Decibel

The decibel, symbolized as dB, constitutes a relative unit of measurement, precisely one-tenth of a bel (B). This unit quantifies the ratio between two values of either a power or root-power quantity, utilizing a logarithmic scale. Specifically, a one-decibel difference between two signal levels corresponds to a power ratio of 101/10 (approximately 1.26) or a root-power ratio of 101/20 (approximately 1.12).

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 10^1/10 (approximately 1.26) or root-power ratio of 10^1/20 (approximately 1.12).

Initially, the decibel's application was strictly limited to denoting relative changes. Nevertheless, its usage has expanded to represent absolute values, which are defined in relation to a predetermined fixed reference. In such instances, the dB symbol is frequently appended with letter codes that specify the particular reference value. For instance, when the reference value is 1 volt, the suffix "V" is commonly employed (e.g., "20 dBV").

Given its genesis in quantifying power ratios, the decibel employs two primary scaling methodologies to ensure consistency, contingent upon whether the scaling pertains to power quantities or root-power quantities. For power ratios, the equivalent decibel change is calculated as ten times the base-10 logarithm of the ratio. Consequently, a tenfold increase in power translates to a 10 dB alteration in level. Conversely, for root-power ratios, a tenfold amplitude variation results in a 20 dB level change. This twofold difference between the decibel scales ensures that, within linear systems where power is directly proportional to the square of amplitude, corresponding power and root-power levels exhibit identical changes.

The decibel's conceptualization emerged from the necessity to measure transmission loss and power within early 20th-century telephony, specifically within the Bell System in the United States. While the bel was named to honor Alexander Graham Bell, its practical application remains infrequent. In contrast, the decibel finds extensive utility across diverse scientific and engineering disciplines, notably in acoustics for sound power, as well as in electronics and control theory. Within electronics, amplifier gains, signal attenuation, and signal-to-noise ratios are routinely quantified using decibels.

History

The genesis of the decibel lies in methodologies developed to quantify signal attenuation within telegraph and telephone circuits. Prior to the mid-1920s, signal loss was measured using the unit of miles of standard cable (MSC). One MSC represented the power loss occurring over a single mile (approximately 1.6 km) of standard telephone cable, specifically at a frequency of 5000 radians per second (795.8 Hz), and closely approximated the minimal attenuation perceptible to a human listener. This standard telephone cable was characterized by "a cable having uniformly distributed resistance of 88 ohms per loop-mile and uniformly distributed shunt capacitance of 0.054 microfarads per mile" (roughly equivalent to 19-gauge wire).

By 1924, Bell Telephone Laboratories garnered positive reception from the International Advisory Committee on Long Distance Telephony in Europe for a novel unit definition, subsequently replacing the MSC with the Transmission Unit (TU). A single TU was defined as ten times the base-10 logarithm of the ratio between a measured power and a reference power. This definition was strategically formulated so that 1 TU closely approximated 1 MSC; precisely, 1 MSC equated to 1.056 TU. In 1928, the Bell System officially renamed the TU as the decibel, establishing it as one-tenth of a newly introduced unit representing the base-10 logarithm of the power ratio. This larger unit was designated the bel, commemorating the telecommunications pioneer Alexander Graham Bell. The bel, however, is rarely employed, as the decibel was the intended operational unit.

The nomenclature and initial definition of the decibel are documented in the 1931 NBS Standard's Yearbook, stating:

From the nascent stages of telephony, the imperative for a standardized unit to quantify the transmission efficiency of telephone infrastructure was acknowledged. The advent of cable technology in 1896 provided a stable foundation for a practical unit, leading to the widespread adoption of the "mile of standard" cable shortly thereafter. This particular unit remained in use until 1923, at which point a novel unit was implemented, deemed more appropriate for contemporary telephone operations. This updated transmission unit has gained extensive acceptance among international telephone organizations and was recently designated the "decibel" following a proposal by the International Advisory Committee on Long Distance Telephony.

The decibel is defined such that a 1-decibel difference between two power amounts corresponds to a ratio of 10^0.1. Consequently, a difference of N decibels signifies a power ratio of 10^N(0.1). This implies that the number of transmission units representing the ratio of any two powers is ten times their common logarithm. Such a methodology for quantifying power gain or loss in telephone circuits facilitates the direct arithmetic combination (addition or subtraction) of efficiency units across various circuit components.

The term 'decibel' quickly became misapplied to denote absolute quantities and ratios beyond power measurements. Several proposals emerged to mitigate this ambiguity. In 1954, J. W. Horton suggested treating 10^0.1 as a fundamental ratio and introduced the term logit. He defined a logit as "a standard ratio with a numerical value of 10^0.1 that combines multiplicatively with similar ratios of the same value," meaning a 10^0.1 ratio of mass units would be termed a "mass logit." This concept diverged from the word unit, which was intended for magnitudes combining additively, and aimed to restrict decibel specifically to unit transmission loss. Another proposed term, the decilog, introduced by N. B. Saunders (1943), A. G. Fox (1951), and E. I. Green (1954), aimed to represent a logarithmic scale division corresponding to a ratio of 10^0.1.

In April 2003, the International Committee for Weights and Measures (CIPM) reviewed a recommendation to incorporate the decibel into the International System of Units (SI) but ultimately rejected the proposal. Nevertheless, the decibel is acknowledged by other international organizations, including the International Electrotechnical Commission (IEC) and the International Organization for Standardization (ISO). The IEC sanctions the application of the decibel to both root-power quantities and power quantities, a guideline adopted by numerous national standards bodies, such as NIST, which supports its use for voltage ratios. Despite their common usage, suffixes (e.g., dBA or dBV) are not officially recognized by either the IEC or ISO.

Definition

IEC Standard 60027-3:2002 specifies the subsequent quantities. A decibel (dB) is defined as one-tenth of a bel, meaning 1 dB = 0.1 B. A bel (B) is equivalent to ⁠§23§/§67§⁠ ln(10) nepers, expressed as 1 B = ⁠§1213§/§1617§⁠ ln(10) Np. The neper represents the alteration in the level of a root-power quantity when that quantity changes by a factor of e, specifically 1 Np = ln(e) = 1. This establishes a relationship among all units as dimensionless natural log of root-power-quantity ratios, yielding 1 dB = 0.115§3334§... Np = 0.115§3940§.... Ultimately, the level of a quantity is defined as the logarithm of the ratio between its value and a reference value of the identical quantity type.

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

Signals exhibiting a 1-decibel difference in their levels possess a power ratio of 10^1/10, approximately 1.25893. Their amplitude (root-power quantity) ratio is 10^1/20, which is approximately 1.12202.

The bel is infrequently employed without a prefix or with SI prefixes other than deci. Customarily, for instance, hundredths of a decibel are used instead of millibels. Therefore, five one-thousandths of a bel would typically be expressed as 0.05 dB, rather than 5 mB.

The methodology for expressing a ratio as a decibel level varies based on whether the measured property constitutes a power quantity or a root-power quantity.

Power quantities

For measurements involving power quantities, a ratio can be converted into a decibel level by calculating ten times the base-10 logarithm of the ratio between the measured quantity and a reference value. Consequently, the ratio of P (measured power) to P§67§ (reference power) is denoted as L_P, representing that ratio in decibels, and is computed using the following formula:

L P = §1819§ §2021§ ln ( P P §3940§ ) Np = §5657§ log §6263§ ( P P §7980§ ) 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 number of bels is defined as the base-10 logarithm of the ratio between two power quantities. A decibel is equivalent to one-tenth of a bel, meaning the number of decibels is ten times the number of bels. For an accurate ratio calculation, P and P§45§ must represent the same type of quantity and be expressed in identical units. Should P equal P§1213§ in the aforementioned equation, then L_P will be zero. If P is greater than P§2425§, then L_P is positive; conversely, if P is less than P§3637§, then L_P is negative.

Rearranging the preceding equation yields the subsequent formula for P, expressed in terms of P§45§ and L_P:

P = §1112§ L P §2425§ dB P §4041§ {\displaystyle P=10^{\frac {L_{P}}{10\,{\text{dB}}}}P_{0}}

Root-Power (Field) Quantities

In the context of root-power quantity measurements, the conventional approach involves evaluating the ratio of the squares of F (the measured value) and F§45§ (the reference value). This methodology stems from the original formulation of these definitions, which aimed to ensure consistent relative ratios for both power and root-power quantities. Consequently, the ensuing definition is employed:

L F = ln ( F F §3132§ ) Np = §4849§ log §5455§ ( F §6970§ F §7778§ §8182§ ) dB = §9899§ log §104105§ ⁡ ( F F §122123§ ) 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 aforementioned formula can be algebraically rearranged to yield the following expression:

F = §1112§ L F §2425§ dB F §4041§ {\displaystyle F=10^{\frac {L_{F}}{20\,{\text{dB}}}}F_{0}}

In a similar vein, within electrical circuits, the power dissipated is generally directly proportional to the square of either the voltage or the current, assuming a constant impedance. Using voltage as an illustrative example, this principle results in the following equation for the power gain level L_G:

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

Here, V_out denotes the root-mean-square (RMS) output voltage, while V_in represents the RMS input voltage. An analogous formula is applicable for current measurements.

The designation root-power quantity was formally introduced by ISO Standard 80000-1:2009, serving as a replacement for the term field quantity. Consequently, field quantity is considered deprecated by this standard, and root-power is consistently employed throughout the present article.

Interrelationship Between Power and Root-Power Levels

Despite the distinct nature of power and root-power quantities, their corresponding levels have historically been quantified using identical units, most commonly decibels. A factor of two is incorporated to ensure that variations in these respective levels align under specific constraints, such as when the transmission medium is linear and the identical waveform is being analyzed for amplitude changes, or when the medium's impedance is linear and invariant with respect to both frequency and time. This alignment is predicated upon the following relationship:

P t ) P §2223§ = ( F ( t ) F §5051§ ) §6061§ {\displaystyle {\frac {P(t)}{P_{0}}}=\left({\frac {F(t)}{F_{0}}}\right)^{2}}

This relationship must hold. Conversely, within a nonlinear system, this correlation is inherently invalid, as dictated by the definition of linearity itself. Furthermore, even within a linear system where the power quantity results from the product of two linearly interdependent quantities (e.g., voltage and current), this relationship generally fails to apply if the impedance exhibits frequency or time dependence. An illustrative instance is when the energy spectrum of the waveform undergoes alteration.

When considering differences in level, the aforementioned relationship is relaxed, transitioning to a proportional one. This implies that the reference quantities P§23§ and F§67§ are not necessarily required to be directly related. Alternatively, this can be expressed as:

P §1213§ P §2021§ = ( F §3839§ F §4647§ ) §5657§ {\displaystyle {\frac {P_{2}}{P_{1}}}=\left({\frac {F_{2}}{F_{1}}}\right)^{2}}

This condition must be satisfied for the power level difference to equate to the root-power level difference, transitioning from power P§23§ and F§67§ to P§10_{11§ and F§1415§. Consider, for instance, an amplifier exhibiting unity voltage gain, irrespective of load and frequency, driving a load with frequency-dependent impedance. In this scenario, the amplifier's relative voltage gain consistently remains 0 dB; however, the power gain is contingent upon the evolving spectral composition of the amplified waveform. Frequency-dependent impedances can be rigorously analyzed by examining power spectral density and its corresponding root-power quantities through the application of the Fourier transform. This methodology facilitates the removal of frequency dependence from the analysis, enabling independent system evaluation at each distinct frequency.}

Conversions

Given that logarithmic differences, when expressed in these units, frequently denote power ratios and root-power ratios, corresponding values for both are presented subsequently. Historically, the bel has served as the standard unit for logarithmic power ratio, whereas the neper is employed for logarithmic root-power (amplitude) ratio.

Illustrative Examples

• The calculation of the decibel ratio between 1 kW (equivalent to 1000 watts) and 1 W is performed as follows: L G = §2425§ log §3031§ ⁡<!-- ⁡ --> ( §4344§ 000 W §5758§ W ) dB = §7980§ dB {\displaystyle L_{G}=10\log _{10}\left({\frac {1\,000\,{\text{W}}}{1\,{\text{W}}}}\right)\,{\text{dB}}=30\,{\text{dB}}}
• The decibel ratio between √1000 V (approximately 31.62 V) and 1 V is calculated as follows: L G = §2425§ log §3031§ ⁡<!-- ⁡ --> ( 31.62 V §5354§ V ) dB = §7576§ dB {\displaystyle L_{G}=20\log _{10}\left({\frac {31.62\,{\text{V}}}{1\,{\text{V}}}}\right)\,{\text{dB}}=30\,{\text{dB}}}

This demonstrates that (31.62 V / 1 V)² approximates 1 kW / 1 W, thereby illustrating a key implication of the preceding definitions: the value of L_G remains constant at 30 dB, irrespective of whether it is derived from power ratios or amplitude ratios, assuming that within the system under consideration, power ratios are equivalent to the square of amplitude ratios.

• To determine the decibel ratio of 10 W to 1 mW (one milliwatt), the following formula is applied: $${\displaystyle L_{G}=10\log _{10}\left({\frac {10{\text{W}}}{0.001{\text{W}}}}\right)\,{\text{dB}}=40\,{\text{dB}}}$$
• The power ratio associated with a 3 dB alteration in level is expressed by the following equation: 28§ = 1.995 §3536§ … ≈ §4344§ {\displaystyle G=10^{\frac {3}{10}}\times 1=1.995\,26\ldots \approx 2}

A tenfold alteration in the power ratio corresponds to a 10 dB change in level. An approximate 3 dB change signifies a power ratio alteration by a factor of 2 or ⁠§45§/§89§⁠. While the precise change is ±3.0103 dB, technical literature almost universally rounds this to 3 dB. This relationship indicates that a voltage increase by a factor of √§1819§ ≈ 1.4142 is implied. Similarly, a doubling or halving of voltage, which correlates to a quadrupling or quartering of power, is typically expressed as 6 dB, rather than the more exact ±6.0206 dB.

When precision is paramount, the decibel value is presented with additional significant figures. For instance, 3.000 dB represents a power ratio of 10^3/10, or approximately 1.9953, which deviates from an exact factor of 2 by about 0.24%. Concurrently, this corresponds to a voltage ratio of 1.4125, differing from precisely √§1112§ by approximately 0.12%. Likewise, a 6.000 dB increase signifies a power ratio of §1415§6/10 ≈ 3.9811, which is approximately 0.5% divergent from an exact factor of 4.

Characteristics

The decibel proves advantageous for expressing extensive ratios and streamlining the depiction of multiplicative phenomena, such as signal attenuation originating from various sources within a transmission path. However, its utility is less straightforward in systems involving additive effects, for example, when calculating the cumulative sound pressure level of two concurrently operating machines. Furthermore, caution is warranted when decibels are directly incorporated into fractions or when considering the units involved in multiplicative operations.

Expressing Extensive Ratios

Due to its logarithmic scale, the decibel enables the concise representation of an exceptionally broad spectrum of ratios. For instance, stating "50 dB" is more efficient than articulating "the two powers exhibit a 100,000 to 1 ratio" or "one power is 10⁵ times the other." Decibels thus facilitate the expression of substantial quantitative variations using a minimal number of digits.

Depiction of Multiplicative Operations

Decibel level values permit addition as an alternative to multiplying the fundamental power values. This implies that the cumulative gain of a multi-component system, such as a cascade of amplifier stages, can be ascertained by summing the individual component gains in decibels, rather than multiplying their respective amplification factors. Mathematically, this is represented as log(A × B × C) = log(A) + log(B) + log(C). In practical terms, by understanding that 1 dB corresponds to an approximate 26% power gain, 3 dB to roughly a 2× power gain, and 10 dB to a 10× power gain, one can calculate a system's power ratio from its decibel gain using only basic addition and multiplication. Consider the following illustration:

• For instance, a system comprising three series-connected amplifiers, exhibiting gains of 10 dB, 8 dB, and 7 dB respectively, yields a cumulative gain of 25 dB. When decomposed into combinations of 10, 3, and 1 dB, this translates to: With an input power of 1 watt, the approximate output power is determined. A precise calculation reveals the output to be 1 W × 10^25/10 ≈ 316.2 W. The approximate value demonstrates a marginal error of only +0.4% compared to the actual value, a deviation considered negligible given the inherent precision of the provided figures and the typical accuracy of most measurement instruments.

Nevertheless, critics contend that the decibel introduces ambiguity, obfuscates logical reasoning, is more aligned with the historical era of slide rules than contemporary digital processing, and is generally unwieldy and challenging to interpret. Decibel quantities are not inherently additive, rendering them "of unacceptable form for use in dimensional analysis." Consequently, meticulous attention to units is crucial in decibel operations. Consider, for instance, the carrier-to-noise-density ratio C/N§45§ (expressed in hertz), which involves carrier power C (in watts) and noise power spectral density N§1011§ (in watts per hertz). When converted to decibels, this ratio becomes a subtraction: (C/N§1718§)_dB = C_dB − N_0 dB. Despite this, the linear-scale units still simplify within the implicit fraction, resulting in outcomes expressed in dB-Hz.

Depiction of Additive Operations

Mitschke asserts that a key benefit of employing a logarithmic scale, such as decibels, in a transmission chain is the simplification of calculating overall gain or attenuation. When numerous elements, each with its own gain or attenuation, are concatenated, summing their decibel values is considerably more practical than multiplying their individual factors. Conversely, despite this advantage, decibels present challenges in operations that are fundamentally additive, precisely because human cognition often favors addition over multiplication.

For instance, if two machines each generate a sound pressure level of 90 dB at a specific location, their combined operation would yield approximately 93 dB, not 180 dB. Similarly, consider a scenario where a machine's noise, including background contributions, measures 87 dBA, while the background noise alone is 83 dBA when the machine is off. The machine's isolated noise level can be determined by logarithmically 'subtracting' the 83 dBA background noise from the 87 dBA combined level, resulting in approximately 84.8 dBA. Furthermore, when calculating a representative sound level for a room from multiple measurements, the distinction between logarithmic and arithmetic averaging becomes apparent. For example, the logarithmic average of 70 dB and 90 dB is 87 dB, whereas the arithmetic average is 80 dB.

Operations such as addition on a logarithmic scale are termed logarithmic addition. This process involves converting values to a linear scale using exponentials, performing the addition, and then reverting to the logarithmic scale by taking logarithms. Consequently, while decibel operations involve logarithmic addition, subtraction, multiplication, or division, the corresponding operations on a linear scale are standard arithmetic procedures.

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

The logarithmic mean is derived from the logarithmic sum through the subtraction of ${\displaystyle 10\log _{10}2}$, a principle consistent with logarithmic division being equivalent to linear subtraction.

Fractional Representations

Attenuation constants, particularly in fields like optical fiber communication and radio propagation path loss, are frequently presented as a fraction or ratio relative to the transmission distance. For instance, dB/m denotes decibels per meter, while dB/mi signifies decibels per mile. These quantities must be processed in accordance with the principles of dimensional analysis; for example, a 100-meter transmission through a fiber with a 3.5 dB/km attenuation results in a loss of 0.35 dB = 3.5 dB/km × 0.1 km.

Applications

Perceptual Aspects

Human perception of sound and light intensity more closely aligns with a logarithmic function of intensity than with a linear relationship, as described by the Weber–Fechner law; consequently, the decibel (dB) scale serves as an effective metric.

Acoustic Applications

In acoustics, the decibel is routinely employed as a unit for sound power level or sound pressure level. The reference pressure for airborne sound is established at the typical threshold of human auditory perception, and various common comparisons are utilized to exemplify distinct sound pressure levels. Given that sound pressure constitutes a root-power quantity, the corresponding unit definition is applied as follows:

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

In this equation, p_rms denotes the root mean square value of the measured sound pressure, while p_ref represents the standard reference sound pressure, which is 20 micropascals in air or 1 micropascal in water.

The application of the decibel in underwater acoustics frequently results in ambiguity, primarily attributable to the variation in reference values.

Given that sound intensity is directly proportional to the square of sound pressure, the sound intensity level can alternatively be defined as:

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

The human auditory system possesses an extensive dynamic range for sound reception. The ratio between the sound intensity capable of inducing permanent damage during brief exposure and the faintest audible sound is at least 1 trillion (10¹²). Such broad measurement ranges are effectively represented using a logarithmic scale: the base-10 logarithm of 10¹² is 12, which translates to a sound intensity level of 120 dB re 1 pW/m§4^{5§. The reference values for I and p in air have been selected to ensure this corresponds approximately to a sound pressure level of 120 dB re 20 μPa.}

The original choice of the decibel over the bel as a logarithmic unit for intensity change stems from the fact that alterations in sound properties below the just-noticeable difference (JND) do not impact auditory perception. For human amplitude perception, the JND is approximately 1 dB.

Given the human ear's differential sensitivity across sound frequencies, the acoustic power spectrum undergoes modification through frequency weighting, with A-weighting representing the prevalent standard. This process yields a weighted acoustic power, which is subsequently converted into a sound or noise level expressed in decibels.

Telephony

The decibel finds application in both telephony and audio contexts. Analogous to its use in acoustics, frequency-weighted power is frequently employed. Specifically, for measuring audio noise in electrical circuits, these weightings are termed psophometric weightings.

Electronics

Within electronics, the decibel is frequently utilized to articulate power or amplitude ratios, particularly for gains, as an alternative to arithmetic ratios or percentages. A significant benefit is the ability to compute the cumulative decibel gain of cascaded components, such as amplifiers and attenuators, by merely summing the individual decibel gains. Correspondingly, in telecommunications, decibels quantify signal gain or loss from a transmitter to a receiver across various media (e.g., free space, waveguides, coaxial cables, fiber optics) through the application of a link budget.

The decibel unit can also be combined with a specified reference level, typically denoted by a suffix, to establish an absolute unit of electric power. For instance, dBW employs a 1 W reference, whereas dBm utilizes a 1 mW reference, with m abbreviating milliwatt. Consequently, a power level of 0 dBm signifies one milliwatt, and 1 dBm represents an increase of one decibel, equating to approximately 1.259 mW.

Within professional audio specifications, the dBu is a widely adopted unit. It is defined relative to the root mean square voltage that delivers 1 mW (equivalent to 0 dBm) into a 600-ohm resistor, which calculates to approximately √1 mW × 600 Ω ≈ 0.775 V_RMS. When applied within a 600-ohm circuit, which historically served as the standard reference impedance in telephone systems, dBu and dBm are numerically identical.

Optics

For an optical link, if a specified optical power, expressed in dBm (referenced to 1 mW), is injected into a fiber, and the decibel losses of each constituent component (such as connectors, splices, and fiber segments) are known, the total link loss can be efficiently determined through the addition and subtraction of these decibel values.

In the fields of spectrometry and optics, the blocking unit, employed for measuring optical density, is equivalent to −1 B.

Video and Digital Imaging

In the context of video and digital image sensors, decibels typically denote ratios of video voltages or digitized light intensities, calculated using 20 log of the ratio. This convention applies even when the represented intensity (optical power) exhibits a direct proportionality to the voltage generated by the sensor, rather than its square, as exemplified by CCD imagers where voltage response is linear with intensity. Consequently, a camera's signal-to-noise ratio or dynamic range specified as 40 dB indicates a 100:1 ratio between optical signal intensity and optical-equivalent dark-noise intensity, rather than the 10,000:1 intensity (power) ratio that 40 dB might otherwise imply. Occasionally, the 20 log ratio definition is directly applied to electron or photon counts, which are inherently proportional to sensor signal amplitude, thereby obviating the need to assess the linearity of voltage response to intensity.

Nevertheless, as previously noted, the 10 log intensity convention is more broadly adopted in physical optics, including fiber optics, which can lead to terminological ambiguity between the conventions of digital photographic technology and physics. Typically, metrics such as dynamic range or signal-to-noise for cameras are expressed in 20 log dB. However, in related applications (e.g., attenuation, gain, intensifier SNR, or rejection ratio), the term necessitates careful interpretation, as conflating the two unit definitions can lead to substantial misinterpretations of the reported values.

Photographers commonly employ a base-2 logarithmic unit, known as the 'stop,' to characterize light intensity ratios or dynamic range.

Suffixes and Reference Values

Suffixes are frequently appended to the fundamental dB unit to specify the reference value against which the ratio is computed. For instance, dBm denotes a power measurement relative to 1 milliwatt.

When the reference unit's value is explicitly specified, the decibel measurement is termed "absolute." Conversely, if the reference unit's value is not explicitly stated, such as in the context of an amplifier's dB gain, the decibel measurement is classified as relative.

The practice of appending suffixes to decibel (dB) values is prevalent, despite contravening the guidelines established by standardization organizations such as ISO and IEC. These bodies deem the "unacceptability of attaching information to units" and the "unacceptability of mixing information with units" as critical issues. The IEC 60027-3 standard, for instance, prescribes an alternative format: L_x (re x_ref) or L_x/xref, where x denotes the quantity symbol and x_ref represents the reference quantity's value. For example, the electric field strength E relative to a 1 μV/m reference value can be expressed as L_E (re 1 μV/m) = 20 dB or L_{E/(1 μV/m)} = 20 dB. When the measurement result of 20 dB is presented independently, additional contextual information can be provided in parentheses, which then functions as part of the surrounding text rather than being integrated into the unit itself, for example: 20 dB (re 1 μV/m) or 20 dB (1 μV/m).

Beyond documentation strictly adhering to SI units, this practice is widely observed, as demonstrated by numerous instances. No universal standard governs these suffixes; instead, diverse discipline-specific conventions prevail. Suffixes may represent unit symbols (e.g., "W", "K", "m"), transliterations of unit symbols (e.g., "uV" for microvolt instead of μV), or acronyms for unit names (e.g., "sm" for square meter, "m" for milliwatt). Alternatively, they can serve as mnemonics indicating the type of quantity being computed (e.g., "i" for antenna gain relative to an isotropic antenna, "λ" for values normalized by the electromagnetic wavelength), or as general attributes or identifiers characterizing the quantity's nature (e.g., "A" for A-weighted sound pressure level). The suffix is frequently linked by a hyphen (e.g., "dB‑Hz"), a space (e.g., "dB HL"), enclosed in parentheses (e.g., "dB(HL)"), or directly appended without any intervening character (e.g., "dBm", a form that does not comply with international standards).

Suffix Nomenclature

Voltage Measurements

Given that the decibel is fundamentally defined in relation to power rather than amplitude, converting voltage ratios into decibels necessitates either squaring the amplitude or employing a multiplication factor of 20 instead of 10, as previously elaborated.

dBV (Decibel-Volt)

dB(V_RMS) denotes voltage measured relative to 1 volt, irrespective of impedance. This metric is applied in assessing microphone sensitivity and in defining the consumer line-level standard of −10 dBV. This lower standard helps mitigate manufacturing expenses compared to devices that utilize the higher +4 dBu line-level standard.

dBu or dBv (Decibel-Unloaded or Decibel-Voltage)

The 0 dBu standard is defined as the RMS voltage required to dissipate 0 dBm (equivalent to 1 mW) into a 600 Ω load. According to Ohm's law, this voltage is calculated as follows: $${\displaystyle {\sqrt {{\text{resistance}}\cdot {\text{power}}}}={\sqrt {600\ {\mathsf {\Omega }}\ \cdot \ 0.001\ {\mathsf {W}}\;}}={\sqrt {0.6}}\ {\mathsf {V_{RMS}}}\approx 0.7746\ {\mathsf {V_{RMS}}}\,.}$$Consequently, a 1 V_RMS signal corresponds to: §126127§ ⋅<!-- ⋅ --> log §135136§ ⁡<!-- ⁡ --> ( §148149§   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}}}~.} The designation was initially dBv but was subsequently changed to dBu to prevent ambiguity with dBV. Rupert Neve stated that the u originated from the volume unit displayed on a VU meter, although it has also been interpreted as signifying unloaded.

In professional audio contexts, equipment is often calibrated to register "0" on VU meters after a specific duration following the application of a signal with an amplitude of +4 dBu. In contrast, consumer-grade equipment typically operates at a lower nominal signal level of −10 dBV. Consequently, many devices incorporate dual voltage operation, featuring distinct gain or "trim" settings to ensure compatibility across different standards. It is common for professional equipment to include a switch or adjustment mechanism that accommodates at least the range between +4 dBu and −10 dBV.

dBmV

dBmV represents the root mean square (RMS) voltage relative to 1 millivolt across a 75 Ω impedance, denoted as dB(mV_RMS). This unit is extensively employed in cable television networks, where the typical strength of a single television signal at receiver terminals is approximately 0 dB_mV. Given that cable television systems utilize 75 Ω coaxial cable, a value of 0 dB_mV is equivalent to −78.75 dBW, −48.75 dBm, or approximately 13 nW.

dBmV0s

This unit is formally defined by Recommendation ITU-R V.574.

dBμV or dBuV

dB(μV_RMS) denotes voltage measured relative to 1 microvolt. It is commonly applied in specifications for television and aerial amplifiers. Notably, 60 dBμV is equivalent to 0 dBmV.

Acoustics

Within acoustics, the most prevalent application of "decibels" for sound level measurement is dB_SPL, which signifies sound pressure level referenced to the nominal threshold of human hearing. Measurements involving pressure, a root-power quantity, employ a factor of 20, whereas power measurements, such as dBSIL and dBSWL, utilize a factor of 10.

dBSPL

dBSPL, or sound pressure level, is defined for sound in air and other gases relative to 20 micropascals (μPa), which is equivalent to 2×10⁻⁵ Pa. A 0 dBSPL level approximates the quietest sound perceptible by humans. For sound in water and other liquids, the reference pressure is 1 μPa. An RMS sound pressure of one pascal corresponds to a level of 94 dB SPL.

dBSIL

dBSIL denotes the sound intensity level, referenced to 10⁻¹² W/m², which approximates the threshold of human hearing in an aerial environment.

dBSWL

dBSWL signifies the sound power level, referenced to 10⁻¹² W.

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

These symbols frequently indicate the application of distinct weighting filters designed to approximate the human ear's response to sound, even though the underlying measurement remains in dB (SPL). Such measurements typically pertain to noise and its impact on humans and other animal species, finding extensive use in industrial contexts for discussions concerning noise control, regulatory compliance, and environmental standards. Alternative notations include dBA or dB(A). According to standards established by the International Electro-technical Committee (IEC 61672-2013) and the American National Standards Institute (ANSI S1.4), the recommended format is to express the measurement as L_A = x dB. Despite this, dB(A) units persist as a common shorthand for A‑weighted measurements. For comparison, dBc is utilized in telecommunications.

dBHL

dB hearing level (dBHL) is employed in audiograms to quantify hearing loss. The reference level for dBHL is frequency-dependent, adhering to a minimum audibility curve specified by ANSI and other relevant standards. This methodology ensures that the audiogram effectively illustrates deviations from what is considered 'normal' hearing.

dBQ

dBQ is occasionally utilized to signify a weighted noise level, typically incorporating the ITU-R 468 noise weighting standard.

dBpp

dBpp refers to a measurement relative to the peak-to-peak sound pressure.

dB(G)

dB(G) refers to the G‑weighted spectrum.

Audio electronics

dBm

dBm

dBm, also known as dBmW, represents power relative to 1 milliwatt. In audio and telephony applications, dBm is conventionally referenced to a 600 Ω impedance, which equates to a voltage level of 0.775 volts or 775 millivolts.

dBm0

dBm0 denotes power expressed in dBm, as previously described, measured at a zero transmission level point.

dBFS

dBFS, or dB(full scale), quantifies the amplitude of a signal in comparison to the maximum level a device can process without clipping. The full-scale reference can be defined either as the power level of a full-scale sinusoid or, alternatively, a full-scale square wave. Consequently, a signal measured against a full-scale sine wave appears 3 dB weaker when referenced to a full-scale square wave, leading to the equivalence: 0 dBFS (full-scale sine wave) = −3 dBFS (full-scale square wave).

dBVU

dBVU refers to the dB volume unit.

dBTP

dBTP, or dB(true peak), represents the peak amplitude of a signal relative to the maximum level a device can accommodate prior to clipping. Within digital systems, 0 dBTP corresponds to the highest numerical level representable by the processor. Measured values are consistently negative or zero, as they do not exceed the full-scale limit.

Radar

dBZ

dBZ denotes decibels relative to Z = 1 mm⁶⋅m⁻³, representing the energy of reflectivity in weather radar. This metric is correlated with the proportion of transmitted power that is returned to the radar receiver. Values exceeding 20 dBZ typically signify the presence of falling precipitation.

dBsm

dB(m²) – Decibels relative to one square meter: This metric quantifies the radar cross-section (RCS) of a target. The magnitude of power reflected from a target is directly proportional to its RCS. Stealth aircraft and insects typically exhibit negative RCS values when measured in dBsm, whereas large, flat plates or conventional aircraft demonstrate positive values.

Radio Power, Energy, and Field Strength Metrics

dBc

Denotes a value relative to the carrier signal. Within telecommunications, this metric expresses the relative magnitudes of noise or sideband power in comparison to the carrier power. It is distinct from dB(C), which is employed in acoustic measurements.

dBpp

Represents a value relative to the maximum peak power.

dBJ

Quantifies energy relative to one joule. Given that one joule equals one watt-second, which is also equivalent to one watt per hertz, power spectral density can consequently be expressed using dBJ.

dBmJ

Quantifies energy relative to one millijoule, or equivalently, one milliwatt per hertz.

dBm

dB(mW) – Represents power relative to one milliwatt. Typically referenced to a 50 Ω load impedance, where 0 dBm equates to 0.224 volts. Notably, 0 dBm is equivalent to -30 dBW.

dBm/Hz

dB(mW/Hz) - Expresses power spectral density relative to one milliwatt per hertz, which is equivalent to dBmJ.

dBμV/m, dBuV/m, or dBμ

dB(μV/m) – Quantifies electric field strength relative to one microvolt per meter. This metric is related to power flux density via the impedance of free space (η₀ = 376.73 Ω). Consequently, 0 dB μV/m corresponds to (1 μV/m)²/η§4_{5§, which calculates to 2.65x10^-15 W/m§8^{9§, equivalent to -145.76 dBW/m§1011§ or -115.76 dBm/m§1213§.}}

dBf

dB(fW) – Represents power relative to one femtowatt.

dBW

dB(W) – Quantifies power relative to one watt. One dBW is equivalent to +30 dBm.

dBW/Hz

dB(W/Hz) - Expresses power spectral density relative to one watt per hertz, which is equivalent to dBJ.

dBW/m²

dB(W/m²) - Quantifies the power flux density of electromagnetic radiation relative to one watt per square meter.

dBk

dB(kW) – Represents power relative to one kilowatt. Notably, 0 dBk equals +30 dBW, which is also +60 dBm. This unit should not be confused with dBK, which denotes temperature relative to one Kelvin.

dBe

Denotes decibels in electrical terms.

dBo

Denotes decibels in optical terms. In a thermal noise-limited system, a one dBo alteration in optical power can induce up to a two dBe change in electrical signal power.

Antenna Measurement Metrics

dBi

dB(isotropic) – Represents the gain of an antenna relative to the gain of a theoretical isotropic antenna, which ideally radiates energy uniformly across all directions. Linear polarization of the electromagnetic (EM) field is presumed unless explicitly stated otherwise.

dBd

dB(dipole) – Quantifies the gain of an antenna relative to the gain of a half-wave dipole antenna. It is established that 0 dBd is equivalent to 2.15 dBi.

dBiC

dB(isotropic circular) – Expresses the gain of an antenna relative to the gain of a theoretical circularly polarized isotropic antenna. A definitive conversion rule between dBiC and dBi does not exist, as this relationship is contingent upon the characteristics of the receiving antenna and the field's polarization.

dBq

dB(quarterwave) – Represents the gain of an antenna relative to the gain of a quarter-wavelength whip antenna. This unit is infrequently employed, primarily appearing in certain marketing contexts; specifically, 0 dBq is equivalent to −0.85 dBi.

dBsm

dB(m²) – Decibels relative to one square meter: This metric quantifies the effective signal capture area of an antenna.

dBm⁻¹

dB(m⁻¹) – Decibels relative to the reciprocal of a meter: This unit serves as a measure of the antenna factor.

Miscellaneous Measurement Units

dBHz

dB(Hz) – Expresses bandwidth relative to one hertz; for instance, 20 dBHz signifies a bandwidth of 100 Hz. This unit is frequently utilized in link budget calculations and also appears in the context of carrier-to-noise-density ratio, which should not be confused with the carrier-to-noise ratio (expressed in dB).

dBov or dBO

dB(overload) quantifies the amplitude of a signal, typically audio, relative to the maximum level a device can process without experiencing clipping. This metric is analogous to dB FS but is also applicable to analog systems. According to ITU-T Recommendation G.100.1, the dB ov level for a digital system is defined by the following equation: $${\displaystyle L_{\mathsf {ov}}=10\log _{10}\left({\frac {P}{\ P_{\mathsf {max}}\ }}\right)\ [{\mathsf {dB_{ov}}}],}$$ where the maximum signal power ${\displaystyle P_{\mathsf {max}}=1.0}$ is established for a rectangular signal possessing the maximum amplitude ${\displaystyle x_{\mathsf {over}}}$. Consequently, the level of a tone with a digital amplitude (peak value) of ${\displaystyle x_{\mathsf {over}}}$ is determined to be ${\displaystyle L_{\mathsf {ov}}=-3.01\ {\mathsf {dB_{ov}}}}$.

dBr

dB(relative) denotes a relative difference from a specified reference, which is typically inferred from the context. An example includes the deviation of a filter's response from its nominal operational levels.

dBrn

Decibels above reference noise.

dBrnC

dB(rnC) signifies an audio level measurement, commonly within a telephone circuit, referenced to a −90 dBm level. This measurement is frequency-weighted using a standard C-message weighting filter. While the C-message weighting filter was predominantly employed in North America, the psophometric filter serves a similar function in international telecommunication circuits.

dBK

dB(K) refers to decibels relative to 1 Kelvin, a unit utilized for expressing noise temperature.

dBK⁻¹ or dB/K

dB(K⁻¹) denotes decibels referenced to 1 K⁻¹, specifically not decibels per kelvin. This unit is employed in satellite communications to quantify the ⁠ G / T ⁠ (G/T) factor, which serves as a figure of merit correlating antenna gain G with the receiver system's equivalent noise temperature T.

Alphabetical Listing of Suffixes

Unpunctuated Suffix Notations

dBA

dBa

dBa

dBB

dBB

dBc

dBc

This designation signifies a measurement relative to the carrier signal. In telecommunications, dBc quantifies the relative power levels of noise or sidebands in comparison to the carrier power.

dBC

dBD

dBD

dBd

dBd

dB(dipole) represents the forward gain of an antenna, expressed relative to a half-wave dipole antenna. A value of 0 dBd is equivalent to 2.15 dBi.

dBe

Denotes decibels referenced to an electrical quantity.

dBf

dB(fW) indicates power measured relative to 1 femtowatt.

dBFS

dB(full scale) quantifies the amplitude of a signal in relation to the maximum level a device can process without incurring clipping. The full-scale reference can be established either by the power level of a full-scale sinusoid or, alternatively, by a full-scale square wave. Consequently, a signal referenced to a full-scale sine wave will register 3 dB lower when referenced to a full-scale square wave; hence, 0 dBFS (full-scale sine wave) equals −3 dBFS (full-scale square wave).

dBG

Refers to a G-weighted frequency spectrum.

dBi

dB(isotropic) represents the forward gain of an antenna, measured against a hypothetical isotropic antenna that radiates energy uniformly across all directions. Unless explicitly stated otherwise, linear polarization of the electromagnetic field is presumed.

dBiC

dB(isotropic circular) denotes the forward gain of an antenna, relative to a circularly polarized isotropic antenna. A direct, fixed conversion rule between dBiC and dBi does not exist, as this relationship is contingent upon the characteristics of the receiving antenna and the polarization of the electromagnetic field.

dBJ

This unit expresses energy relative to 1 joule. Given that 1 joule is equivalent to 1 watt-second or 1 watt per hertz, power spectral density can consequently be quantified in dBJ.

dBk

dB(kW) signifies power measured relative to 1 kilowatt.

dBK

dB(K) denotes decibels relative to kelvin, primarily utilized for expressing noise temperature.

dBm

dB(mW) indicates power measured relative to 1 milliwatt.

dBm² or dBsm

dB(m²) represents decibels relative to one square meter.

dBm0

This refers to power, expressed in dBm, measured at a zero transmission level point.

dBm0s

This term is defined by Recommendation ITU-R V.574.

dBmV

dB(mV_RMS) quantifies voltage relative to 1 millivolt across a 75 Ω impedance.

dBo

Denotes decibels referenced to an optical quantity. In a thermal noise-limited system, a 1 dBo alteration in optical power can induce an electrical signal power change of up to 2 dBe.

dBO

dBov or dBO

dBov or dBO

dB(overload) expresses the amplitude of a signal, typically an audio signal, relative to the maximum level a device can accommodate prior to the onset of clipping.

dBpp

Indicates a measurement relative to the peak-to-peak sound pressure.

dBpp

Denotes a measurement relative to the maximum value of the peak electrical power.

dBq

dB(quarterwave) quantifies the forward gain of an antenna in comparison to a quarter-wavelength whip antenna. This unit is infrequently employed, primarily appearing in certain marketing contexts. A value of 0 dBq is equivalent to −0.85 dBi.

dBr

dB(relative) signifies a relative difference from a specified reference, which is typically established by the context. An illustrative application is the quantification of a filter's response deviation from nominal operational levels.

dBrn

Represents decibels above a reference noise level.

dBrnC

This term denotes an audio level measurement, commonly applied within a telephone circuit, relative to the inherent circuit noise level. The measurement of this level is frequency-weighted by a standard C-message weighting filter, a filter predominantly utilized in North America.

dBsm

dBTP

dBTP

dB(true peak) quantifies the peak amplitude of a signal in relation to the maximum level a device can process without incurring clipping.

dBu or dBv

The calculation for RMS voltage relative to ${\displaystyle \ {\sqrt {0.6\ }}\ {\mathsf {V}}\ \approx 0.7746\ {\mathsf {V}}\ \approx -2.218\ {\mathsf {dB_{V}}}~.}$

dBu0s

This term is formally defined by Recommendation ITU-R V.574.

dBuV

dBuV/m

dBuV/m

dBv

dBv

dBV

dBV

This denotes dB(V_RMS), representing voltage measured relative to 1 volt, irrespective of impedance.

dBVU

dB(VU) signifies the decibel volume unit.

dBW

This refers to dB(W), indicating power measured relative to 1 watt.

dB W·m⁻²·Hz⁻¹

This represents spectral density, expressed relative to 1 W·m⁻²·Hz⁻¹.

dBZ

This denotes dB(Z), a decibel value relative to Z = 1 mm⁶⋅m⁻³.

dBμ

dBμV or dBuV

dBμV or dBuV

This refers to dB(μV_RMS), representing voltage measured relative to 1 root mean square microvolt.

dBμV/m, dBuV/m, or dBμ

This denotes dB(μV/m), which quantifies electric field strength relative to 1 microvolt per meter.

Suffixes preceded by a space

dB HL

Decibel hearing level (dB HL) is employed in audiograms to quantify hearing loss.

dB Q

This designation is occasionally utilized to indicate a weighted noise level.

dB SIL

This refers to dB sound intensity level (dB SIL), which is measured relative to 10⁻¹² W/m².

dB SPL

dB SPL, or sound pressure level, is applied to sound in air and other gases, with measurements relative to 20 μPa in air or 1 μPa in water.

dB SWL

This denotes dB sound power level (dB SWL), measured relative to 10⁻¹² W.

Suffixes within parentheses

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

These symbols frequently indicate the application of distinct weighting filters, which are designed to approximate the human ear's auditory response, even though the underlying measurement remains in dB (SPL). Such measurements typically pertain to noise and its impact on humans and other animal species, finding extensive application in industrial contexts for discussions concerning noise control, regulatory compliance, and environmental standards. Alternative notations include dB_A or dBA.

Other suffixes

dBHz or dB-Hz

This represents dB(Hz), signifying bandwidth measured relative to one hertz.

dBHz² or dB/s²

This denotes dB(Hz²), which quantifies the squared magnitude of an impulse response (or its envelope) relative to the squared magnitude of an impulse response possessing unity amplitude.

dBK⁻¹ or dB/K

This refers to dB(K⁻¹), indicating decibels measured relative to the reciprocal of kelvin.

dBm⁻¹

This denotes dB(m⁻¹), a decibel value relative to the reciprocal of a meter, serving as a measure of the antenna factor.

mBm

This refers to mB(mW), which represents power measured relative to 1 milliwatt, expressed in millibels (one hundredth of a decibel). Notably, 100 mBm is equivalent to 1 dBm. This unit is incorporated within the Wi-Fi drivers of the Linux kernel and relevant regulatory domain specifications.

Notes

• Tuffentsammer, Karl (1956). "Das Dezilog, eine Brücke zwischen Logarithmen, Dezibel, Neper und Normzahlen" [The Decilog: A Bridge Between Logarithms, Decibels, Nepers, and Preferred Numbers]. VDI-Zeitschrift (in German). 98: 267–274.Paulin, Eugen (1 September 2007). Logarithmen, Normzahlen, Dezibel, Neper, Phon - natürlich verwandt! [Logarithms, Preferred Numbers, Decibels, Nepers, Phons – Naturally Related!] (PDF) (in German). Archived (PDF) from the original on 18 December 2016. Retrieved 18 December 2016.
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