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Chapter 14. Decibels (dB)

Power and Voltage Ratios

If you browse through the technical specs of your stereo amplifier or your boom box, you'll notice that some parameters are specified in dB. For example: S/N ratio: 70dB; channel separation: 60dB.

What does this mean?

dB is defined as 10∙log(P1/P2)

Since P1 = V12/R and P2 = V22/R, we can also write: dB = 10∙log(V12/V22) = 20∙log(V1/V2)

In case of a signal-to-noise ratio (S/N ratio or SNR), dB = 20∙log(Vsig/Vnoise)

Knowing this, we can calulate the Vsig:Vnoise ratio if the S/N ratio is 70dB:

70dB = 20∙log(Vsig/Vnoise) => log(Vsig/Vnoise) = 70/20 = 3.5 => Vsig/Vnoise = 103.5 = 3162. This means that the music signal is 3162 times stronger than the noise generated by the amplifier.

Channel separation indicates how much signal meant for the right channel is present in the left channel and vice versa. If the channel separation is 60dB, the wanted channel signal is 1060/20 = 1000 times stronger than the unwanted channel signal. In other words: if you only listen to the left loudspeaker, you will also hear the music that should only come from the right speaker. However, this 'unwanted channel signal' is 1000 times weaker than the music coming from the right speaker.

In the previous lesson, we learnt that the attenuation of an RL filter is about 10 times per decade. How much is this in dB?

Since we were looking at the voltage attenuation, the attenuation of an RL filter is 20∙log(10) = 20dB per decade.