Neper
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For Neper as a mythological god, see Neper (mythology).
In electronics, a neper (Np) is a non-SI unit, accepted for use with SI, used to express ratios, such as gain, 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 bel uses base-10 logarithms to compute ratios, the neper uses base e (2.71828182846...). The value of a ratio in nepers, Np, is given by
- <math>Np = \ln\frac{x_1}{x_2} = \ln x_1 - \ln x_2<math>
where <math>x_1<math> and <math>x_2<math> 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 is usually used to express power ratios. Taking that into account we have
- <math>1\ \mbox{Np} = \frac{20}{\ln 10}\ \mbox{dB} \approx 8.686\ \mbox{dB}<math>
Like the decibel, the neper is a dimensionless unit. The ITU recognizes both units.