Neper

Neper

The neper is a 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


L_{Np} = \ln\frac{x_1}{x_2} = \ln x_1 - \ln x_2. \,

where x1 and x2 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:


1\ \mbox{Np} = 20 \log_{10} e\ \mbox{dB} \approx 8{.}685889638 \ \mbox{dB} \,

and


1\ \mbox{dB} = \frac{1}{20 \log_{10} e}\ \mbox{Np} \approx 0{.}115129254 \ \mbox{Np}. \,

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


\begin{align}
L & = 10 \log_{10} \frac{x_1^2}{x_2^2} & \mathrm{dB} \\
  & = 10 \log_{10} {\left(\frac{x_1}{x_2}\right)}^2 & \mathrm{dB} \\
  & = 20 \log_{10} \frac{x_1}{x_2} & \mathrm{dB} \\
  & = \ln \frac{x_1}{x_2} & \mathrm{Np}. \\
\end{align}

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

See also

References

  1. ^ Bureau International des Poids et Mesures (2006), The International System of Units (SI) Brochure, 8th edition, pp 127-128.

External links


Wikimedia Foundation. 2010.

Игры ⚽ Нужно сделать НИР?

Look at other dictionaries:

  • neper — ou Napier (John, baron de Merchiston) (1550 1617) mathématicien écossais. Il publia la première table de logarithmes et inventa un instrument appelé bâtons de Neper, ancêtre de la règle à calcul. ⇒NÉPER, subst. masc. PHYS. Unité d expression du… …   Encyclopédie Universelle

  • neper — NEPÉR, neperi, s.m. Unitate de măsură a nivelului de transmisiune al unui semnal electric sau acustic. – Din fr. néper. Trimis de LauraGellner, 10.06.2004. Sursa: DEX 98  néper s. m., pl. néperi; simb. N Trimis de siveco, 10.08.2004. Sursa:… …   Dicționar Român

  • NEPER (J.) — NEPER ou NAPIER JOHN (1550 1617) Mathématicien écossais, John Neper, baron de Merchiston, passa la majeure partie de sa vie dans le manoir familial de Merchiston (près d’Édimbourg) où il naquit et mourut. Violemment anticatholique, il se consacra …   Encyclopédie Universelle

  • Neper — Néper Le néper (symbole Np), bien qu en dehors du système international (SI)[1], est en usage avec lui. Le néper est utilisé pour exprimer la valeur de grandeurs logarithmiques telles que le niveau de champ, le niveau de puissance, le niveau de… …   Wikipédia en Français

  • Neper — Neper, Johann, s. Napier …   Pierer's Universal-Lexikon

  • Neper — Neper, s. Napier 1). Nepersche Rechenstäbchen, s. Rechenmaschine …   Meyers Großes Konversations-Lexikon

  • Neper — Neper, Mathematiker, s. Napier, John …   Kleines Konversations-Lexikon

  • neper — nȅper m DEFINICIJA brojčana jedinica razine, ob. razine snage, upotrebljava se u telekomunikacijama (znak Np) ETIMOLOGIJA prema škotskom matematičaru J. Napieru (1550 1617) …   Hrvatski jezični portal

  • neper — NEPER, Voyez Precopie …   Thresor de la langue françoyse

  • Neper — Ne|per 〈n. 13; ; Math.〉 Kennwort, das auf die Verwendung des natürlichen Logarithmus beim Vergleich zweier Größen bei Dämpfung od. Verstärkung von Stromstärken, Spannungen, Schalldrücken u. a. Feldgrößen hinweist; →a. Bel [nach dem engl.… …   Universal-Lexikon

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”