English

Etymology

From a misspelling of Napier English mathematician.

Pronunciation

• Rhymes with: -eɪpə(r)

Noun

1. A unit of attenuation used in transmission line theory; equivalent to 8.686 dB.

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 Napier.

A neper (Symbol: Np) is a logarithmic 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 = \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 ratios of voltage and current amplitudes in electrical circuits (or pressure in acoustics), whereas the decibel is used to express power ratios. Taking into account that the power is proportional to the square of the current or voltage, we have 1\ \mbox = \frac\ \mbox = 20 \log_ e\ \mbox \approx 8685889638 \ \mbox \,

and 1\ \mbox = \frac\ \mbox = \frac\ \mbox \approx 0115129254 \ \mbox \, .

The decibel and the neper have a fixed ratio to each other. The (voltage) level is: \begin L & = 10 \lg \frac & \mathrm \\ & = 10 \lg ^2 & \mathrm \\ & = 20 \lg \frac & \mathrm \\ & = \ln \frac & \mathrm \\ \end

Like the decibel, the neper is a dimensionless unit. The ITU recognizes both units.

External links

• What's a neper?
• Conversion of level gain and loss: neper, decibel, and bel
• Calculating transmission line losses

Sources

• Federal Standard 1037C
• MIL-STD-188