# Question on bel and decibel?

• 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 $\text{decibel}$.
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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 $10 \log_{10}(x) = 20 \log_{10}(\sqrt{x})$.

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