Decibel
The decibel (symbol: dB) is a relative unit of measurement equal to one tenth of a bel (B).
The definition of the decibel originated in the measurement of transmission loss and power in telephony of the early 20th century in the Bell System in the United States.
Instead, the decibel is used for a wide variety of measurements in science and engineering, most prominently for sound power in acoustics, in electronics and control theory.
In electronics, the gains of amplifiers, attenuation of signals, and signal-to-noise ratios are often expressed in decibels.
The decibel originates from methods used to quantify signal loss in telegraph and telephone circuits.
1 MSC corresponded to the loss of power over one mile (approximately 1.6 km) of standard telephone cable at a frequency of 5000 radians per second (795.8 Hz), and matched closely the smallest attenuation detectable to a listener.
In 1928, the Bell system renamed the TU into the decibel,[8] being one tenth of a newly defined unit for the base-10 logarithm of the power ratio.
The new transmission unit is widely used among the foreign telephone organizations and recently it was termed the "decibel" at the suggestion of the International Advisory Committee on Long Distance Telephony.
This method of designating the gain or loss of power in telephone circuits permits direct addition or subtraction of the units expressing the efficiency of different parts of the circuit ...In 1954, J. W. Horton argued that the use of the decibel as a unit for quantities other than transmission loss led to confusion, and suggested the name logit for "standard magnitudes which combine by multiplication", to contrast with the name unit for "standard magnitudes which combine by addition".
This is because the definitions were originally formulated to give the same value for relative ratios for both power and root-power quantities.
Thus, the following definition is used: The formula may be rearranged to give Similarly, in electrical circuits, dissipated power is typically proportional to the square of voltage or current when the impedance is constant.
A factor of 2 is introduced to make changes in the respective levels match under restricted conditions such as when the medium is linear and the same waveform is under consideration with changes in amplitude, or the medium impedance is linear and independent of both frequency and time.
Its application in systems with additive effects is less intuitive, such as in the combined sound pressure level of two machines operating together.
The logarithmic scale nature of the decibel means that a very large range of ratios can be represented by a convenient number, in a manner similar to scientific notation.
For example: However, according to its critics, the decibel creates confusion, obscures reasoning, is more related to the era of slide rules than to modern digital processing, and is cumbersome and difficult to interpret.
According to Mitschke,[26] "The advantage of using a logarithmic measure is that in a transmission chain, there are many elements concatenated, and each has its own gain or attenuation.
To obtain the total, addition of decibel values is much more convenient than multiplication of the individual factors."
Attenuation constants, in topics such as optical fiber communication and radio propagation path loss, are often expressed as a fraction or ratio to distance of transmission.
These quantities are to be manipulated obeying the rules of dimensional analysis, e.g., a 100-meter run with a 3.5 dB/km fiber yields a loss of 0.35 dB = 3.5 dB/km × 0.1 km.
[34] Use of the decibel in underwater acoustics leads to confusion, in part because of this difference in reference value.
The reference values of I and p in air have been chosen such that this corresponds approximately to a sound pressure level of 120 dB re 20 μPa.
Since the human ear is not equally sensitive to all sound frequencies, the acoustic power spectrum is modified by frequency weighting (A-weighting being the most common standard) to get the weighted acoustic power before converting to a sound level or noise level in decibels.
Similarly, in telecommunications, decibels denote signal gain or loss from a transmitter to a receiver through some medium (free space, waveguide, coaxial cable, fiber optics, etc.)
In an optical link, if a known amount of optical power, in dBm (referenced to 1 mW), is launched into a fiber, and the losses, in dB (decibels), of each component (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.
Most commonly, quantities called "dynamic range" or "signal-to-noise" (of the camera) would be specified in 20 log dB, but in related contexts (e.g. attenuation, gain, intensifier SNR, or rejection ratio) the term should be interpreted cautiously, as confusion of the two units can result in very large misunderstandings of the value.
Photographers typically use an alternative base-2 log unit, the stop, to describe light intensity ratios or dynamic range.
Suffixes are commonly attached to the basic dB unit in order to indicate the reference value by which the ratio is calculated.
This form of attaching suffixes to dB is widespread in practice, albeit being against the rules promulgated by standards bodies (ISO and IEC),[15] given the "unacceptability of attaching information to units"[a] and the "unacceptability of mixing information with units".
[b] The IEC 60027-3 standard recommends the following format:[14] Lx (re xref) or as Lx/xref, where x is the quantity symbol and xref is the value of the reference quantity, e.g., LE (re 1 μV/m) = 20 dB or LE/(1 μV/m) = 20 dB for the electric field strength E relative to 1 μV/m reference value.
Sometimes the suffix is a unit symbol ("W","K","m"), sometimes it is a transliteration of a unit symbol ("uV" instead of μV for microvolt), sometimes it is an acronym for the unit's name ("sm" for square meter, "m" for milliwatt), other times it is a mnemonic for the type of quantity being calculated ("i" for antenna gain with respect to an isotropic antenna, "λ" for anything normalized by the EM wavelength), or otherwise a general attribute or identifier about the nature of the quantity ("A" for A-weighted sound pressure level).
