Bode Plot - why 20log instead of 10log

[phiby]

Since the deci in decibels means 10, why is decibels of Magnitude in the Bode plot calculated as 20log instead of 10log?

 

[I like Serena]

Hi phiby!

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:

$$P \propto A^2$$
$$10 \cdot \log {P \over P_0} = 10 \cdot \log {A^2 \over A_0^2} = 20 \cdot \log {A \over A_0}$$