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 HallofFamer
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 highschool
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
