Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Bode Plot - why 20log instead of 10log

  1. Nov 19, 2011 #1
    Since the deci in decibels means 10, why is decibels of Magnitude in the Bode plot calculated as 20log instead of 10log?
  2. jcsd
  3. Nov 19, 2011 #2

    I like Serena

    User Avatar
    Homework Helper

    Hi phiby! :smile:

    The Bode plot shows the power gain in dB.
    Power is correlated to the square of the amplitude.
    Since amplitude is used as input, you get an extra factor 2.

    In formula form:

    [tex]P \propto A^2[/tex]
    [tex]10 \cdot \log {P \over P_0} = 10 \cdot \log {A^2 \over A_0^2} = 20 \cdot \log {A \over A_0}[/tex]
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook