Hello everyone...... I would like to put another question in this forum. Why do we consider only 3db point for measuring the bandwidth of a signal.If you say that... Half of the output power must be considered for measuring bandwidth.... THEN WHY HALF OF THE OUTPUT POWER?????I mean why not 1/3 or 1/4 of power.can you please clear this doubt...
The attenuation curve does not fall off the cliff abruptly. So you have to choose a reference point somewhere. Half power is as good a reference point as any, similar to half-life and FWHM (full width at half max).
We don't pick ONLY 3db. If you need a noise level or a power supply rejection ratio 60 db below the signal level, you pick -60db. If you are describing a standard bandwidth measurement, use the standard everybody else uses. -3db is on the straight part of the graph and is easy to convert using db/decade or db/octave.
Another consideration is that, in audio, 3dB is near the minimum readily noticeable change in audible sound level.
Yet another reason is that it is nice from a mathematical sense from several viewpoints. For a first order circuit: It occurs when the real and imaginary parts are equal in magnitude in the pole. It's also where the phase angle is half way between where it started and where it will end up. Also, if you define the cutoff frequency to be the reciprocal of the time constant, that is the half power point. Also, if you draw the Bode plot and just point at what looks like a good point to call the cutoff frequency, that is what you are going to pick (or pretty close). Also, if you draw the asymptotes (in a log-log plot) and look at where they intersect, that will be at the half-power frequency. Lots of different things that just scream out, "Use Me!!!" As MrChips noted, we need SOME agreed upon reference and so we might as well pick one that is convenient and easy to work with. If a particular application needs something different, then translating between the normal reference and one that is more applicable is usually pretty simple to do.
What is it that you are hoping to hear? That there is some exact and precise reason why that is the one and only possible value that can be used? Well, it's not. Numerous reasons have been offered as to why half power was a reasonable choice, but at the end of the day it was an arbitrary choice that has become widely, almost universally, accepted as the standard way to describe the frequency response of circuits (and other things).
If you don't like the above stated reason then you will just need to accept it as was sung in Fiddler on the Roof, it's "Tradition".
As WBahn pointed out, the phase shift at -3dB for a simple RC filter is 45°, halfway between 0 and 90°. That sounds like another perfect reason to choose the -3dB point.