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-3db equates to half of the original power.
if you had 1 watt input. and the output is 1/2 watt.
The power gain is calculated by 10 log (Pin/Pout)
( in bels its log(Pin/Pout) in decibels its 10 log (Pin/Pout) )
That is 10 log (1/ 1/2) = 10 log 2 = -3 that's -3db for you
It communications and in so many other fields. the 3db mark is taken as kind of datum for useful power. that is to say beyond this the magnitude will reduce below half.
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