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The decibel (dB) is a logarithmic unit of measurement that expresses the magnitude of a physical quantity (usually power

Power (physics)

In physics, power is the rate at which work is performed or energy is converted. It is an energy per unit of time. As a rate of change of work done or the energy of a subsystem, power iswhere P is power, W is work and t is time....

or intensity

Intensity (physics)

In physics, intensity is a measure of the time-averaged energy flux. The word "intensity" here is not synonymous with "strength", "amplitude", or "level", as it sometimes is in colloquial speech...

) relative to a specified or implied reference level. Since it expresses a ratio of two quantities with the same unit, it is a dimensionless unit. A decibel is one tenth of a bel, a seldom-used unit.

The decibel is useful for a wide variety of measurements in science and engineering

Engineering

Engineering is the discipline, art and profession of acquiring and applying technical, scientific and mathematical knowledge to design and implement materials, structures, machines, devices, systems, and processes that safely realize a desired objective or inventions.The American Engineers' Council...

(particularly acoustics

Acoustics

Acoustics is the interdisciplinary science that deals with the study of sound, ultrasound and infrasound . A scientist who works in the field of acoustics is an acoustician. The application of acoustics in technology is called acoustical engineering...

, electronics

Electronics

Electronics is a branch of science and technology that deals with the controlled flow of electrons. The ability to control electron flow is usually applied to information handling or device control. Electronics is distinct from electrical science and technology, which deals with the generation,...

, and control theory

Control theory

Control theory is an interdisciplinary branch of engineering and mathematics, that deals with the behavior of dynamical systems. The desired output of a system is called the reference...

) and other disciplines. It confers a number of advantages, such as the ability to conveniently represent very large or small numbers, a logarithmic scaling that roughly corresponds to the human perception of sound and light, and the ability to carry out multiplication of ratios by simple addition and subtraction.

The decibel symbol is often qualified with a suffix, which indicates which reference quantity or frequency weighting function

A-weighting

A Weighting curve is a graph of a set of factors, that are used to 'weight' measured values of a variable according to their importance in relation to some outcome. The most commonly known example is frequency weighting in sound level measurement where a specific set of weighting curves known as A,...

has been used. For example, "dBm" indicates that the reference quantity is one milliwatt, while "dBu" is referenced to 0.775 volts RMS

Root mean square

In mathematics, the root mean square , also known as the quadratic mean, is a statistical measure of the magnitude of a varying quantity. It is especially useful when variates are positive and negative, e.g., sinusoids....

.

The definitions of the decibel and bel use base-10 logarithms. For a similar unit using natural logarithms to base e

E (mathematical constant)

The mathematical constant e is the unique real number such that the value of the derivative of the function f = e^x at the point x = 0 is exactly 1. The function e^x so defined is called the exponential function, and its inverse is the natural logarithm, or logarithm...

, see neper

Neper

A neper is a logarithmic unit of ratio. It is not an SI unit but is accepted for use alongside the SI. It is used to express ratios, such as gain and loss, and relative values...

History

The decibel originates from methods used to quantify reductions in audio levels in telephone circuits. These losses were originally measured in units of Miles of Standard Cable (MSC), where 1 MSC corresponded to the loss of power over a 1 mile

Mile

A mile is a unit of length in a number of different systems. In contemporary English, mile most commonly refers to the statute mile of 1,609.344 meters or the nautical mile of 1,852 meters...

(approximately 1.6 km) length of standard telephone

Telephone

The telephone is a telecommunications device that transmits and receives sound, most commonly the human voice. It is one of the most common household appliances in the developed world, and has long been considered indispensable to business, industry and government...

cable at a frequency of 5000 radians per second (795.8 Hz) and roughly matched the smallest attenuation detectable to an average listener. Standard telephone cable was defined as "a cable having uniformly distributed resistances of 88 ohms per loop mile and uniformly distributed shunt

Shunt

Shunt may refer to:* Shunt - a hole or passage allowing fluid to move from one part of the body to another* Shunt - a device allowing electrical current to pass around a point in a circuit...

capacitance

Capacitance

In electromagnetism and electronics, capacitance is the ability of a body to hold an electrical charge.Capacitance is also a measure of the amount of electric charge stored for a given electric potential. A common form of charge storage device is a parallel-plate capacitor...

of .054 microfarad per mile" (approximately 19 gauge).

The transmission unit or TU was devised by engineers of the Bell Telephone Laboratories

Bell Labs

Bell Laboratories is the research and development organization of Alcatel-Lucent and previously of the American Telephone & Telegraph Company .Bell Laboratories has had its headquarters at Murray Hill, New Jersey, and it has research and development facilities...

in the 1920s to replace the MSC. 1 TU was defined as the ten times the base-10 logarithm of the ratio of measured power to reference power. The definitions were conveniently chosen such that 1 TU approximately equalled 1 MSC (specifically, 1.056 TU = 1 MSC). Eventually, international standards bodies adopted the base-10 logarithm of the power ratio as a standard unit, which was named the "bel" in honor of the Bell System

Bell System

The Bell System was the AT&T monopoly that provided telephone service in the United States from 1877 to 1984 when it was broken up into separate companies by a Federal mandate....

's founder and telecommunications pioneer Alexander Graham Bell

Alexander Graham Bell

Alexander Graham Bell was an eminent scientist, inventor, engineer and innovator who is credited with inventing the first practical telephone....

. The bel was a factor of ten larger than the TU, such that 1 TU equalled 1 decibel. In many situations, the bel proved inconveniently large, so the decibel has become more common.

In April 2003, the International Committee for Weights and Measures

International Committee for Weights and Measures

The International Committee for Weights and Measures is the English name of the Comité international des poids et mesures . It consists of eighteen persons from Member States of the Metre Convention...

(CIPM) considered a recommendation for the decibel's inclusion in the SI system, but decided not to adopt the decibel as an SI unit. However, the decibel is recognized by other international bodies such as the International Electrotechnical Commission

International Electrotechnical Commission

The International Electrotechnical Commission is a not-for-profit, non-governmental international standards organization that prepares and publishes International Standards for all electrical, electronic and related technologies – collectively known as "electrotechnology"...

(IEC). The IEC permits the use of the decibel with field quantities as well as power and this recommendation is followed by many national standards bodies, such as NIST, which justifies the use of the decibel for voltage ratios.

Power

When referring to measurements of power
Power (physics)
In physics, power is the rate at which work is performed or energy is converted. It is an energy per unit of time. As a rate of change of work done or the energy of a subsystem, power iswhere P is power, W is work and t is time....

or intensity, a ratio can be expressed in decibels by evaluating ten times the base-10 logarithm

Logarithm

In mathematics, the logarithm of a number to a given base is the power or exponent to which the base must be raised in order to produce the number....

of the ratio of the measured quantity to the reference level. Thus, if L represents the ratio of a power value P₁ to another power value P₀, then L_dB represents that ratio expressed in decibels and is calculated using the formula:
Naturally, P₁ and P₀ must have the same dimension

Dimension

In mathematics and physics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify each point within it. Thus a line has a dimension of one because only one coordinate is needed to specify a point on it...

(that is, must measure the same type of quantity), and must as necessary, be converted to the same units before calculating the ratio of their numerical values: however, the choice of scale for this common unit is irrelevant, as it changes both quantities by the same factor, and thus cancels in the ratio (the ratio of two quantities is scale-invariant). Note that if P₁ = P₀ in the above equation, then L_dB = 0. If P₁ is greater than P₀ then L_dB is positive; if P₁ is less than P₀ then L_dB is negative.

Rearranging the above equation gives the following formula for P₁ in terms of P₀ and L_dB:.

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

Amplitude, voltage and current

When referring to measurements of amplitude
Amplitude
Amplitude is the magnitude of change in the oscillating variable, with each oscillation, within an oscillating system. For instance, sound waves are oscillations in atmospheric pressure and their amplitudes are proportional to the change in pressure during one oscillation...

it is usual to consider the ratio of the squares of A₁ (measured amplitude) and A₀ (reference amplitude). This is because in most applications power is proportional to the square of amplitude, and it is desirable for the two decibel formulations to give the same result in such typical cases. Thus the following definition is used:
This formula is sometimes called the 20 log rule, and similarly the formula for ratios of powers is the 10 log rule, and similarly for other factors. The factor of 20 is explained as: 10 is because it is in decibels (10ths of bels), and 2 is because it is a ratio of powers (squares of amplitudes): the product is 20. Thus provided that power ratios equal amplitude ratios squared, the two definitions -- 10-log and 20-log rules -- yield the same result in decibels ; bear in mind though, that in some usages the equivalence condition is not fulfilled and the equivalence does not hold as in, e.g., dBu and dBV. Note also that no constant factor is needed for the power (one can take power ratio to be the square of the amplitude ratio, whatever the units), since any constant cancels in the ratio.

The formula may be rearranged to give

Similarly, in electrical circuits

Electronic circuit

An electronic circuit is a closed path or paths formed by the interconnection of electronic components through which an electric current can flow....

, dissipated power is typically proportional to the square of voltage

Voltage

Voltage is commonly used as a short name for electrical potential difference. Its corresponding SI unit is the volt...

or current

Electric current

Electric current can mean, depending on the context, a flow of electric charge or the rate of flow of electric charge ....

when the impedance

Electrical impedance

Electrical impedance, or simply impedance, describes a measure of opposition to a sinusoidal alternating current . Electrical impedance extends the concept of resistance to AC circuits, describing not only the relative amplitudes of the voltage and current, but also the relative phases...

is held constant. Taking voltage as an example, this leads to the equation:

where V₁ is the voltage being measured, V₀ is a specified reference voltage, and G_dB is the power gain expressed in decibels. A similar formula holds for current.

Examples

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

To calculate the ratio of 1 kW (one kilowatt, or 1000 watts) to 1 W in decibels, use the formula

To calculate the ratio of to in decibels, use the formula

Notice that , illustrating the consequence from the definitions above that has the same value, , regardless of whether it is obtained with the 10-log or 20-log rules; provided that in the specific system being considered power ratios are equal to amplitude ratios squared.

To calculate the ratio of 1 mW (one milliwatt) to 10 W in decibels, use the formula

To find the power ratio corresponding to a 3 dB change in level, use the formula

An example illustrating the subtleties of the 20-log vs. 10-log rules is given by the so-called polarization ellipticity, the minor-to-major-axis ratio of the polarization ellipse. It is an amplitude ratio, thus when reported in decibels, it follows the 20-log rule, . A reader unfamiliar with the applicability of each 20- and 10-log rules might find inconsistent, arguing that it redefines the original as a power ratio rather than an amplitude ratio. The crux is that the subscript dB might imply either of two different mathematical operations, thus it can only be interpreted unambiguously given additional information about the nature of the quantity being reported (power ratio or amplitude ratio).

A change in power ratio by a factor of 10 is a 10 dB change. A change in power ratio by a factor of two is approximately a 3 dB change. (More precisely, the factor is 10^3/10, or 1.9953, about 0.24% different from exactly 2.) Similarly, an increase of 3 dB implies an increase in voltage by a factor of approximately √2, or about 1.41, an increase of 6 dB corresponds to approximately four times the power and twice the voltage, and so on. (In exact terms the power ratio is 10^6/10, or about 3.9811, a relative error of about 0.5%.)

Merits

The use of the decibel has a number of merits:

The decibel's logarithm
Logarithm
In mathematics, the logarithm of a number to a given base is the power or exponent to which the base must be raised in order to produce the number....

ic nature means that a very large range of ratios can be represented by a convenient number, in a similar manner to scientific notation
Scientific notation
Scientific notation, also known as standard form or as exponential notation, is a way of writing numbers that accommodates values too large or small to be conveniently written in standard decimal notation...

. This allows one to clearly visualize huge changes of some quantity. (See Bode Plot
Bode plot
A Bode plot is a graph of the logarithm of the transfer function of a linear, time-invariant system versus frequency, plotted with a log-frequency axis, to show the system's frequency response...

and half logarithm graph.)
The mathematical properties of logarithms mean that the overall decibel gain of a multi-component system (such as consecutive amplifiers) can be calculated simply by summing the decibel gains of the individual components, rather than needing to multiply amplification factors. Essentially this is because log(A × B × C × ...) = log(A) + log(B) + log(C) + ...
The human perception of, for example, sound or light, is, roughly speaking, such that a doubling of actual intensity causes perceived intensity to always increase by the same amount, irrespective of the original level. The decibel's logarithmic scale
Logarithmic scale
A logarithmic scale is a scale of measurement that uses the logarithm of a physical quantity instead of the quantity itself.A simple example is when equally-spaced divisions on the vertical axis of a chart are labelled 1, 10, 100, 1000, instead of 1, 2, 3, 4.Presentation of data on a logarithmic...

, in which a doubling of power or intensity always causes an increase of approximately 3 dB, corresponds to this perception.

Acoustics

The decibel is commonly used in acoustics

Acoustics

to quantify sound

Sound

Sound is a travelling wave which is an oscillation of pressure transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a level sufficiently strong to be heard, or the sensation stimulated in organs of hearing by such vibrations.- Perception of sound...

levels relative to some 0 dB reference. The reference level is typically set at the threshold of perception of an average human and there are common comparisons used to illustrate different levels of sound pressure. As with other decibel figures, normally the ratio expressed is a power ratio (rather than a pressure ratio).

A reason for using the decibel is that the ear is capable of detecting a very large range of sound pressure

Sound pressure

Sound pressure is the local pressure deviation from the ambient pressure caused by a sound wave. Sound pressure can be measured using a microphone in air and a hydrophone in water. The SI unit for sound pressure is the pascal...

s. The ratio of the sound pressure that causes permanent damage during short exposure to the lower limit that (undamaged) ears can hear is above a million

Million

One million or one thousand thousand, is the natural number following 999,999 and preceding 1,000,001. The name is derived from Italian, where mille was 1,000, and 1,000,000 became milione, "a large thousand"....

. Because the power in a sound wave is proportional to the square of the pressure, the ratio of the maximum power to the minimum power is above one (short scale

Long and short scales

The long and short scales are two of several different large number naming systems used throughout the world: It refers to a system of large number names in which every new term greater than million is 1,000 times the previous term: billion means a thousand millions , trillion means a...

) trillion. To deal with such a range, logarithmic units are useful: the log of a trillion is 12, so this ratio represents a difference of 120 dB. Since the human ear is not equally sensitive to all the frequencies of sound within the entire spectrum, noise levels at maximum human sensitivity — for example, the higher harmonic

Harmonic

In acoustics and telecommunication, a harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency. For example, if the fundamental frequency is...

s of middle A

A (musical note)

La or A is the sixth note of the solfège. "A" is generally used as a standard for tuning. When the orchestra tunes, the oboe plays an "A" and the rest of the instruments tune to match that pitch. Every string instrument in the orchestra has an A string, from which each player can tune the rest of...

(between 2 and 4 kHz

Hertz

The hertz is a unit of frequency. It is defined as the number of complete cycles per second. It is the basic unit of frequency in the International System of Units , and is used worldwide in both general-purpose and scientific contexts...

) — are factored more heavily into sound descriptions using a process called frequency weighting.

Electronics

In electronics, the decibel is often used to express power or amplitude ratios (gain

Gain

Gain is a measure of a system's response to feedback. If the gain in a positive feedback loop is less than 1, the feedback is not of itself sufficient to make the system become unstable. For example, water evaporating from the World's oceans causes a positive feedback, as it is a greenhouse gas...

s), in preference to arithmetic

Arithmetic

Arithmetic or arithmetics is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting to advanced science and business calculations, such as addition, subtraction, multiplication and division...

ratios or percentages. One advantage is that the total decibel gain of a series of components (such as amplifier

Amplifier

Generally, an amplifier or simply amp, is any device that changes, usually increases, the amplitude of a signal. The relationship of the input to the output of an amplifier—usually expressed as a function of the input frequency—is called the transfer function of the amplifier, and the magnitude of...

s and attenuators) can be calculated simply by summing the decibel gains of the individual components. Similarly, in telecommunications, decibels are used to account for the gains and losses of a signal from a transmitter to a receiver through some medium (free space

Free space

In classical physics, free space is a concept of electromagnetic theory, corresponding to a theoretically perfect vacuum and sometimes referred to as the vacuum of free space, or as classical vacuum, and is appropriately viewed as a reference medium.The definitions of the ampere and meter SI units...

, wave guides, coax, fiber optics, etc.) using a link budget

Link budget

A link budget is the accounting of all of the gains and losses from the transmitter, through the medium to the receiver in a telecommunication system. It accounts for the attenuation of...

.

The decibel unit can also be combined with a suffix to create an absolute unit of electric power. For example, it can be combined with "m" for "milliwatt" to produce the "dBm

DBm

For other uses, see DBM dBm is an abbreviation for the power ratio in decibels of the measured power referenced to one milliwatt . It is used in radio, microwave and fiber optic networks as a convenient measure of absolute power because of its capability to express both very large and very small...

". Zero dBm is the power level corresponding to a power of one milliwatt, and 1 dBm is one decibel greater (about 1.259 mW).

In professional audio, a popular unit is the dBu (see below for all the units). The "u" stands for "unloaded", and was probably chosen to be similar to lowercase "v", as dBv was the older name for the same thing. It was changed to avoid confusion with dBV. This unit (dBu) is an RMS

Root mean square

measurement of voltage which uses as its reference 0.775 V_RMS. Chosen for historical reasons, it is the voltage level which delivers 1 mW of power in a 600 ohm resistor, which used to be the standard reference impedance in telephone audio circuits.

The bel is used to represent noise power levels in hard drive specifications. It shares the same symbol (B) as the byte

Byte

A byte is a unit of information storage representing the smallest addressable element for a given computer architecture. It often designates a sequence of bits whose length is determined by the architecture...

Optics

In an optical link

Optical link

An optical link is a communications link that consists of a single end-to-end optical circuit. A cable of optical fiber, possibly concatenated into a dark fiber link, is the simplest form of an optical link....

, if a known amount of optical

Optics

Optics is the branch of physics which studies the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light...

power, in dBm

DBm

(referenced to 1 mW), is launched into a fiber

Optical fiber

An optical fiber is a glass or plastic fiber that carries light along its length. Fiber optics is the overlap of applied science and engineering concerned with the design and application of optical fibers...

, and the losses, in dB (decibels), of each electronic component

Electronic component

An electronic component is a basic electronic element usually packaged in a discrete form with two or more connecting leads or metallic pads....

(e.g., connectors, splices, and lengths of fiber) are known, the overall link loss may be quickly calculated by addition and subtraction of decibel quantities.

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

Apparent magnitude

The apparent magnitude of a celestial body is a measure of its brightness as seen by an observer on Earth, normalized to the value it would have in the absence of the atmosphere...

measures the brightness of a star logarithmically, since, just as the ear responds logarithmically to acoustic power, the eye responds logarithmically to brightness; however astronomical magnitudes reverse the sign with respect to the bel, so that the brightest stars have the lowest magnitudes, and the magnitude increases for fainter stars.

Video and digital imaging

In connection with digital and video image sensor

Image sensor

An image sensor is a device that converts an optical image to an electric signal. It is used mostly in digital cameras and other imaging devices. An image sensor is typically a charge-coupled device or a complementary metal–oxide–semiconductor active-pixel sensor.- CCD vs CMOS :Today, most...

s, decibels generally represent ratios of video voltages or digitized light levels, using 20 log of the ratio, even when the represented optical power is directly proportional to the voltage or level, not to its square. Thus, a camera signal-to-noise ratio

Signal-to-noise ratio

Signal-to-noise ratio is an electrical engineering measurement, also used in other fields , defined as the ratio of a signal power to the noise power corrupting the signal...

of 60 dB represents a power ratio of 1000:1 between signal power and noise power, not 1,000,000:1.

"Absolute" and "relative" decibel measurements

Although decibel measurements are always relative to a reference level, if the numerical value of that reference is explicitly and exactly stated, then the decibel measurement is called an "absolute" measurement, in the sense that the exact value of the measured quantity can be recovered using the formula given earlier. For example, since dBm indicates power measurement relative to 1 milliwatt,

0 dBm means no change from 1 mW. Thus, 0 dBm is the power level corresponding to a power of exactly 1 mW.
3 dBm means 3 dB greater than 0 dBm. Thus, 3 dBm is the power level corresponding to 10^3/10 × 1 mW, or approximately 2 mW.
−6 dBm means 6 dB less than 0 dBm. Thus, −6 dBm is the power level corresponding to 10^−6/10 × 1 mW, or approximately 250 μW (0.25 mW).

If the numerical value of the reference is not explicitly stated, as in the dB gain of an amplifier, then the decibel measurement is purely relative. The practice of attaching a suffix to the basic dB unit, forming compound units such as dBm, dBu, dBA, etc, is not permitted by SI. However, outside of documents adhering to SI units, the practice is very common as illustrated by the following examples.

Electric power

dBm
DBm
For other uses, see DBM dBm is an abbreviation for the power ratio in decibels of the measured power referenced to one milliwatt . It is used in radio, microwave and fiber optic networks as a convenient measure of absolute power because of its capability to express both very large and very small...

or dBmW

dB(1 mW) — power measurement relative to 1 milliwatt. X_dBm = X_dBW + 30.

dBW

dB(1 W) — similar to dBm, except the reference level is 1 watt

Watt

The watt is a derived unit of power in the International System of Units . It measures rate of energy conversion. One watt is equivalent to 1 joule of energy per second....

. 0 dBW = +30 dBm; −30 dBW = 0 dBm; X_dBW = X_dBm − 30.

Voltage

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

dBV

dB(1 V_{RMSRoot mean square
In mathematics, the root mean square , also known as the quadratic mean, is a statistical measure of the magnitude of a varying quantity. It is especially useful when variates are positive and negative, e.g., sinusoids....}) — volt

Volt

The volt is the SI derived unit of electromotive force, commonly called "voltage". It is also the unit for the related but slightly different quantity electric potential difference...

age relative to 1 volt, regardless of impedance.

dBu or dBv

dB(0.775 V_{RMSRoot mean square
In mathematics, the root mean square , also known as the quadratic mean, is a statistical measure of the magnitude of a varying quantity. It is especially useful when variates are positive and negative, e.g., sinusoids....}) — volt

Volt

The volt is the SI derived unit of electromotive force, commonly called "voltage". It is also the unit for the related but slightly different quantity electric potential difference...

age relative to 0.775 volts. Originally dBv, it was changed to dBu to avoid confusion with dBV. The "v" comes from "volt", while "u" comes from "unloaded". dBu can be used regardless of impedance, but is derived from a 600 Ω load dissipating 0 dBm (1 mW). Reference voltage

dBmV

dB(1 mV_{RMSRoot mean square
In mathematics, the root mean square , also known as the quadratic mean, is a statistical measure of the magnitude of a varying quantity. It is especially useful when variates are positive and negative, e.g., sinusoids....}) — volt

Volt

The volt is the SI derived unit of electromotive force, commonly called "voltage". It is also the unit for the related but slightly different quantity electric potential difference...

age relative to 1 millivolt, regardless of impedance. Widely used in cable television

Cable television

Cable television is a system of providing television to consumers via radio frequency signals transmitted to televisions through fixed optical fibers or coaxial cables as opposed to the over-the-air method used in traditional television broadcasting in which a television antenna is required...

networks, where the nominal strength of a single TV signal at the receiver terminals is about 0 dBmV. Cable TV uses 75 Ω coaxial cable, so 0 dBmV corresponds to −78.75 dBW (-48.75 dBm) or ~13 nW.

dBμV or dBuV

dB(1 μV_{RMSRoot mean square
In mathematics, the root mean square , also known as the quadratic mean, is a statistical measure of the magnitude of a varying quantity. It is especially useful when variates are positive and negative, e.g., sinusoids....}) — volt

Volt

The volt is the SI derived unit of electromotive force, commonly called "voltage". It is also the unit for the related but slightly different quantity electric potential difference...

age relative to 1 microvolt. Widely used in television and aerial amplifier specifications. 60 dBμV = 0 dBmV.

Acoustics

Probably the most common usage of "decibels" in reference to sound loudness is dB SPL, referenced to the nominal threshold of human hearing:

dB(SPL)

dB (sound pressure level) — for sound in air and other gases, relative to 20 micropascals (μPa) = 2×10⁻⁵ Pa, the quietest sound a human can hear. This is roughly the sound of a mosquito flying 3 metres away. This is often abbreviated to just "dB", which gives some the erroneous notion that "dB" is an absolute unit by itself. For sound in water

Underwater acoustics

Underwater acoustics is the study of the propagation of sound in water and the interaction of the mechanical waves that constitute sound with the water and its boundaries. The water may be in the ocean, a lake or a tank. Typical frequencies associated with underwater acoustics are between 10 Hz and...

and other liquids, a reference pressure of 1 μPa is used.Morfey, C. L. (2001). Dictionary of Acoustics. Academic Press, San Diego.

dB SIL

dB sound intensity level

Sound intensity level

Sound intensity level or acoustic intensity level is a logarithmic measure of the sound intensity , in comparison to the reference level of 10^-12 W/m²....

— relative to 10⁻¹² W/m², which is roughly the threshold of human hearing in air.

dB SWL

dB sound power level

Sound power level

Sound power level or acoustic power level is a logarithmic measure of the sound power in comparison to a specified reference level.The sound power level of a signal with sound power W is where W₀ is the 0 dB SWL reference level:...

— relative to 10⁻¹² W.

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

These symbols are often used to denote the use of different weighting filter

Weighting filter

A weighting filter is used to emphasise or suppress some aspects of a phenomenon compared to others, for measurement or other purposes.- Audio applications :...

s, used to approximate the human ear's response

Response

Response may refer to:*Response , a line answering a versicle*Response or antiphon, a response to a psalm or other part of a religious service* Output or response, the result of telecommunications input...

to sound, although the measurement is still in dB (SPL). These measurements usually refer to noise and noisome effects on humans and animals, and are in widespread use in the industry with regard to noise control issues, regulations and environmental standards. Other variations that may be seen are dB_A or dBA

A-weighting

. According to ANSI standards, 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

DBc

dBc is the power ratio of a signal to a carrier signal, expresses in decibels. For example, phase noise is expressed in dBc/Hz at a given frequency offset from the carrier...

, used in telecommunications.

dB HL or dB hearing level is used in audiogram

Audiogram

An audiogram is a standard way of representing a person's hearing loss. Most audiograms cover the limited range 100Hz to 8000Hz which is most important for clear understanding of speech, and they plot the threshold of hearing relative to a standardised curve that represents 'normal' hearing, in dBHL...

s as a measure of hearing loss. The reference level varies with frequency according to a minimum audibility curve

Minimum audibility curve

Minimum audibility curve is a standardised graph of the threshold of hearing versus frequency for an average human, and is used as the reference level when measuring hearing loss with an audiometer as shown on an audiogram....

as defined in ANSI and other standards, such that the resulting audiogram shows deviation from what is regarded as 'normal' hearing.

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

ITU-R 468 noise weighting

The ITU-R 468-weighting curve is widely used when measuring noise in audio systems, especially in the UK, Europe, and former countries of the British Empire such as Australia and South Africa...

Radar

dBZ
DBZ (meteorology)
dBZ stands for decibels of Z. It is a meteorological measure of equivalent reflectivity of a radar signal reflected off a remote object. The reference level for Z is 1 mm⁶ m^-3, which is equal to 1 μm³...

dB(Z) - energy of reflectivity (weather radar), or the amount of transmitted power returned to the radar receiver. Values above 15-20 dBZ usually indicate falling precipitation.

dBsm

dBsm - decibel (referenced to one) square meter, measure of reflected energy from a target compared to the RCS

Radar cross section

Radar cross section is a measure of how detectable an object is with a radar. A larger RCS indicates that an object is more easily detected.When radar waves are beamed at a target, only a certain amount are reflected back...

of a smooth perfectly conducting sphere at least several wavelengths in size with a cross-sectional area of 1 square meter. "Stealth" aircraft and insects have negative values of dBsm, large flat plates or non-stealthy aircraft have positive values.

Radio power, energy, and field strength

dBc

DBc

dBc is the power ratio of a signal to a carrier signal, expresses in decibels. For example, phase noise is expressed in dBc/Hz at a given frequency offset from the carrier...

dBc — relative to carrier — in telecommunication

Telecommunication

Telecommunication is transmission over a distance for the purpose of communication. In earlier times, this may have involved the use of smoke signals, drums, semaphore, flags or heliograph. In modern times, telecommunication typically involves the use of electronic devices such as the telephone,...

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

dBJ

dB(J) — energy relative to 1 joule

Joule

The joule , named for James Prescott Joule, is the derived unit of energy in the International System of Units. It is the energy exerted by a force of one newton acting to move an object through a distance of one metre...

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

dBm

DBm

dB(mW) — power relative to 1 milliwatt. When used in audio work the milliwatt is referenced to a 600 ohm load, with the resultant voltage being 0.775 volts. When used in the 2-way radio field, the dB is referenced to a 50 ohm load, with the resultant voltage being 0.224 volts. There are times when spec sheets may show the voltage & power level e.g. -120 dBm = 0.224 microvolts.

dBμV/m or dBuV/m

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

dBf

dB(fW) — power relative to 1 femtowatt.

dBW

dB(W) — power relative to 1 watt

Watt

The watt is a derived unit of power in the International System of Units . It measures rate of energy conversion. One watt is equivalent to 1 joule of energy per second....

dBk

dB(kW) — power relative to 1 kilowatt.

Antenna measurements

dBi

dB(isotropic) — the forward gain of an antenna compared with the hypothetical isotropic antenna, which uniformly distributes energy in all directions. Linear polarization

Linear polarization

In electrodynamics, linear polarization or plane polarization of electromagnetic radiation is a confinement of the electric field vector or magnetic field vector to a given plane along the direction of propagation...

of the EM field is assumed unless noted otherwise.

dBd

dB(dipole) — the forward gain of an antenna compared with a half-wave dipole antenna

Dipole antenna

A dipole antenna, created by Heinrich Rudolph Hertz around 1886, is an antenna that can be made by a simple wire, with a center-fed driven element for transmitting or receiving radio frequency energy...

. 0dBd = 2.15dBi

dBiC

dB(isotropic circular) — the forward gain of an antenna compared to a circularly polarized

Circular polarization

In electrodynamics, circular polarization of electromagnetic radiation is a polarization such that the tip of the electric field vector, at a fixed point in space, describes a circle as time progresses. The electric vector, at one point in time, describes a helix along the direction of wave...

isotropic antenna. There is no fixed conversion rule between dBiC and dBi, as it depends on the receiving antenna and the field polarization.

dBq

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

Other measurements

dBFS
DBFS
dBFS means "decibels relative to full scale". It is an abbreviation for decibel amplitude levels in digital systems which have a maximum available peak level; like PCM encoding.- Peak levels :...

or dBfs

dB(full scale

Full scale

In electronics and signal processing, full scale or full code represents the maximum amplitude a system can present.-Electronics and signal processing:...

) — the amplitude

Amplitude

Amplitude is the magnitude of change in the oscillating variable, with each oscillation, within an oscillating system. For instance, sound waves are oscillations in atmospheric pressure and their amplitudes are proportional to the change in pressure during one oscillation...

of a signal (usually audio) compared with the maximum which a device can handle before clipping

Clipping (signal processing)

Clipping is a form of distortion that limits a signal once it exceeds a threshold. Clipping may occur when a signal is recorded by a sensor that has constraints on the range of data it can measure, it can occur when a signal is digitized, or it can occur any other time an analog or digital signal...

occurs. In digital systems, 0 dBFS (peak) would equal the highest level (number) the processor is capable of representing. Measured values are always negative or zero, since they are less than the maximum or full-scale. Full-scale is typically defined as the power level of a full-scale sinusoid, though some systems will have extra headroom for peaks above the nominal full scale.

dB-Hz

dB(hertz

Hertz

) — bandwidth relative to 1 Hz. E.g., 20 dB-Hz corresponds to a bandwidth of 100 Hz. Commonly used in link budget

Link budget

A link budget is the accounting of all of the gains and losses from the transmitter, through the medium to the receiver in a telecommunication system. It accounts for the attenuation of...

calculations. Also used in carrier-to-noise-density ratio

Carrier-to-receiver noise density

Carrier-to-receiver noise density : In satellite communications, the ratio of the received carrier power to the receiver noise power density.Note 1: The carrier-to-receiver noise density ratio is usually expressed in dBHz....

(not to be confused with carrier-to-noise ratio

Carrier-to-noise ratio

In telecommunications, the carrier-to-noise ratio, often written CNR or C/N, is the signal-to-noise ratio of a modulated signal. The CNR is the quotient between the average received modulated carrier power C and the average received noise power N after the receiver filters.The aim of the term is...

, in dB).

dBov or dBO

dB(overload

Overload

Overload may refer to:* One of the studio album's name of the Japanese Heavy Metal Band Anthem* Overload * Overload * Overload , an episode of the television series CSI: Crime Scene Investigation...

) — the amplitude

Amplitude

of a signal (usually audio) compared with the maximum which a device can handle before clipping

Clipping (signal processing)

occurs. Similar to dBFS, but also applicable to analog systems.

dBr

dB(relative) — simply a relative difference from something else, which is made apparent in context. The difference of a filter's response to nominal levels, for instance.

dBrn
DBrn
The symbol dBrn or dB is an abbreviation for decibels above reference noise.Weighted noise power in dB is referred to 1.0 picowatt. Thus, 0 dBrn = -90 dBm...

dB above reference noise

Reference noise

In telecommunication, reference noise is the magnitude of circuit noise chosen as a reference for measurement.Many different levels with a number of different weightings are in current use, and care must be taken to ensure that the proper parameters are stated.Specific ones include: dBa, dBa, dBa,...

. 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. The Psophometric...

Decibel

History

Power

Amplitude, voltage and current

Examples

Merits

Acoustics

Electronics

Optics

Video and digital imaging

"Absolute" and "relative" decibel measurements

Electric power

Voltage

Acoustics

Radar

Radio power, energy, and field strength

Antenna measurements

Other measurements

See also

External links