Current ratio expressed in nepers

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SUMMARY

The current input of a system is 250mA, and with a current ratio of 15dB, the output current is calculated to be 1.406A. The conversion of the current ratio from decibels to nepers results in a value of 1.727Np. The formula used for the conversion is α[dB] = 20 log10(Iout/Iin), and the relationship between nepers and decibels is defined as 1 Np ≡ 20 / ln(10) = 8.685889638 dB.

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Homework Statement


The current input of a system is 250mA. If the current ratio of the system is 15dB , determine (i) the current output and (ii) the current ratio expressed in nepers

Homework Equations



\alpha[dB]=20log_{10}(I_{out}/I_{in})

The Attempt at a Solution



current ratio \alpha=15dB, Iin=250mA=0.25A

I_{out}=I_{in}x10^\frac{\alpha [dB]}{20}==0.25x100.75

Iout=0.25x5.623=1.406A

1 Np ≡ 20 / ln(10) = 8.685889638 dB

\alpha[Np]=\alpha[dB]/8.686=1.727Np

Homework Statement

 
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Was there a question associate with this? Your calculation of the output current and Neper value look fine.
 

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