Neper

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For Neper as a mythological god, see Neper (mythology), for the lunar crater named Neper, see Neper (crater), and for the Scottish mathematician, phycisist and astronomer, see John Neper.

A neper (Symbol: Np) is a unit of ratio. It is not an SI unit but is accepted for use alongside the SI.

It is used to express ratios, such as gain and loss, and relative values. The name is derived from John Napier, the inventor of logarithms.

Like the decibel, it is a unit in a logarithmic scale, the difference being that where the decibel uses base-10 logarithms to compute ratios, the neper uses base e ≈ 2.71828. The value of a ratio in nepers, Np, is given by

$Np = \ln\frac{x_1}{x_2} = \ln x_1 - \ln x_2$

where $x 1$ and $x 2$ are the values of interest, and ln is the natural logarithm.

The neper is often used to express voltage and current ratios, whereas the decibel was used in early times to express power ratios. Taking that into account we have

$1\ \mbox{Np} = \frac{20}{\ln 10}\ \mbox{dB} = 20 \log_{10} e\ \mbox{dB} = 8{.}685889638 \ \mbox{dB}$