# What is the physical interpretation of the dB scale on a bode plot and what is a negative dB?

I have no physical interpretation of the Bode plot. What does it mean for a bode plot to have negative dB over its entire duration on the log-scale frequency?

Decibels (dB) are used to represent a power ratio with a logarithmic scale. Specifically, a power ratio can be expressed in dB as follows:

$$R|_{dB} = 10 \log_{10}R = 10 \ \log_{10}\frac{P_1}{P_2}$$

What does a negative number of dB mean? Manipulate the above equation a bit:

$$R|_{dB} = 10 \log_{10}R$$

$$\frac{R|_{dB}}{10} = \log_{10}R$$

$$10^{\frac{R|_{dB}}{10}} = R$$

If the ratio measured in dB is less than zero, then the exponent on the left hand side will be negative. 10 raised to a negative power results in a number that is in the range $(0, 1)$.

Therefore, if a power ratio measured in dB is less than zero, this implies that, when measured on a linear scale, the ratio is less than one. For a Bode plot, that would mean that the frequency response in question has an amplitude response that is less than unity (for all frequencies, if the Bode plot measured in dB is less than zero everywhere).