Neper
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The neper (symbol: Np) is a logarithmic unit for
ratio In mathematics, a ratio () shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ...
s of measurements of physical field and power quantities, such as gain and loss of electronic signals. The unit's name is derived from the name of
John Napier John Napier of Merchiston ( ; Latinisation of names, Latinized as Ioannes Neper; 1 February 1550 – 4 April 1617), nicknamed Marvellous Merchiston, was a Scottish landowner known as a mathematician, physicist, and astronomer. He was the 8 ...
, the inventor of logarithms. As is the case for the
decibel The decibel (symbol: dB) is a relative unit of measurement equal to one tenth of a bel (B). It expresses the ratio of two values of a Power, root-power, and field quantities, power or root-power quantity on a logarithmic scale. Two signals whos ...
and bel, the neper is a unit defined in the
international standard An international standard is a technical standard developed by one or more international standards organizations. International standards are available for consideration and use worldwide. The most prominent such organization is the International O ...
ISO 80000 ISO/IEC 80000, ''Quantities and units'', is an international standard describing the International System of Quantities (ISQ). It was developed and promulgated jointly by the International Organization for Standardization (ISO) and the Intern ...
. It is not part of the
International System of Units The International System of Units, internationally known by the abbreviation SI (from French ), is the modern form of the metric system and the world's most widely used system of measurement. It is the only system of measurement with official s ...
(SI), but is accepted for use alongside the SI.


Definition

Like the
decibel The decibel (symbol: dB) is a relative unit of measurement equal to one tenth of a bel (B). It expresses the ratio of two values of a Power, root-power, and field quantities, power or root-power quantity on a logarithmic scale. Two signals whos ...
, the neper is a unit in a
logarithmic scale A logarithmic scale (or log scale) is a method used to display numerical data that spans a broad range of values, especially when there are significant differences among the magnitudes of the numbers involved. Unlike a linear Scale (measurement) ...
. While the bel uses the decadic (base-10)
logarithm In mathematics, the logarithm of a number is the exponent by which another fixed value, the base, must be raised to produce that number. For example, the logarithm of to base is , because is to the rd power: . More generally, if , the ...
to compute ratios, the neper uses the
natural logarithm The natural logarithm of a number is its logarithm to the base of a logarithm, base of the e (mathematical constant), mathematical constant , which is an Irrational number, irrational and Transcendental number, transcendental number approxima ...
, based on Euler's number (). The level of a ratio of two signal amplitudes or root-power quantities, with the unit neper, is given by : L = \ln\frac\mathrm, where x_1 and x_2 are the signal amplitudes, and is the natural logarithm. The level of a ratio of two power quantities, with the unit neper, is given by : L = \frac \ln\frac\mathrm, where p_1 and p_2 are the signal powers. In the
International System of Quantities The International System of Quantities (ISQ) is a standard system of Quantity, quantities used in physics and in modern science in general. It includes basic quantities such as length and mass and the relationships between those quantities. This ...
, the neper is defined as .


Units

The neper is defined in terms of ratios of field quantities — also called ''root-power quantities'' — (for example,
voltage Voltage, also known as (electrical) potential difference, electric pressure, or electric tension, is the difference in electric potential between two points. In a Electrostatics, static electric field, it corresponds to the Work (electrical), ...
or current amplitudes in electrical circuits, or
pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and eve ...
in
acoustics Acoustics is a branch of physics that deals with the study of mechanical waves in gases, liquids, and solids including topics such as vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician ...
), whereas the decibel was originally defined in terms of power ratios. A power ratio 10 log ''r'' dB is equivalent to a field-quantity ratio 20 log ''r'' dB, since power in a linear system is proportional to the square ( Joule's laws) of the amplitude. Hence the decibel and the neper have a fixed ratio to each other: : 1\ \text = 20 \log_ e\ \text \approx \text and : 1\ \mathrm = \frac \ln(10)\ \mathrm \approx \text . The (voltage) level ratio is : \begin L & = 10 \log_ \frac & \text \\ & = 10 \log_ ^2 & \text \\ & = 20 \log_ \frac & \text \\ & = \ln \frac & \text. \\ \end Like the decibel, the neper is a dimensionless unit. The
International Telecommunication Union The International Telecommunication Union (ITU)In the other common languages of the ITU: * * is a list of specialized agencies of the United Nations, specialized agency of the United Nations responsible for many matters related to information ...
(ITU) recognizes both units. Only the neper is coherent with the SI.


Applications

The neper is a natural linear unit of
relative difference In any quantitative science, the terms relative change and relative difference are used to compare two quantities while taking into account the "sizes" of the things being compared, i.e. dividing by a ''standard'' or ''reference'' or ''starting'' ...
, meaning in nepers (logarithmic units) relative differences add rather than multiply. This property is shared with logarithmic units in other bases, such as the bel. The derived units decineper (1 dNp = 0.1 neper) and centineper (1 cNp = 0.01 neper) are also used. The centineper for root-power quantities corresponds to a log point or log percentage, see '.


See also

*
Nat (unit) The natural unit of information (symbol: nat), sometimes also nit or nepit, is a unit of information or information entropy, based on natural logarithms and powers of e (mathematical constant), ''e'', rather than the powers of 2 and binary loga ...
* Nepers per metre


References


Works

*


Further reading

* *


External links


What's a neper?Calculating transmission line losses
{{SI units Units of level