NationMaster - Encyclopedia: Bell unit

The decibel (dB) is a logarithmic unit of measurement that expresses the magnitude of a physical quantity (usually power) relative to a specified or implied reference level. Its logarithmic nature allows very large or very small ratios to be represented by a convenient number, in a similar manner to scientific notation. Being essentially a ratio, it is a dimensionless unit. Decibels are useful for a wide variety of measurements in acoustics, physics, electronics and other disciplines. Logarithmic units are generic mathematical units in which we can express any quantities (physical or mathematical) that are defined as being proportional to values of a logarithm function. ... In physics, power (symbol: P) is the rate at which work is performed or energy is transferred. ... Logarithms to various bases: is to base e, is to base 10, and is to base 1. ... Scientific notation, also known as standard form, is a notation for writing numbers that is often used by scientists and mathematicians to make it easier to write large and small numbers. ... In the physical sciences, a dimensionless number (or more precisely, a number with the dimensions of 1) is a quantity which describes a certain physical system and which is a pure number without any physical units; it does not change if one alters ones system of units of measurement... Acoustics is a branch of physics and is the study of sound (mechanical waves in gases, liquids, and solids). ... This is a discussion of a present category of science. ... This article is about the engineering discipline. ...

The decibel is not an SI unit, although the International Committee for Weights and Measures (CIPM) has recommended its inclusion in the SI system. Following the SI convention, the d is lowercase, as it represents the SI prefix deci-, and the B is capitalized, as it is an abbreviation of a name-derived unit, the bel (see below). The full name decibel follows the usual English capitalization rules for a common noun. The decibel symbol is often qualified with a suffix, which indicates which reference quantity has been assumed. For example, "dBm" indicates that the reference quantity is one milliwatt. Look up si, Si, SI in Wiktionary, the free dictionary. ... The International Committee for Weights and Measures is the English name of the ComitÃ© international des poids et mesures (CIPM, sometimes written in English ComitÃ© International des Poids et Mesures). ... deci- (symbol d) is a prefix in the SI system of units denoting a factor of 10âˆ’1 (1/10). ... The English language is a West Germanic language that originates in England. ... A noun, or noun substantive, is a word or phrase that refers to a person, place, thing, event, substance or quality. ...

A decibel is one tenth of a bel (B). Devised by engineers of the Bell Telephone Laboratory to quantify the reduction in audio level over a 1 mile (approximately 1.6 km) length of standard telephone cable, the bel was originally called the transmission unit or TU, but was renamed in 1923 or 1924 in honor of the Bell System's founder and telecommunications pioneer Alexander Graham Bell. In many situations, however, the bel proved inconveniently large, so the decibel has become more common. Bell Laboratories (also known as Bell Labs and formerly known as AT&T Bell Laboratories and Bell Telephone Laboratories) was the main research and development arm of the United States Bell System. ... A mile is a unit of length, usually used to measure distance, in a number of different systems, including Imperial units, United States customary units and Norwegian/Swedish mil. ... For other uses, see Telephone (disambiguation). ... The Bell System was a trademark and service mark used by the United States telecommunications company American Telephone & Telegraph Company (AT&T) and its affiliated companies to co-brand their extensive circuit-switched telephone network and their affiliations with each other. ... Alexander Graham Bell (3 March 1847 â€“ 2 August 1922) was a Scottish scientist and inventor. ...

The definitions of the decibel and bel use base-10 logarithms. For a similar unit using natural logarithms to base e, see neper. A neper (Symbol: Np) is a unit of ratio. ...

An increase of 3 dB corresponds to an approximate doubling of power. (In exact terms, the factor is 10^3/10, or 1.9953, about 0.24% different from exactly 2.) Since in many electrical applications power is proportional to the square of voltage, an increase of 3 dB implies an increase in voltage by a factor of approximately √2, or about 1.41. Similarly, an increase of 6 dB corresponds to approximately four times the power and twice the voltage, and so on. (In exact terms the power factor is 10^6/10, or about 3.9811, a relative error of about 0.5%.) See the formulas below for further details.

Definitions

Power

When referring to measurements of power or intensity, a ratio can be expressed in decibels by evaluating ten times the base-10 logarithm of the ratio of the measured quantity to the reference level. Thus, X_dB is calculated using the formula:

$X_mathrm{dB} = 10 log_{10} bigg(frac{X}{X_0}bigg)$

where X is the actual value of the quantity being measured, X₀ is a specified or implied reference level, and then X_dB is the quantity expressed in units of decibels, relative to X₀. Which reference is used depends on convention and context (see later in this article). X and X₀ must have the same dimensions (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. The reference level itself is always at 0 dB, as shown by setting X = X₀ in the above equation. If X is greater than X₀ then X_dB is positive; if X is less than X₀ then X_dB is negative. 2-dimensional renderings (ie. ...

Rearranging the above equation gives the following formula for X in terms of X₀ and X_dB:

$X = 10^frac{X_mathrm{dB}}{10} X_0.$

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

$X_mathrm{B} = log_{10} bigg(frac{X}{X_0}bigg)$

$X = 10^{X_mathrm{B}} X_0.$

Amplitude, voltage and current

When referring to measurements of amplitude it is usual to consider the ratio of the squares of X (measured amplitude) and X₀ (reference amplitude). This is because in most applications power is proportional to the square of amplitude. Thus the following definition is used:

$X_mathrm{dB} = 10 log_{10} bigg(frac{X^2}{X_0^2}bigg) = 20 log_{10} bigg(frac{X}{X_0}bigg)$

The formula may be rearranged to give

$X = 10^frac{X_mathrm{dB}}{20} X_0$

Similarly, in electrical circuits, dissipated power is typically proportional to the square of voltage or current when the impedance is held constant. Taking voltage as an example, this leads to the equation: An electronic circuit is an electrical circuit that also contains active electronic devices such as transistors or vacuum tubes. ... International safety symbol Caution, risk of electric shock (ISO 3864), colloquially known as high voltage symbol. ... Electric current is the flow (movement) of electric charge. ... Electrical impedance, or simply impedance, is a measure of opposition to a sinusoidal alternating electric current. ...

$V_mathrm{dB} =20 log_{10} left (frac{V}{V_0} right ) quad mathrm quad$

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

Examples

These examples assume that X in the formulas above measures power relative to 1 W (one watt); i.e. X₀ = 1 W.

To convert 1 kW (one kilowatt, or 1000 W) to decibels, use the formula

$X_mathrm{dB} = 10 log_{10} bigg(frac{1000 mathrm{W}}{1 mathrm{W}}bigg) = 30 mathrm{dB}$

To convert 1 mW (one milliwatt, or 0.001 W) to decibels, use the formula

$X_mathrm{dB} = 10 log_{10} bigg(frac{0.001 mathrm{W}}{1 mathrm{W}}bigg) = -30 mathrm{dB}$

To find the actual value of 3 dB, use the formula

$X = 10^frac{3}{10} times 1 mathrm{W} = 1.99526... mathrm{W} approx 2 mathrm{W}$

It will be seen that there is a 10 dB increase (decrease) for each factor 10 increase (decrease) in the ratio of X to X₀, and approximately a 3 dB increase (decrease) for every factor 2 increase (decrease).

Merits

The use of decibels has a number of merits:

The mathematical laws of exponents 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.
A very large range of ratios can be expressed with decibel values in a range of moderate size, allowing one to clearly visualize huge changes of some quantity. (See Bode Plot and half logarithm graph.)
In acoustics, the decibel scale approximates the human perception of loudness (which is itself roughly logarithmic).

Exponentiation is a mathematical operation, written an, involving two numbers, the base a and the exponent n. ... An amplifier is a device which changes a small movement into a larger movement. ... The Bode plot for a first-order Butterworth filter A Bode plot, named after Hendrik Wade Bode, is usually a combination of a Bode magnitude plot and Bode phase plot: A Bode magnitude plot is a graph of log magnitude against log frequency often used in signal processing to show... The horizontal axis shows frequency in Hz Loudness is the quality of a sound that is the primary psychological correlate of physical intensity. ...

Uses

Acoustics

Main article: Acoustics

The decibel is commonly used in acoustics to quantify sound levels relative to some 0 dB reference. The reference level is typically set at the threshold of human perception; see sound pressure. Acoustics is a branch of physics and is the study of sound (mechanical waves in gases, liquids, and solids). ... Sound is a disturbance of mechanical energy that propagates through matter as a wave. ... Sound pressure is the pressure deviation from the local ambient pressure caused by a sound wave. ...

A reason for using the decibel is that the ear is capable of detecting a very large range of sound pressures (see Examples of sound pressure and sound pressure levels). The ratio of the sound pressure that causes permanent damage from short exposure to the limit that (undamaged) ears can hear is above a million. 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) 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 — middle A and its higher harmonics (between 2 and 4 kHz) — are factored more heavily into sound descriptions using a process called frequency weighting. Sound is a disturbance of mechanical energy that propagates through matter as a wave. ... Sound is a disturbance of mechanical energy that propagates through matter as a wave. ... This article does not cite any references or sources. ... The long and short scales are two different numerical systems used throughout the world: Short scale is the English translation of the French term Ã©chelle courte. ... One million million (1,000,000,000,000) is the natural number following 999,999,999,999 and preceding 1,000,000,000,001. ... This article is about the components of sound. ... MHZ redirects here. ... The A, B, C, and D weighting curves A weighting filter or weighting curve is a type of linear filter used in audio signal processing to approximate the response of the human ear to a given sound pressure level. ...

Electronics

The decibel is used rather than arithmetic ratios or percentages because when certain types of circuits, such as amplifiers and attenuators, are connected in series, expressions of power level in decibels may be arithmetically added and subtracted. It is also common in disciplines such as audio, in which the properties of the signal are best expressed in logarithms due to the response of the human ear. Arithmetic tables for children, Lausanne, 1835 Arithmetic or arithmetics (from the Greek word Î±ÏÎ¹Î¸Î¼ÏŒÏ‚ = number) is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple daily counting to advanced science and business calculations. ... A percentage is a way of expressing a proportion, a ratio or a fraction as a whole number, by using 100 as the denominator. ... An electronic circuit is an electrical circuit that also contains active electronic devices such as transistors or vacuum tubes. ... An attenuator is a telecommunication device that reduces the amplitude of a signal without appreciably distorting its waveform. ...

In radio electronics and telecommunications, the decibel is used to describe the ratio between two measurements of electrical power. It can also be combined with a suffix to create an absolute unit of electrical power. For example, it can be combined with "m" for "milliwatt" to produce the "dBm". Zero dBm is one milliwatt, and 1 dBm is one decibel greater than 0 dBm, or about 1.259 mW. Transmission lines in Lund, Sweden Electric power, often known as power or electricity, involves the production and delivery of electrical energy in sufficient quantities to operate domestic appliances, office equipment, industrial machinery and provide sufficient energy for both domestic and commercial lighting, heating, cooking and industrial processes. ... The correct title of this article is . ...

Decibels are used to account for the gains and losses of a signal from a transmitter to a receiver through some medium (free space, wave guides, coax, fiber optics, etc.) using a link budget. A link budget is the accounting of all of the gains and losses from the transmitter, through the medium (free space, cable, waveguide, fiber, etc. ...

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 measurement of voltage which uses as its reference 0.775 V_RMS. Chosen for historical reasons, it is the voltage level at which you get 1 mW of power in a 600 ohm resistor, which used to be the standard reference impedance in almost all professional low impedance audio circuits. In mathematics, the root mean square or rms is a statistical measure of the magnitude of a varying quantity. ...

The bel is used to represent noise power levels in hard drive specifications. Typical hard drives of the mid-1990s. ...

Optics

In an optical link, if a known amount of optical power, in dBm (referenced to 1 mW), is launched into a fibre, and the losses, in dB (decibels), of each electronic component (e.g., connectors, splices, and lengths of fibre) are known, the overall link loss may be quickly calculated by simple addition and subtraction of decibel quantities. An optical link is a communications link that consists of a single end-to-end optical circuit. ... For the book by Sir Isaac Newton, see Opticks. ... The correct title of this article is . ... Optical fibers An optical fiber (or fibre) is a glass or plastic fiber designed to guide light along its length by confining as much light as possible in a propagating form. ... Various components An electronic component is a basic electronic element usually packaged in a discrete form with two or more connecting leads or metallic pads. ...

In spectrometry and optics, the blocking unit used to measure optical density is equivalent to −1 B. In astronomy, the apparent magnitude 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. Optical density is the absorbance of an optical element for a given wavelength Î» per unit distance: Where: Although absorbance does not have true units, it is quite often reported in Absorbance Units or AU. Accordingly, optical density is measured in ODU, which are equivalent to AU cmâˆ’1. ... The apparent magnitude (m) of a star, planet or other celestial body is a measure of its apparent brightness as seen by an observer on Earth. ...

Seismology

Earthquakes were formerly measured on the Richter scale, which is expressed in bels, though they are not labeled with a unit. The more modern moment magnitude scale is designed to produce values comparable to those of the Richter scale. The Richter magnitude scale, or more correctly local magnitude ML scale, assigns a single number to quantify the amount of seismic energy released by an earthquake. ... The moment magnitude scale was introduced in 1979 by Tom Hanks and Hiroo Kanamori as a successor to the Richter scale and is used by seismologists to compare the energy released by earthquakes. ...

Common reference levels and corresponding units

"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 formulas given earlier. For example, since dBm indicates power measurement relative to 1 milliwatt,

0 dBm means no change from 1 mW, in other words 0 dBm is 1 mW.
3 dBm means 3 dB greater than 1 mW. 3 dBm is 10^3/10 × 1 mW, or approximately 2 mW.
−6 dBm means 6 dB less than 1 mW. −6 dBm is 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.

Absolute measurements

Electric power

dBm or dBmW The correct title of this article is . ...

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

dBW dBW is an abbreviation for the strength of a signal expressed in decibels relative to one Watt. ...

dB(1 W) — similar to dBm, except the reference level is 1 watt. 0 dBW = +30 dBm; -30 dBW = 0 dBm; X_dBW = X_dBm - 30.

For other uses, see Watt (disambiguation). ...

Voltage

Note that the decibel has a different definition when applied to voltage (as contrasted with power). See the "Definitions" section above.

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

dBu or dBv Image File history File links Relationship_between_dBu_and_dBm. ... Image File history File links Relationship_between_dBu_and_dBm. ... The decibel is a dimensionless unit (like percent) that is a measure of ratios on a logarithmic scale. ... It has been suggested that this article or section be merged with Current source. ... The correct title of this article is . ... For other uses, see Heat (disambiguation) In physics, heat, symbolized by Q, is energy transferred from one body or system to another due to a difference in temperature. ... Resistor symbols (non-European) Resistor symbols (Europe, IEC) Axial-lead resistors on tape. ...

dB(0.775 V_RMS) — voltage relative to 0.775 volts.^[1] Originally dBv, it was changed to dBu to avoid confusion with dBV.^{[citation needed]} 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).

dBV In mathematics, the root mean square or rms is a statistical measure of the magnitude of a varying quantity. ... Josephson junction array chip developed by NIST as a standard volt. ...

dB(1 V_RMS) — voltage relative to 1 volt, regardless of impedance.^[2]

dBmV In mathematics, the root mean square or rms is a statistical measure of the magnitude of a varying quantity. ... Josephson junction array chip developed by NIST as a standard volt. ...

dB(1 mV_RMS) — voltage relative to 1 millivolt, regardless of impedance. Widely used in cable television networks, where the nominal strength of a single TV signal at the receiver terminals is about 0 dBmV. Cable TV uses 75 Ω coaxial cable, so 0 dBmV corresponds to -48.75 dBm or ~13 nW.

In mathematics, the root mean square or rms is a statistical measure of the magnitude of a varying quantity. ... Josephson junction array chip developed by NIST as a standard volt. ... Coaxial cable is often used to transmit cable television into the house. ...

Acoustics

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 and other liquids, a reference pressure of 1 μPa is used.^[3]

dB SIL It has been suggested that this article or section be merged into Sound pressure. ... 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. ...

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

dB SWL Sound intensity level or acoustic intensity level is a logarithmic measure of the sound intensity in comparison to the reference level of 0 dB (decibels). ... Threshold of hearing is the sound pressure level SPL of 20 µPa (micropascals) = 2 × 10-5 pascal (Pa). ...

dB Sound Power Level — relative to 10⁻¹² W.

dB(A), dB(B), and dB(C) Sound power level or acoustic power level is a logarithmic measure of the sound power in comparison to a specified reference level. ...

These symbols are often used to denote the use of different frequency weightings, used to approximate the human ear's response to sound, although the measurement is still in dB (SPL). Other variations that may be seen are dB_A or dBA. According to ANSI standards, the preferred usage is to write L_A = x dB, as dBA implies a reference to an "A" unit, not an A-weighting. They are still used commonly as a shorthand for A-weighted measurements, however.

The A, B, C, and D weighting curves A weighting filter or weighting curve is a type of linear filter used in audio signal processing to approximate the response of the human ear to a given sound pressure level. ... A response is the following: Often a response is the result of a stimulus. ... The A-weighting curve is one of a family of curves defined in IEC179 and various other standards for use in sound level meters. ...

Radio power or energy

dBJ

dB(J) — energy relative to 1 joule. 1 joule = 1 watt-second, so noise spectral density can be expressed in dBJ, where 0 dBJ = 0 dBW/Hz. Boltzmann's constant is -228.6 dBJ/K.

dBm The joule (IPA: or ) (symbol: J) is the SI unit of energy. ... There are very few or no other articles that link to this one. ... The Boltzmann constant (k or kB) is the physical constant relating temperature to energy. ...

dB(mW) — power relative to 1 milliwatt.

dBμ or dBu Milliwatt (SI symbol: mW) is a unit for measuring electrical power, equal to one-thousandth (10-3) of a watt. ...

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

dBf In physics, an electric field or E-field is an effect produced by an electric charge that exerts a force on charged objects in its vicinity. ... The volt is the SI derived unit for electric potential and voltage (derived from the ampere and watt). ... â€¹ The template below (Unit of length) is being considered for deletion. ...

dB(fW) — power relative to 1 femtowatt.

dBW The watt (symbol: W) is the SI derived unit for power. ...

dB(W) — power relative to 1 watt.

dBk For other uses, see Watt (disambiguation). ...

dB(kW) — power relative to 1 kilowatt.

The kilowatt (symbol: kW) is a unit for measuring power, equal to one thousand watts. ...

Relative measurements

dBd

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

dBFS or dBfs A yagi antenna Most simply, an antenna is an electronic component designed to send or receive radio waves. ... A simple half-wave dipole antenna that a shortwave listener might build. ... dBFS means decibels full scale. It is an abbreviation for decibel amplitude levels in digital systems which have a maximum available level (like PCM encoding). ...

dB(full scale) — the amplitude of a signal (usually audio) compared to the maximum which a device can handle before clipping occurs. In digital systems, 0 dBFS (peak) would equal the highest level (number) the processor is capable of representing. Measured values are usually negative, since they should be less than the maximum.

dB-Hz The maximum amplitude a digital system can represent. ... It has been suggested that pulse amplitude be merged into this article or section. ... Look up clipping in Wiktionary, the free dictionary. ...

dB(Hertz) — Bandwidth relative to 1 Hz. E.g., 20 dB-Hz is equal to 100 Hz. Commonly used in link budget calculations.

dBi MHZ redirects here. ... A link budget is the accounting of all of the gains and losses from the transmitter, through the medium (free space, cable, waveguide, fiber, etc. ...

dB(isotropic) — the forward gain of an antenna compared to a fictitious isotropic antenna, which uniformly distributes energy in all directions.

dBiC For literary uses see Fiction For Legal uses see legal fiction Fictitious defendants Feigned action Ejectment - an action to recover land John Doe - commonly named as a fictitious defendant. ... An isotropic antenna is an ideal antenna that radiates power with unit gain uniformly in all directions and is often used to reference antenna gains in wireless systems. ...

dB(isometric circular) — power measurement relative to a circularly polarized isometric antenna.

dBov or dBO

dB(overload) — the amplitude of a signal (usually audio) compared to the maximum which a device can handle before clipping occurs. Similar to dBFS, but also applicable to analog systems.

dBr Overload can refer to: Electrical overload, a situation where an electrical machine or system is subjected to a greater load than it was designed for. ... It has been suggested that pulse amplitude be merged into this article or section. ... Look up clipping in Wiktionary, the free dictionary. ...

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

dBrn The title given to this article is incorrect due to technical limitations. ...

dB above reference noise. See also dBrnC.

dBc In telecommunication, reference noise is the magnitude of circuit noise chosen as a reference for measurement. ... dBrnC The correct title of this article is dBrnC. It appears here with an initial capital letter due to technical restrictions. ... DBC may refer to: Detroit Boat Club, a historic rowing club. ...

dB relative to carrier — in telecommunications, this indicates the relative levels of noise or sideband peak power, compared to the carrier power.

Copy of the original phone of Alexander Graham Bell at the MusÃ©e des Arts et MÃ©tiers in Paris Telecommunication is the transmission of signals over a distance for the purpose of communication. ...

Reckoning

Decibels are handy for mental calculation, because adding them is easier than multiplying ratios. First, however, one has to be able to convert easily between ratios and decibels. The most obvious way is to memorize the logs of small primes, but there are a few other tricks that can help.

Round numbers

The values of coins and banknotes are round numbers. The rules are:

One is a round number
Twice a round number is a round number: 2, 4, 8, 16, 32, 64
Ten times a round number is a round number: 10, 100
Half a round number is a round number: 50, 25, 12.5, 6.25
The tenth of a round number is a round number: 5, 2.5, 1.25, 1.6, 3.2, 6.4

Now 6.25 and 6.4 are approximately equal to 6.3, so we don't care. Thus the round numbers between 1 and 10 are these:

 Ratio 1 1.25 1.6 2 2.5 3.2 4 5 6.3 8 10 dB 0 1 2 3 4 5 6 7 8 9 10

This useful approximate table of logarithms is easily reconstructed or memorized.

The 4 → 6 energy rule

To one decimal place of precision, 4.x is 6.x in dB (energy).

Examples:

10 log₁₀(4.0) → 6.0 dB
10 log₁₀(4.3) → 6.3 dB
10 log₁₀(4.7) → 6.7 dB
10 log₁₀(4.9) → 6.9 dB

The "789" rule

To one decimal place of precision, x → (½ • x + 5.0 dB) for 7.0 ≤ x ≤ 10.

Examples:

10 log₁₀(7.0) → ½ • 7.0 + 5.0 dB = 3.5 + 5.0 dB = 8.5 dB
10 log₁₀(7.5) → ½ • 7.5 + 5.0 dB = 3.75 + 5.0 dB = 8.75 dB
10 log₁₀(8.2) → ½ • 8.2 + 5.0 dB = 4.1 + 5.0 dB = 9.1 dB
10 log₁₀(9.9) → ½ • 9.9 + 5.0 dB = 4.95 + 5.0 dB = 9.95 dB
10 log₁₀(10.0) → ½ • 10.0 + 5.0 dB = 5.0 + 5.0 dB = 10 dB

−3 dB ≈ ½ power

A level difference of ±3 dB is roughly double/half power (equal to a ratio of 1.995). That is why it is commonly used as a marking on sound equipment and the like.

Another common sequence is 1, 2, 5, 10, 20, 50 ... . These preferred numbers are very close to being equally spaced in terms of their logarithms. The actual values would be 1, 2.15, 4.64, 10 ... . In industrial design, product developers must choose numerous lengths, distances, diameters, volumes, and other characteristic quantities. ...

The conversion for decibels is often simplified to: "+3 dB means two times the power and 1.414 times the voltage", and "+6 dB means four times the power and two times the voltage ".

While this is accurate for many situations, it is not exact. As stated above, decibels are defined so that +10 dB means "ten times the power". From this, we calculate that +3 dB actually multiplies the power by 10^3/10. This is a power ratio of 1.9953 or about 0.25% different from the "times 2" power ratio that is sometimes assumed. A level difference of +6 dB is 3.9811, about 0.5% different from 4.

To contrive a more serious example, consider converting a large decibel figure into its linear ratio, for example 120 dB. The power ratio is correctly calculated as a ratio of 10¹² or one trillion. But if we use the assumption that 3 dB means "times 2", we would calculate a power ratio of 2^120/3 = 2⁴⁰ = 1.0995 × 10¹², giving a 10% error.

6 dB per bit

In digital audio linear pulse-code modulation, the first bit (least significant bit, or LSB) produces residual quantization noise (bearing little resemblance to the source signal) and each subsequent bit offered by the system doubles the (voltage) resolution, corresponding to a 6 dB (power) ratio. So for instance, a 16-bit (linear) audio format offers 15 bits beyond the first, for a dynamic range (between quantization noise and clipping) of (15 × 6) = 90 dB, meaning that the maximum signal (see 0 dBFS, above) is 90 dB above the theoretical peak(s) of quantization noise. The negative impacts of quantization noise can be reduced by implementing dither. Digital audio comprises audio signals stored in a digital format. ... Pulse-code modulation (PCM) is a digital representation of an analog signal where the magnitude of the signal is sampled regularly at uniform intervals, then quantized to a series of symbols in a digital (usually binary) code. ... This article is about the unit of information. ... For other uses, see Dynamic range (disambiguation). ... Quantization noise is a noise error introduced by the analogue to digital conversion (ADC) process in telecommunication systems and signal processing. ... Dither is a form of noise, or erroneous signal or data which is deliberately added to sample data for the purpose of minimizing quantization error. ...

dB chart

As is clear from the above description, the dB level is a logarithmic way of expressing not only power ratios, but also voltage ratios The following tables are cheat-sheets that provide values for various dB power ratios and also "voltage" ratios. In mathematics, if two variables of bn = x are known, the third can be found. ...

Commonly used dB values

dB level	power ratio	dB level	voltage ratio
−30 dB	1/1000 = 0.001	−30 dB	$sqrt{1/1000}$ = 0.03162
−20 dB	1/100 = 0.01	−20 dB	$sqrt{1/100}$ = 0.1
−10 dB	1/10 = 0.1	−10 dB	$sqrt{1/10}$ = 0.3162
−3 dB	1/2 = 0.5 (approx.)	−3 dB	$sqrt{1/2}$ = 0.7071
3 dB	2 (approx.)	3 dB	$sqrt{2}$ = 1.414
10 dB	10	10 dB	$sqrt{10}$ = 3.162
20 dB	100	20 dB	$sqrt{100}$ = 10
30 dB	1000	30 dB	$sqrt{1000}$ = 31.62

References

^ http://www.analog.com/Analog_Root/static/techSupport/designTools/interactiveTools/dbconvert/dbconvert.html
^ http://www.analog.com/Analog_Root/static/techSupport/designTools/interactiveTools/dbconvert/dbconvert.html
^ Morfey, C. L. (2001). Dictionary of Acoustics. Academic Press, San Diego.

Martin, W. H., "DeciBel — The New Name for the Transmission Unit", Bell System Technical Journal, January 1929.

Stevens, S. S. (1957). On the psychophysical law. Psychological Review 64(3):153—181. PMID 13441853.

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Encyclopedia > Bell unit

Contents

Definitions

Power

Amplitude, voltage and current

Examples

Merits

Uses

Acoustics

Electronics

Optics

Seismology

Common reference levels and corresponding units

"Absolute" and "relative" decibel measurements

Absolute measurements

Electric power

Voltage

Acoustics

Radio power or energy

Relative measurements

Reckoning

Round numbers

The 4 → 6 energy rule

The "789" rule

−3 dB ≈ ½ power

6 dB per bit

dB chart

Commonly used dB values

See also

References

External links

Converters