Neper
Encyclopedia
The neper is a logarithmic unit for ratio
s of measurements of physical field and power quantities, such as gain
and loss of electronic signals. It has the unit symbol Np. The unit's name is derived from the name of John Napier
, the inventor of logarithms. As is the case for the decibel
and bel, the neper is not a unit in the International System of Units
(SI), but it is accepted for use alongside the SI.
, the neper is a unit in a logarithmic scale
. While the bel uses the decadic (base-10) logarithm
to compute ratios, the neper uses the natural logarithm
, based on Euler's number (e
≈2.71828). The value of a ratio in nepers is given by
where
and 
are the values of interest, and ln is the natural logarithm.
The neper is defined in terms of ratios of field quantities (for example, voltage
or current amplitudes in electrical circuits, or pressure
in acoustics
), whereas the decibel was originally defined in terms of power
ratios. A power ratio 10log(ratio) dB is equvalent to a field-quantity ratio 20log(ratio) dB, since power is proportional to the square (Joule's laws) of the amplitude. Hence the neper and dB are related via:
and
The decibel and the neper have a fixed ratio to each other. The (voltage) level ratio is
Like the decibel, the neper is a dimensionless unit. The International Telecommunication Union
(ITU) recognizes both units.
Ratio
In mathematics, a ratio is a relationship between two numbers of the same kind , usually expressed as "a to b" or a:b, sometimes expressed arithmetically as a dimensionless quotient of the two which explicitly indicates how many times the first number contains the second In mathematics, a ratio is...
s of measurements of physical field and power quantities, such as gain
Gain
In electronics, gain is a measure of the ability of a circuit to increase the power or amplitude of a signal from the input to the output. It is usually defined as the mean ratio of the signal output of a system to the signal input of the same system. It may also be defined on a logarithmic scale,...
and loss of electronic signals. It has the unit symbol Np. The unit's name is derived from the name of John Napier
John Napier
John Napier of Merchiston – also signed as Neper, Nepair – named Marvellous Merchiston, was a Scottish mathematician, physicist, astronomer & astrologer, and also the 8th Laird of Merchistoun. He was the son of Sir Archibald Napier of Merchiston. John Napier is most renowned as the discoverer...
, the inventor of logarithms. As is the case for the decibel
Decibel
The decibel is a logarithmic unit that indicates the ratio of a physical quantity relative to a specified or implied reference level. A ratio in decibels is ten times the logarithm to base 10 of the ratio of two power quantities...
and bel, the neper is not a unit in the International System of Units
International System of Units
The International System of Units is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. The older metric system included several groups of units...
(SI), but it is accepted for use alongside the SI.
Definition
Like the decibelDecibel
The decibel is a logarithmic unit that indicates the ratio of a physical quantity relative to a specified or implied reference level. A ratio in decibels is ten times the logarithm to base 10 of the ratio of two power quantities...
, the neper is a unit in a logarithmic scale
Logarithmic scale
A logarithmic scale is a scale of measurement using the logarithm of a physical quantity instead of the quantity itself.A simple example is a chart whose vertical axis increments are labeled 1, 10, 100, 1000, instead of 1, 2, 3, 4...
. While the bel uses the decadic (base-10) logarithm
Logarithm
The logarithm of a number is the exponent by which another fixed value, the base, has to be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the power 3: More generally, if x = by, then y is the logarithm of x to base b, and is written...
to compute ratios, the neper uses the natural logarithm
Natural logarithm
The natural logarithm is the logarithm to the base e, where e is an irrational and transcendental constant approximately equal to 2.718281828...
, based on Euler's number (e
E (mathematical constant)
The mathematical constant ' is the unique real number such that the value of the derivative of the function at the point is equal to 1. The function so defined is called the exponential function, and its inverse is the natural logarithm, or logarithm to base...
≈2.71828). The value of a ratio in nepers is given by
where
and are the values of interest, and ln is the natural logarithm.The neper is defined in terms of ratios of field quantities (for example, voltage
Voltage
Voltage, otherwise known as electrical potential difference or electric tension is the difference in electric potential between two points — or the difference in electric potential energy per unit charge between two points...
or current amplitudes in electrical circuits, or pressure
Sound pressure
Sound pressure or acoustic pressure is the local pressure deviation from the ambient atmospheric pressure caused by a sound wave. Sound pressure can be measured using a microphone in air and a hydrophone in water...
in acoustics
Acoustics
Acoustics is the interdisciplinary science that deals with the study of all mechanical waves in gases, liquids, and solids including vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician while someone working in the field of acoustics...
), whereas the decibel was originally defined in terms of power
Power (physics)
In physics, power is the rate at which energy is transferred, used, or transformed. For example, the rate at which a light bulb transforms electrical energy into heat and light is measured in watts—the more wattage, the more power, or equivalently the more electrical energy is used per unit...
ratios. A power ratio 10log(ratio) dB is equvalent to a field-quantity ratio 20log(ratio) dB, since power is proportional to the square (Joule's laws) of the amplitude. Hence the neper and dB are related via:
and
The decibel and the neper have a fixed ratio to each other. The (voltage) level ratio is
Like the decibel, the neper is a dimensionless unit. The International Telecommunication Union
International Telecommunication Union
The International Telecommunication Union is the specialized agency of the United Nations which is responsible for information and communication technologies...
(ITU) recognizes both units.