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 Vout and Vin, we would calculate as follows (here log is the base 10 logarithm):
magnitude = 10 log(Vout/Vin)2 = 20 log Vout/Vin = 20 log 1/√2 = 20 log 0.707 = -3
Fischer-Cripps. A.C., The Electronics Companion. Institute of Physics, 2005.
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