-3dB on filters, just approximated?

I have been told that -3dB is when you get half the power or equivalently the original voltage divided by the square root of 2.

Nonetheless, doing the calculations I get 3.01029dB.

I figure this is because the 3dB value is just the aproximated value of what I have gotten but maybe I am mistaken somewhere, so is the 3dB just an approximation or am I mistaken?

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1 Answer

You are not mistaken, it is 3.01 dB

20log$_{10}(\dfrac{1}{\sqrt2})$ = 3.01029995664 !

As a percentage to a voltage ratio, the 0.0103 dB is 0.1186% so not entirely dismissible.

If you were talking about the signal to quantizing-noise ratio of a 24-bit ADC, the error you'd get for using 6 dB (as opposed to 6.02 dB) would be about 0.5 dB. That's an example when the more precise number is used.

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I consider the situation somewhat analogous to "3.58Mhz" crystals. I'm not sure if any devices actually use 3,580,000Hz crystals, but it's faster and easier to refer to a "3.58Mhz" crystal than a "3,579,545hz" crystal even though 3,580,000Hz would be outside the tolerance range of most such crystals. – supercat May 16 '14 at 17:24