Quote: Decibels (dB). A logarithmic representation of amplitude ratio, defined as 20 times the base ten logarithm of the ratio of the measured amplitude to a reference.
dB = 20 log (Vx/Vref). In this instance, Vref = 1, dB = -3
-3/20 = log Vx
Vx= 10^(-0.15) = 0.70795
Bizarrely, I think that I've often seen that rounded to 70.7%, even though it should be 70.8%. Maybe it's because it's so close to root 2.
For reference, this is when talking about voltage or current. When talking about power the equation changes and becomes 10 log (Vx/Vref) as you expected.
Let's say that you have an amplifier driving a speaker. The power from the speaker is given as V^2/R. So let's look at our power at that -3dB point relative to the peak;
Now at this -3dB voltage point, the power generated in the speaker is (0.708^2)/R = 0.501/R, ie half that generated at the peak. That is why the -3dB voltage point is also known as the half power point.
So the -3dB point is -3dB regardless of whether we are talking about voltage or power, even though one is a function of the other squared. It also holds for current equations too, dB(I) = 20 log (Ix/Iref), as Power = I^2R.
Basically it all boils down to log a^b = b log a. The equations are different to give the same answer despite the square relationship between voltage/current and power.
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