Decibel

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 L_P, that ratio expressed in decibels,[20] which is calculated using the formula:[21]

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

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 L_P = 0. If P is greater than P₀ then L_P is positive; if P is less than P₀ then L_P is negative.

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

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

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:

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

The formula may be rearranged to give

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

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 L_G:

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

where V_out is the root-mean-square (rms) output voltage, V_in 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.

Although power and root-power quantities are different quantities, their respective levels are historically measured 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

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

holding.[22] 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,

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

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 0 dB, 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.

Since logarithm differences measured 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.

The unit dBW is often used to denote a ratio for which the reference is 1 W, and similarly dBm for a 1 mW reference point.

• Calculating the ratio in decibels of 1 kW (one kilowatt, or 1000 watts) to 1 W yields:
  $${\displaystyle L_{G}=10\log _{10}\left({\frac {1\,000\,{\text{W}}}{1\,{\text{W}}}}\right)\,{\text{dB}}=30\,{\text{dB}}.}$$

  
• The ratio in decibels of √1000 V ≈ 31.62 V to 1 V is
  $${\displaystyle L_{G}=20\log _{10}\left({\frac {31.62\,{\text{V}}}{1\,{\text{V}}}}\right)\,{\text{dB}}=30\,{\text{dB}}.}$$

  

(31.62 V / 1 V)² ≈ 1 kW / 1 W, illustrating the consequence from the definitions above that L_G has the same value, 30 dB, 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
  $${\displaystyle L_{G}=10\log _{10}\left({\frac {10{\text{ W}}}{0.001{\text{ W}}}}\right){\text{ dB}}=40{\text{ dB}}.}$$

  
• The power ratio corresponding to a 3 dB change in level is given by
  $${\displaystyle G=10^{\frac {3}{10}}\times 1=1.995\,26\ldots \approx 2.}$$

  

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 3 dB. More precisely, the change is ±3.0103 dB, but this is almost universally rounded to 3 dB in technical writing. This implies an increase in voltage by a factor of √2 ≈ 1.4142. Likewise, a doubling or halving of the voltage, and quadrupling or quartering of the power, is commonly described as 6 dB rather than ±6.0206 dB.

Should it be necessary to make the distinction, the number of decibels is written with additional significant figures. 3.000 dB corresponds to a power ratio of 10^3⁄10, or 1.9953, about 0.24% different from exactly 2, and a voltage ratio of 1.4125, 0.12% different from exactly √2. Similarly, an increase of 6.000 dB corresponds to the power ratio is 10^6⁄10 ≈ 3.9811, about 0.5% different from 4.

The logarithmic scale nature of the decibel means that a very large range of ratios can be represented by a convenient number, in a manner similar to scientific notation. This allows one to clearly visualize huge changes of some quantity. See Bode plot and Semi-log plot. For example, 120 dB SPL may be clearer than "a trillion times more intense than the threshold of hearing".

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 1 dB is a power gain of approximately 26%, 3 dB is approximately 2× power gain, and 10 dB 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 10 dB, 8 dB, and 7 dB respectively, for a total gain of 25 dB. Broken into combinations of 10, 3, and 1 dB, this is:
  25 dB = 10 dB + 10 dB + 3 dB + 1 dB + 1 dB
  With an input of 1 watt, the output is approximately
  1 W × 10 × 10 × 2 × 1.26 × 1.26 ≈ 317.5 W
  Calculated precisely, the output is 1 W × 10^25⁄10 ≈ 316.2 W. 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.[23][24] Quantities in decibels are not necessarily additive,[25][26] thus being "of unacceptable form for use in dimensional analysis".[27] 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 watts) and noise power spectral density N₀ (in W/Hz). Expressed in decibels, this ratio would be a subtraction (C/N₀)_dB = C_dB − N_0dB. However, the linear-scale units still simplify in the implied fraction, so that the results would be expressed in dB-Hz.

According to Mitschke,[28] "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:[29]

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

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/subtraction and logarithmic multiplication/division, while operations on the linear scale are the usual operations:

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

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

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

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 × 0.1 km.

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.[30][31][32][33][34][35]

Examples of sound levels in decibels from various sound sources and activities, taken from the "How loud is too loud" screen of the NIOSH Sound Level Meter app

The decibel is commonly used in acoustics as a unit of 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:

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

where p_rms is the root mean square of the measured sound pressure and p_ref is the standard reference sound pressure of 20 micropascals in air or 1 micropascal in water.[36]

Use of the decibel in underwater acoustics leads to confusion, in part because of this difference in reference value.[37]

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 1 trillion (10¹²).[38] Such large measurement ranges are conveniently expressed in logarithmic scale: the base-10 logarithm of 10¹² is 12, which is expressed as a sound pressure level of 120 dB re 20 μPa.

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.[39]

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.[40]

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, it can be combined with "m" for "milliwatt" to produce the "dBm". A power level of 0 dBm corresponds to one milliwatt, and 1 dBm is one decibel greater (about 1.259 mW).

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

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 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.[41]

In spectrometry and optics, the blocking unit used to measure optical density is equivalent to −1 B.

In connection with video and digital image sensors, decibels generally represent ratios of video voltages or digitized light intensities, using 20 log 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.[42] Thus, a camera signal-to-noise ratio or dynamic range quoted as 40 dB 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 40 dB might suggest.[43] Sometimes the 20 log 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.[44]

However, as mentioned above, the 10 log 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 an alternative base-2 log unit, the stop, to describe light intensity ratios or dynamic range.

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.

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

dBV

dB(V_RMS) – voltage relative to 1 volt, regardless of impedance.[3] 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 a +4 dBu line-level signal.[45]

dBu or dBv

RMS voltage relative to ${\displaystyle V={\sqrt {600\,\Omega \cdot 0.001\,{\text{W}}}}\approx 0.7746\,{\text{V}}}$ (i.e. the voltage that would dissipate 1 mW into a 600 Ω load). An RMS voltage of 1 V therefore corresponds to ${\displaystyle 20\cdot \log _{10}\left({\frac {1\,V_{\text{RMS}}}{{\sqrt {0.6}}\,V}}\right)=2.218\,{\text{dBu}}.}$[3] Originally dBv, it was changed to dBu to avoid confusion with dBV.[46] The v comes from volt, while u comes from the volume unit used in the VU meter.[47]

dBu can be used as a measure of voltage, regardless of impedance, but is derived from a 600 Ω load dissipating 0 dBm (1 mW). The reference voltage comes from the computation ${\displaystyle V={\sqrt {R\cdot P}}}$ where ${\displaystyle R}$ is the resistance and ${\displaystyle P}$ is the power.

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.[48] Therefore, many devices offer dual voltage operation (with different gain or "trim" settings) for interoperability reasons. A switch or adjustment that covers at least the range between +4 dBu and −10 dBV is common in professional equipment.

dBm0s

Defined by Recommendation ITU-R V.574.; dBmV: dB(mV_RMS) – voltage relative to 1 millivolt across 75 Ω.[49] 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 approximately 13 nW.

dBμV or dBuV

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

Probably the most common usage of "decibels" in reference to sound level is dB SPL, sound pressure level referenced to the nominal threshold of human hearing:[50] The measures of pressure (a root-power quantity) use the factor of 20, and the measures of power (e.g. dB SIL and dB SWL) use the factor of 10.

dB SPL

dB SPL (sound pressure level) – for sound in air and other gases, relative to 20 micropascals (μPa), or 2×10⁻⁵ Pa, approximately the quietest sound a human can hear. For sound in water and other liquids, a reference pressure of 1 μPa is used.[51]

An RMS sound pressure of one pascal corresponds to a level of 94 dB SPL.

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.

dBA, dBB, and dBC

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 dB_A or dB(A). According to standards from the International Electro-technical Committee (IEC 61672-2013)[52] and the American National Standards Institute, ANSI S1.4,[53] the preferred usage is to write L_A = x dB. Nevertheless, the units dBA and dB(A) are still commonly used as a shorthand for A‑weighted measurements. Compare dBc, used in telecommunications.

dB HL

dB hearing level is used in audiograms as a measure of hearing loss. The reference level varies with frequency according to a minimum audibility curve as defined in ANSI and other standards, such that the resulting audiogram shows deviation from what is regarded as 'normal' hearing.

dB Q

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

dBpp

relative to the peak to peak sound pressure.[54]

dBG

G‑weighted spectrum[55]

See also dBV and dBu above.

dBm

dB(mW) – power relative to 1 milliwatt. In audio and telephony, dBm is typically referenced relative to a 600 Ω impedance,[56] which corresponds to a voltage level of 0.775 volts or 775 millivolts.

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 3 dB weaker when referenced to a full-scale square wave, thus: 0 dBFS(fullscale sine wave) = −3 dBFS(fullscale square wave).

dBVU

dB volume unit[57]

dBTP

dB(true peak) – peak amplitude of a signal compared with the maximum which a device can handle before clipping occurs.[58] In digital systems, 0 dBTP 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.

dBZ

dB(Z) – decibel relative to Z = 1 mm⁶⋅m⁻³:[59] energy of reflectivity (weather radar), related to the amount of transmitted power returned to the radar receiver. Values above 20 dBZ usually indicate falling precipitation.[60]

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.[61]

dBc

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

dBpp

relative to the maximum value of the peak power.

dBJ

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

dBm

dB(mW) – power relative to 1 milliwatt. In the radio field, dBm is usually referenced to a 50 Ω load, with the resultant voltage being 0.224 volts.[62]

dBμV/m, dBuV/m, or dBμ

[63] dB(μV/m) – electric field strength relative to 1 microvolt per meter. The unit is often used to specify the signal strength of a television broadcast at a receiving site (the signal measured at the antenna output is reported in dBμV).

dBf

dB(fW) – power relative to 1 femtowatt.

dBW

dB(W) – power relative to 1 watt.

dBk

dB(kW) – power relative to 1 kilowatt.

dBe

dB electrical.

dBo

dB optical. A change of 1 dBo in optical power can result in a change of up to 2 dBe in electrical signal power in a system that is thermal noise limited.[64]

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 a half-wave dipole antenna. 0 dBd = 2.15 dBi

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) – decibel relative to one square meter: measure of the antenna effective area.[65]

dBm⁻¹

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

dB‑Hz

dB(Hz) – bandwidth relative to one hertz. 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. According to ITU-T Rec. G.100.1 the level in dBov of a digital system is defined as:

${\displaystyle L_{\text{ov}}=10\log _{10}\left({\frac {P}{P_{0}}}\right)\ [{\text{dBov}}]}$,

with the maximum signal power ${\displaystyle P_{0}=1.0}$, for a rectangular signal with the maximum amplitude ${\displaystyle x_{\text{over}}}$. The level of a tone with a digital amplitude (peak value) of ${\displaystyle x_{\text{over}}}$ is therefore ${\displaystyle L=-3.01\ {\text{dBov}}}$.[66]

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

dBrnC represents an audio level measurement, typically in a telephone circuit, relative to a -90 dBm 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. See Psophometric weighting to see a comparison of frequency response curves for the C-message weighting and Psophometric weighting filters.[67]

dBK

dB(K) – decibels relative to 1 K; used to express noise temperature.[68]

dB/K

dB(K⁻¹) – decibels relative to 1 K⁻¹.[69] — not decibels per kelvin: Used for the G/T factor, a figure of merit utilized in satellite communications, relating the antenna gain G to the receiver system noise equivalent temperature T.[70][71]

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. 0 dBd = 2.15 dBi

dBe

dB electrical.

dBf

dB(fW) – power relative to 1 femtowatt.

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 3 dB weaker when referenced to a full-scale square wave, thus: 0 dBFS(fullscale sine wave) = −3 dBFS(fullscale 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 1 joule. 1 joule = 1 watt second = 1 watt per hertz, so power spectral density can be expressed in dBJ.

dBk

dB(kW) – power relative to 1 kilowatt.

dBK

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

dBm

dB(mW) – power relative to 1 milliwatt.

dBm0

Power in dBm measured at a zero transmission level point.

dBm0s

Defined by Recommendation ITU-R V.574.

dBmV

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

dBo

dB optical. A change of 1 dBo in optical power can result in a change of up to 2 dBe 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 power.

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

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

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

dB(m²) – decibel relative to one square meter

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 ${\displaystyle {\sqrt {0.6}}\,{\text{V}}\,\approx 0.7746\,{\text{V}}\,\approx -2.218\,{\text{dBV}}}$.

dBu0s

Defined by Recommendation ITU-R V.574.

dBuV

see dBμV

dBuV/m

see dBμV/m

dBv

see dBu

dBV

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

dBVU

dB volume unit

dBW

dB(W) – power relative to 1 watt.

dBW·m⁻²·Hz⁻¹

spectral density relative to 1 W·m⁻²·Hz⁻¹[72]

dBZ

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

dBμ

see dBμV/m

dBμV or dBuV

dB(μV_RMS) – voltage relative to 1 microvolt.

dBμV/m, dBuV/m, or dBμ

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

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 10⁻¹² W/m²

dB SPL

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

dB SWL

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

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 dB_A or dBA.

dB-Hz

dB(Hz) – bandwidth relative to one hertz.

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.