decibel

photograph of Alexander Graham Bell

Alexander Graham Bell

For examples of noise levels in dB, see noise.

One-tenth of a bel. Symbol, dB, but see below. (Though the decibel is not an SI unit, the SI convention that if a letter in a symbol represents a person's name, it is capitalized, is observed with this unit. The bel is named for Alexander Graham Bell.) A unit used in electrical engineering and acoustics to express on a logarithmic scale the ratio between two values with the same dimensions. The quantities compared may be two voltages, two power levels, two sound pressure levels, and so on. The decibel itself is dimensionless; since the quantities in the ratio always have the same dimensions, they cancel out.  For any measurement expressed in decibels, a reference level must be specified, explicitly or implicitly.

The decibel began as the transmission unit, a unit of power ratio used in telephone engineering.1  Renamed the bel (for Bell), it was adopted as an international unit at the First International Acoustical Conference (Paris, July 1937) for scales of energy and pressure levels.2 The decibel was originally primarily used in Britain and the United States; in continental Europe the neper played the same role. In the early 21st century, the CCU considered recommending adding the neper to the list of SI units as a coherent unit of logarithmic decay, leaving the bel outside SI. To date nothing has come of this effort.3

A variety of other names have been proposed for the decibel, including logit, decilit, decilog4, decomlog and decilu.

In audio and broadcast engineering, various decibels (see below) are used to describe the power or voltage of a signal in an electrical circuit. The decibel is made a unit by specifying the magnitude of one element of the ratio; this is the reference level. For power, the decibel is 10 times the common logarithm of the ratio of the power of the signal being described to the power of the reference level. For voltages, the decibel is 20 times the common logarithm of the ratio of voltage being measured to the reference voltage.  For either power or voltage, when the signal being measured equals the reference level it will be at 0 dB.

In acoustics, decibels are used to express sound intensity levels (10 times the common logarithm of the ratio between the measured intensity and a reference intensity), and sound pressure levels (20 times the common logarithm of the ratio between the measured pressure level and a reference pressure level).

Choice of a reference point has given rise to a variety of decibels. In several cases the abbreviations have themselves become the names of units (recording engineers, for example, refer to “dee-bee-you”). Frequently the portion after "dB" is printed as a subscript.

Power ratios for electric signals

dBm

The reference level is 1 milliwatt across an impedance of 600 ohms. The “m” stands for milliwatt. The 600 ohms came from standards in the telephone industry, the technology of the early 20th century, in which maximizing power transfer by matching output and input impedances was an important consideration. Note that a 0 dBm signal in a circuit with an impedance of 600 ohms corresponds to 0.775 volt rms. A signal change of −3 dBm is about a halving of the power.

See also volume unit.

dBW

The reference level is 1 watt.

Voltage ratios for electric signals

As tubes (valves) gave way to transistors, matching impedances became less important.  Audio engineers went from using decibels based on power to those based on voltage.

dBV

The reference level is 1 volt rms across any impedance. To convert dBV to dBu, add 2.2 dB. Consumer audio gear is designed for an normal input level of −10 dBV, which corresponds to 0.316 volt rms. This voltage level arose because it was the optimal maximum level for a signal fed directly to an electron tube (valve to Brits), which was a practice in consumer equipment.

dBv

The reference level is 0.775 volt rms across any impedance. The 0.775 volt value comes from the definition of dBm, since it is the voltage when a 0 dBm sine wave is fed into 600 ohms. This symbol was too easily confused with dBV, and so was renamed dBu.
Some writers do not observe the distinction between the upper and lower case V and treat both dBV and dBv as referenced to 1 volt rms.

dBu

The reference level is 0.775 volt rms across any impedance. See dBm above for the origin of the value. The “u” stands for unterminated.  Professional audio equipment is designed for a normal input level (“line level”) of +4 dBu, which corresponds to 1.23 volts rms. A signal change of −6 dBu is about a halving of the voltage.

dBFS

“FS” stands for “full scale.” A unit used in monitoring signal levels in digital signal processing, such as digital audio. To record audio (or any analog signal) digitally, the signal level is measured at equal, small intervals and the value recorded as a number. For audio this requires recording as many as 192,000 numbers each second, so it is necessary to choose a way of representing numbers that a computer can process very quickly and efficiently. All such systems for representing numbers have a biggest number that can be represented (and also a smallest negative number, what follows applies to negative numbers as well). This is the full scale point. If the level of the analog signal is greater than the level assigned to the biggest possible number, there is no way of recording its actual value. Every level greater than the one assigned to the largest possible number is usually simply recorded as the largest possible number. The signal is "clipped." The dBFS scale provides a way of indicating how close one is coming to this undesirable situation.

In such a system, the maximum level before clipping of a sine wave is -3 dBFS.

The relevant standard is IEC 6106-3 ed 1.0 (2008-10). The corresponding Audio Engineering Society standard is AES17.

The AES Information Document for Digital audio engineering

– Guidelines for the use of the AES3 interface,

AES-2id-2006 defines Full-Scale Amplitude as: “the rms voltage that corresponds with a sine wave whose positive peak value reaches the maximum positive digital value and whose negative peak reaches one LSB greater than the minimum negative digital value.” This means a full scale sine wave input would read +3 dBFS, and so would a full-scale square wave, and its rms value would equal +3 dBFS.

Further, AES Information Document for Digital audio engineering – Personal computer audio quality measurements, AES-6id-2006 defines Decibels, Fullscale (dB FS): “Digital signal rms amplitude expressed as a level in decibels relative to full-scale amplitude (20 times the common logarithm of the amplitude over the full-scale amplitude [defined as the ‘rms amplitude of a 997 Hz sine wave in the digital domain whose positive peak value reaches the positive digital full scale, leaving the negative maximum code unused.’]). Note that dB FS expresses a signal level of a digital signal and should not be used to express the signal level of an analog signal.”

For a good discussion of the use and misuse of the dBFS scale, see the papers by Nielsen and Lund at www.tcelectronic.com/TechLibrary#LoudnessControl%20and%20Mastering

 

dBr

A reference level is specified in the immediate context.

Sound intensity levels

dB

The reference level is usually 1 picowatt per square meter.

dBA, dBB, dBC

The measurement is frequency-weighted according to the "A" curve. B and C curves also exist.

Sound pressure levels

dB SPL

The reference level is usually 20 micropascals, the level of the faintest sound that can be heard.

1. W. H. Martin.
Decibel–The name for the Transmission Unit.
Bell System Technical Journal, January 1929.

2. The First International Acoustical Conference.
Nature, volume 140, page 370 (August 28, 1937).

V. V. L. Rao.
The Decibel Notation.
New York: Chemical Publishing Co., 1946.

The first edition was published in Madras, India.

3. Consultative Committee for Units (CCU).
Report of the 15th meeting (17-18 April 2003) to the International Committee for Weights and Measures.
Reports of CCU meetings are now only published on line, at www.bipm.org  Retrieved 22 May 2007.

See Section 3, President's Report, which states in part:

“At the CIPM meeting in October 2001 (90th meeting) he had reported that the CCU recommended the neper should be recognized as the (only) coherent unit of logarithmic decay, and recommended recognizing the bel and the decibel as widely used non-coherent units. The reasons for this recommendation are summarized in the 2001 paper in Metrologia by Mills, Taylor and Thor. After a brief discussion this recommendation was approved, although without enthusiasm.

“Although there was no meeting of the CCU in 2003, the President discussed the situation with many users of these units, and found widespread dissatisfaction with the proposal that only the neper should be recognized as a coherent SI unit. This arises from the fact that the decibel is very widely used as a unit, but the neper almost never used, by workers in the field. In fact most of the community have difficulty in recalling the definition of the neper.

“After discussion with experts in the field, and with colleagues on the CCU, the President decided to present a modified proposal to the CIPM at its meeting in 2002 (91st meeting), recommending that we should recognize two coherent SI units of logarithmic decay for two slightly different quantities: the neper for logarithmic amplitude ratio, and the bel for ‘power-like quantities’. ... However, after a lengthy discussion, the CIPM decided that it did not yet wish to make any change in the present situation, in which neither the neper nor the bel are recognized as SI units.”

4. Subcommittee on Methods of Measurement of Gain, Amplification, Loss, Attenuation, and Amplitude-Frequency-Response 1949-1955.
IRE Standards on Audio Systems and Components: Methods of Measurement of Gain, Amplification, Loss, Attenuation, and Amplitude-Frequency-Response, 1956.
Proceedings of the IRE, May 1956.

“Gain and loss are generally stated in decibels. Because of long established usage in the audio field, amplification and attenuation ratios are expressed in terms of decibels in this standard, although the more recently introduced term ‘decilog’ is more appropriate.” Page 668.

“By long-standing audio practice amplification is frequently expressed in decibels by multiplying the common logarithm of the ratio by 20, although it would be more appropriate to express this ratio in decilogs.” Page 674.

“By long-standing audio practice attenuation is frequently expressed in decibels by multiplying the common logarithm of the ratio by 20 although it would be more appropriate to express this ratio in decilogs.” Page 681.

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