The *cut-off frequency*, or *3dB point*, is the frequency at which the ratio of input
voltage to output voltage of a
filter or amplifier
is 1/√2.
Note that these are not instantaneous voltages but peak-to-peak or RMS.
The reason for the name "3dB point" comes from the fact that 20 log 1/√2 = -3.
Say we have V_{out} and V_{in}, we would calculate as follows
(here log is the base 10 logarithm):

magnitude = 10 log(V_{out}/V_{in})^{2}= 20 log V_{out}/V_{in}= 20 log 1/√2 = 20 log 0.707 = -3

Fischer-Cripps. A.C., *The Electronics Companion.* Institute of Physics, 2005.

Copyright © 2014 Barry Watson. All rights reserved.