V}}\ \approx 0.7746\ {\mathsf {V}}\ \approx -2.218\ {\mathsf {dB_{V}}}~.}

dBu0s

Defined by Recommendation ITU-R V.574.

dBuV

see dBμV

dBuV/m

see dBμV/m

dBv

see dBu

dBV

dB(VRMS) – voltage relative to 1volt, regardless of impedance.

dBVU

dB(VU) dB volume unit

dBW

dB(W) – power relative to 1watt.

dB W·m−2·Hz−1

spectral density relative to 1 W·m−2·Hz−1

dBZ

dB(Z) – decibel relative to Z= 1mm6⋅m−3

dBμ

see dBμV/m

dBμV or dBuV

dB(μVRMS) – voltage relative to 1root mean square microvolt.

dBμV/m, dBuV/m, or dBμ

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

Suffixes preceded by a space

dB HL

dB hearing level is used in audiograms as a measure of hearing loss.

dB Q

sometimes used to denote weighted noise level

dB SIL

dB sound intensity level – relative to 10−12W/m2

dB SPL

dB SPL (sound pressure level) – for sound in air and other gases, relative to 20μPa in air or 1μPa in water

dB SWL

dB sound power level – relative to 10−12W.

Suffixes within parentheses

dB(A), dB(B), dB(C), dB(D), dB(G), and dB(Z)

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 its effects on humans and other animals, and they are widely used in industry while discussing noise control issues, regulations and environmental standards. Other variations that may be seen are dBA or dBA.

Other suffixes

dBHz or dB-Hz

dB(Hz) – bandwidth relative to one hertz

dBHz2 or dB/s2

dB(Hz2) – the squared magnitude of an impulse response (or impulse response envelope) relative to the squared magnitude of an impulse response with unity amplitude.

dBK−1 or dB/K

dB(K−1) – decibels relative to reciprocal of kelvin

dBm−1

dB(m−1) – decibel relative to reciprocal of meter: measure of the antenna factor

mBm

mB(mW) – power relative to 1milliwatt, in millibels (one hundredth of a decibel). 100mBm = 1dBm. This unit is in the Wi-Fi drivers of the Linux kernel and the regulatory domain sections.

See also

• Apparent magnitude
• Cent (music)
• Day–evening–night noise level
• Day-night average sound level
• dB drag racing
• Decade (log scale)
• Loudness
• Neper
• One-third octave §Base 10
• pH
• Phon
• Richter magnitude scale
• Sone

Notes

Further reading

• Tuffentsammer, Karl (1956). "Das Dezilog, eine Brücke zwischen Logarithmen, Dezibel, Neper und Normzahlen" [The decilog, a bridge between logarithms, decibel, neper and preferred numbers]. VDI-Zeitschrift (in German). 98: 267–274.
• Paulin, Eugen (1 September 2007). [Logarithms, preferred numbers, decibel, neper, phon - naturally related!] (PDF) (in German). (PDF) from the original on 18 December 2016.

External links

• (RF signal and field strengths)