# Neper

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The neper is a dimensionless logarithmic unit for ratios 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.[1]

## Contents

### Definition

Like the decibel, 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 x1 and x2 are the values of interest, and ln is the natural logarithm.

The neper is used, albeit not frequently, to express ratios of voltage and current amplitudes in electrical circuits, or pressure in acoustics, whereas the decibel is used to express power ratios. One kind of ratio may be converted into the other. Wave power is proportional to the square (Joule's laws) of the amplitude:

and

The decibel and the neper have a fixed ratio to each other. The (voltage) level is

Like the decibel, the neper is a dimensionless unit. The International Telecommunication Union (ITU) recognizes both units.

### References

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