Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.
  • What do these units of measurement mean?

In Analogue Electronic class, the Prof uses $20 \log_{10}$ and in my Networks and Protocols class, the Prof uses $10 \log_{10}$ but they both refer to $\text{decibel}$ (unless my hearing is impaired.)

  • I would like to understand the connection of these two ($20 \log_{10}$ and $10 \log_{10}$) to $\text{bel}$ and $\text{decibel}$.
share|improve this question

1 Answer 1

up vote 4 down vote accepted

The Analogue Electronics prof is talking about amplitudes and the Networks and Protocols prof is talking about powers or intensities. If a signal has intensity $x$ times the intensity of the reference level, it is $\log_{10}(x)$ bels or $10 \log_{10}(x)$ decibels. The intensity is proportional to the square of the amplitude, so this signal's amplitude is $\sqrt{x}$ times the amplitude of the reference level, and $10 \log_{10}(x) = 20 \log_{10}(\sqrt{x})$.

share|improve this answer
    
This makes perfect sense. -b Thank you! –  user31280 Nov 22 '12 at 0:35

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.