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The decibel is a "dimensionless unit" (like percent) that is a measure of ratios on a logarithmic scale.
Usually, it is ten times the base-10 logarithm of the ratio.
It's not an SI unit, although the International Committee for Weights and Measures (BIPM) has recommended its inclusion in the SI system.
History of Bels and Decibels
A bel (symbol B) is a unit of measure of ratios; (such as power levels and voltage levels). It was 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 was too large for everyday use, so the decibel (dB), equal to 0.1 B, became more commonly used:
- decibels = 10 log10(ratio)
(However, note that ratios of voltages and currents are calculated differently, because of the historical use of decibels to measure power ratios. See below.)
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 explicitly stated.
Uses
Acoustics
The decibel is often used in acoustics to quantify sound levels relative to some 0 dB reference. The reference may be defined as a sound pressure level (SPL), commonly 20 micropascal (20 μPa). To avoid confusion with other decibel measures, the term dB(SPL) is used for this. The reference (0 dB SPL) can also be defined as the sound pressure at the threshold of human hearing, which is conventionally taken to be 2 newton per square metre, 2 N/m² or 2 pascal. That is roughly the sound of a mosquito flying 10 feet (3 m) away. The ears are only sensitive to sound pressure deviations.
The reason for using the decibel is that the ear is capable of hearing a very large range of sound pressures. The ratio of the sound pressure that causes permanent damage from short exposure to the limit that (undamaged) ears can hear is more than 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 more than 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.
Psychologists have found that our perception of loudness is roughly logarithmic—see the Weber-Fechner Law. In other words, you have to multiply the sound pressure by the same factor to have the same increase in loudness. This is why the numbers around the volume control dial on a typical audio amplifier are related not to the voltage amplification, but to its logarithm.
Various frequency weightings are used for acoustical measurements to approximate the changes in sensitivity of the ear to different frequencies at different levels. These include the dBA, dBB, and dBC weightings.
Sounds above 85 dB are considered harmful, while 120 dB is unsafe and 150 dB causes physical damage to the human body. Windows break at about 163 dB. Jet airplanes are about 133 dBA at 33 m, or 100 dBA at 170m. Eardrums rupture at 190 to 198 dB. Shock waves and sonic booms are about 200 dB at 330 m. Sounds around 200 dB can cause death to humans and are generated near bomb explosions (e.g. 23 kg of TNT detonated 3 m away). The space shuttle is around 215 dB (or about 175 dBA at 17m). Nuclear bombs are 240 dB to 258 dB (distance unknown—values useless). Even louder are earthquakes, tornadoes, hurricanes and volcanoes.
Some other values:
All dBSPL values of noise sources need the distance of the measurement. When that is forgotten the given value is really useless.
Weighting
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 2,000 and 4,000 hertz)—are factored more heavily into sound descriptions in a process called "A-weighting", written as dBA. The A-weighted scale parallels the sensitivity of the human ear, and uses the lowest audible sound that the human ear can detect as the reference point for determining the decibel level of a noise.
Under controlled conditions, in an acoustical laboratory, the trained healthy human ear is able to discern changes in sound levels of 1 dBA, when exposed to steady, single frequency ("pure tone") signals in the mid-frequency range. It is widely accepted that the average healthy ear, however, can barely perceive noise level changes of 3 dBA.
On this scale, the normal range of human hearing extends from about 0 dBA to about 140 dBA. One dBA is the threshold of hearing. A 10 dBA increase in the level of a continuous noise represents a perceived doubling of loudness; a 5 dBA increase is a readily noticeable change, while a 3 dBA increase is barely noticeable to most people.
From other point of view, the most widely used sound level filter is the A scale, which roughly corresponds to the inverse of the 40 dB (at 1 kHz) equal-loudness curve. Using this filter, the sound level meter is thus less sensitive to very high and very low frequencies. Measurements made on this scale are expressed as dBA.
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 ear.
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". Zero dBm is one milliwatt, and 1 dBm 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.
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 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.
Telecommunications
In telecommunications, decibels are commonly used to measure signal-to-noise ratios and other ratio measurements.
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 analog audio, power measurement relative to 1 milliwatt into a 600 ohm load
- dBW
- dB(1 W@600 Ω)—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
- dBm
- dB(mV/m²)—millivolts per square metre. Signal strength of a radio signal.
- dBμ or dBu
- dB(μV/m²)—microvolts per square metre. The strength of a radio signal.
- dBf
- dB(fW)—femtowatts. The amount of power required to drive a radio receiver.
- dBW
- dB(W)—watts. The amount of power transmitted by a low-power radio station.
- dBk
- dB(kW)—kilowatts. The amount of power transmitted by a broadcast radio station.
Acoustics
- dBSPL
- dB(Sound Pressure Level)—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 meters away.
Relative measurements
- dBA, dBB, dBC weighting
- Different frequency weightings used to approximate the human ear's response to sound. Also written dBA or sometimes dB(A).
- dBd
- dB(dipole)—the effective radiated power compared to a dipole antenna.
- dBi
- dB(isotropic)—the effective radiated power compared to an imaginary isotropic antenna.
- dBFS or dBfs
- 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 would equal the highest level (number) the processor is capable of representing. (Measured values are negative, since they are less than the maximum.)
- dBr
- 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
- dB above reference noise.
Common misconceptions
+/-3dB is roughly double/half power (equal to a ratio of 1.995). That's 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 numbers are very close to being equally spaced in terms of their logarithms. The actual values would be 1, 2.15, 4.64, 10 ... .
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 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.
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.
The 4 → 6 Rule
To one decimal place of precision, 4.x is 6.x in dB.
Examples:
- 4.0 → 6.0 dB
- 4.3 → 6.3 dB
- 4.7 → 6.7 dB
The "789" Rule
To one decimal place of precision, x → (½ x + 5.0 dB) for 7.0 ≤ x ≤ 10.
Examples:
- 7.0 → ½ 7.0 + 5.0 dB = 3.5 + 5.0 dB = 8.5 dB
- 7.5 → ½ 7.5 + 5.0 dB = 3.75 + 5.0 dB = 8.75 dB
- 8.2 → ½ 8.2 + 5.0 dB = 4.1 + 5.0 dB = 9.1 dB
- 9.9 → ½ 9.9 + 5.0 dB = 4.95 + 5.0 dB = 9.95 dB
- 10.0 → ½ 10.0 + 5.0 dB = 5.0 + 5.0 dB = 10 dB
See also
External links
Reference
- Martin, W. H., "DeciBel – The New Name for the Transmission Unit", Bell System Technical Journal, January 1929.
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