Larry Brasfield said:
For a single pole low-pass filter, that drop (3.01 dB, actually)
occurs at the frequency where the straight-line projection of the
passband intersects the asymptote of the stopband. For a
series R/shunt C filter, it also where the magnitude of drop
across the R equals the magnitude on the C. So it is readily
calculated by hand, (as things were when that standard arose).
A Larry said, the -3.01 db value falls out of the maths. For a single RC
combination, phase moves between 0 and 90 degrees : at -3.01 db the phase is
half way - 45 degrees.
Also, -3db frequency in radians per sec = 1/( C R )
{ farads, ohms )
When you sketch a Bode diagram, for example when checking the stability of a
feedback loop, you just draw straight lines to the -3db frequency asymptote
intersection points Larry mentioned, and you are close enough in engineering
terms.
So we got 70+ good years out of the -3db concept and that value still pops
out at me when I am writing the transfer function for some network on paper.
However, programs like Spice present a mass of result data and those special
frequencies are less special to us.
Engineering is all about getting a feel for the thing you work with, and
the -3db frequency is like this : its an *interesting* frequency for an
engineer. You generally know your circuit resistance- an estimate of your
capacitance and you calculate the "hot frequency" at -3db. At 3db changes
are happening : rolloff slopes are starting or finishing.
This was especially so in the valve/tube days where you would increase gain
by increasing load resistance, to the point where the -3db frequency was as
low as you could allow.
3 db was a nice fit with the audio world too, because tests on humans showed
that a 3 db change was just discernable to the ordinary listener. Of
course, many careful listeners can do better than that.
Roger Lascelles