Relation between nepers and decibels

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Problem 2.17

The natural logarithm of the ratio of two amplitudes is measured in nepers. Show that one neper = 8.68 dB.

Background

By definition, if and are energies, is the value of the ratio in bels. One bel = 10 decibels (dB), and energy is proportional to (amplitude), so


(2.17a)

Solution

Let value measured in nepers, dB = same value in decibels. Then,

Since .

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Relation between nepers and decibels
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