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What's a Neper?

Updated April 18, 2014

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The Neper (Np) is similar to the decibel (dB). It's unitless and is used to express ratios. The Neper uses the natural logarithm, and is named after Microwave Hall-of-Famer John Napier. Instead of using the logarithm function (base 10), the Neper uses the base "e". For voltage ratio of a/b, the difference in calculation is shown here:

dB=20*log(a/b)

Np=ln(a/b)

The difference between a dB and a Neper is just a fixed ratio. This is computed by dividing the two equations:

dB/Np=20*log(a/b)/ln(a/b) = 20/ln(10)=8.68588

The simplification is done by noting that ln(x)=log(x)*ln(10), if you remember your high-school math. Nepers are typically used in loss calculations in the attenuation constant of the propagation constant:

= + j

where is in nepers/meter.

This is important, so remember it!

How about we immortalize the Neper conversion as Microwaves101 Rule of Thumb #119:

To convert Nepers to decibels, multiply by (approximately) 8.68.

More accurately,

dB/Np = 20/ln(10)=8.68588

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