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Bel.
Bel
For Bel as a Semitic title of a god, see Bel (god); for the Celtic deity, see Belenus
A bel (symbol B) is a unit of measure of ratios of power levels, i.e., relative power levels. It is mostly used in telecommunication, electronics and acoustics. Invented by engineers of the Bell Telephone Laboratory,it was originally called the transmission unit or TU, but was renamed in 1923 or 1924 in honour of the laboratory's founder and telecommunications pioneer Alexander Graham Bell.
The bel is a logarithmic measure. The number of bels for a given ratio of power levels is calculated by taking the logarithm, to the base 10, of the ratio. Therefore, one bel corresponds to a power ratio of 10:1. Mathematically, the number of bels is calculated as b = log10(P1/P2) where P1 and P2 are power levels. The neper is a similar unit which uses the natural logarithm. The Richter scale uses numbers expressed in bels as well, though this is implied by definition rather than expressly stated.
The bel is too large for everyday use, so the decibel (dB), equal to 0.1 B, is more commonly used. One decibel is equivalent to a ratio of about 1.259:1.
The number of decibels is calculated as 10 log10(P1/P2) where P1 and P2 are the powers.
The decibel is a dimensionless "unit". The decibel is not an SI unit, although the CIPM has recommended its inclusion in the SI system.
Table of contents showTocToggle("show","hide")
1 Uses
1.1 Optics
1.2 Acoustics
1.3 Electronics
1.4 Telecommunications
1.5 Seismology
2 Typical abbreviations
3 Common misconceptions
3.1 +3 dB means "two times" the power and 1.414 times the voltage
3.2 +6 dB means "two times" the voltage and four times the power
4 References
4.1 External links
Uses
Optics
In an optical link, if a known amount of optical power, in dBm (decibel.milliwatts), is launched into a fibre, and the losses, in dB (decibels), of each 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.
Acoustics
See Bel (Acoustics)
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.
In radio electronics, 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". 0 dBm is one milliwatt, and 1dBm is one decibel greater than 0 dBm, or about 1.259 mW.
Although decibels were originally used for power ratios, they are nowadays commonly used in electronics to describe voltage or current ratios. In a constant resistive load, power is proportional to the square of the voltage or current in the circuit. Therefore, the decibel ratio of two voltages V1 and V2 is defined as 20 log10(V1/V2), and similarly for current ratios. Thus, for example, a factor of 2.0 in voltage is equivalent to 6.02 dB (not 3.01 dB!).
This practice is fully consistent with power-based decibels, provided the circuit resistance remains constant. However, voltage-based decibels are frequently used to express such quantities as the voltage gain of an amplifier, where the two voltages are measured in different circuits which may have very different resistances. For example, a unity-gain buffer amplifier with a high input resistance and a low output resistance may be said to have a "voltage gain of 0 dB", even though it is actually providing a considerable power gain when driving a low-resistance load. Although this is pedantically deplorable, it is actually a very common practice and seems likely to persist.
Telecommunications
In telecommunications, decibels are commonly used to measure signal-to-noise ratios.
Seismology
Earthquakes are measured on the Richter scale, which is expressed in bels. (The units in this case are always assumed, rather than explicit.)
Typical abbreviations
Absolute measurements:
Electric power:
- dBm or dBmW - dB(1 mW@600 Ω) - in analogue audio, power measurement relative to 1 milliwatt into a 600-ohm load
- dBW - same as dBm, with reference level of 1 watt.
Electric voltage:
- dBu or dBv - dB(0.775 V) - (usually RMS) voltage amplitude referenced to 0.775 volts, not related to any impedance. dBu is preferable, since dBv is easily confused with dBV. The "u" comes from "unloaded".
- dBV - dB(1 V) - (usually RMS) voltage amplitude of an audio signal in a wire, relative to 1 volt, not related to any impedance.
Radio power:
Acoustics:
- dB SPL - (Sound Pressure Level) relative to 20 micropascals (μPa), the quietest sound a human can hear. Roughly the sound of a mosquito flying 3 meters away.
Relative measurements:
- dB(A), dB(B), or dB(C) - different frequency weightings used to approximate the human ear's response to sound. Also written dBA, etc.
- dBd - dB(dipole) - effective radiated power compared to a dipole antenna
- dBi - dB(isotropic) - effective radiated power compared to an imaginary isotropic antenna
- dBFS or dBfs - dB(full scale) - amplitude of a signal (usually audio) compared to the maximum which a device can handle before clipping occurs. In digital systems, 0 dBFS would equal the highest level (number) the processor is capable of representing.
- dBr - simply a relative difference to something else, which is made apparent in context. Difference of a filter's response to nominal levels, for instance.
Common misconceptions
+3 dB means "two times" the power and 1.414 times the voltage
+6 dB means "two times" the voltage and four times the power
Not exactly. 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 103/10. 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 2120/3 = 240 = 1.0995 × 1012, for a 10% error.
But the voltage ratio is only 106 or one million. Clear?
References
- Martin, W. H., "DeciBel – The New Name for the Transmission Unit", Bell System Technical Journal, January 1929.
External links
The above article is adapted from from Wikipedia All Wikipedia article text is available under the terms of the GNU Free Documentation License
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