when we consider -3dB bandwidth, the power gets reduced to 50% (and vtg comes down to 70.7%), the response for this value of power shows a linear phase response.

The max power of any system lies above 0.707 times its max value.when we convert it to the db scale,we get -3db i.e bandwidth lies 3b below its max value.

it is the half power point where system achieves maximum power transfer.

@savnaya - i didnt got ur point can u plz elaborate/prove it

http://www.edaboard.com/thread149349.html#post640024

3dB is popular in electrical engineering b/c it is the half-power point (power level reduced by half)

The acoustic sum of 2 identical signals is equal in +3dB.

In the case of a panoramic potentiometer on a console, the present signal on both output is thus decreasing of -3dB in central position.

The 3 DB points are the half power points .Below that the power of a signal drops to less than half of the maximum value and hence are useless from practical point of view as they would need to be amplified to a large extent.That is why bandwidth is defined in terms of the 3DB points .The frequencies that lie within the bandwidth can be used without modification i.e., these are the useful set of frequencies.

My answer did not concern the cutoff frequency, but the general level.

On this subject, we can say that if we place both output in mono, the balance of the information changes as this information was on sides or in the center (+3dB for the information of the center with regard to those of the sides).

also 3dB is the point where an average person can usually detect a volume difference, reliably.. wle..

As it has been mentioned in previous comments, the cutoff frequency by definition corresponds to the point where the output power has dropped to half of its level.

In decibel, if you consider the logarithm of the half power 0.5W you get log10(0.5W) = log10(W) + log10(0.5) = log10(W) - 3.0103. Which is why the -3dB approximation is considered ( and not -1 or -2dB) to get the cutoff frequency.

For all systems the cut-off frequency will not be taken at 3 dB. It represents half power point. For antennas the resonant frequency is taken at 10 dB or 15 dB. It all depends on the system which u r designing.

Your signal is divided by 100 to -3db. Which is already a good attenuation. But the cut-off frequency will depend on your problem. I'm agree with Mr. Jagadeesh Babu.

when the frequency (in X-axis) matches with the cutoff frequency of the filter , the over all gain which is nothing but the magnitude of the transfer function becomes 1/sqt(2).

Eg: if the transfer function looks like: 1/(sT+a), which has one pole inturn contributes one roll off. Here the cut off frequency is 1/T=f and let a=1. Now sub s=jw,

1/iwT+1, whose magnitude is 1/Sqt(w^2 T^2+1^2)

Now, when the frequency w matches with the cut off frequency , i.e. w=1/T, then the magnitude becomes 1/Sqt(2)... As said already , the magnitude is nothing but gain of the transfer function, therefore gain in dB can be calculated as 20log(1/Sqt(2))= -3.010299957

which is ~= -3dB. The negative sign indicates a roll off which is contributed by a pole .

Therefore, when ever your magnitude is reduced by 1/Sqt(2), the gain is 3dB. And when again reduced by the same amount of 1/Sqt(2), it becomes simply as 1/2 , for which the gain will be 6dB.and it goes on .....

So the 'engineers' can only tell us a cow is a cow and 3dB represents 'half' and spend page after page of maths and waffle obfuscating that they really don't have a clue (chuckles), The question was WHY 3dB, not HOW it is arrived-at mathematically and answers (notably plagiarised across internet) give no statement of 'why'.

Because it is "half power" is no explanation, nor is a complex log equation. The maximum power transfer of one explanation above is achieved when load and line have the same impedance, but not 'at 3dB'.

The '3dB' explanation of 'discernible audible change' is not truly objective and has no application above audible frequency. It is true that 3 dB has become a 'convention'...but that again avoids explanation. Could it be that it is the point at a certain roll-off where in achieving it first order R and C exhibit the same impedance?...and that became a convention? Could it be that 'just below the knee of the performance curve' is a practical point' for filter design parameter based on the starting point of R and C impedance influence? without unacceptable signal loss?

Could it be a practical attenuation?...well, one might ask what that has to do with practical bandwidth... If a signal at IF frequency is being shaved of nearby signals the bandpass must be limited in practical use. If very narrow or very wide it may frustrate the human user and at peak on a narrow bandwidth the signal might be indecipherable. Could it be that when impedance of components in the bandpass filter match, there is minimal distortion in the roll-off .

That 3 dB might correspond with '0.707' is a result, not an explanation and not specific to the issue. 3 dB "of itself" is irrelevant to the issue as is the maths used to obfuscate the fact they have no idea.....

For 'some' reason ("what reason"?..is the real issue here) we WORK to a 3dB parametric cut off. Could it be that competent designers want to see a point at which distortion of the waveform (as well as slope) are minimised and thus looking at ultimately "pure resistance" influences in a circuit design. Such influences will not even exist at optimum factors...frequency stability, no external influences, component perfection and application but are, at some point in moment or desired achievement, gauged as starting point, working parameter and finishing point in design. The concept of pure resistance depends on capacitance and inductance 'equalling each other out" which is poor English of course. A resistor made of say spiral cutting or wire wound or layered construction has electronic features other than resistance. This is relevant to filter design.

Resistance and impedance are not the same thing even though they may have the same unit. Capacitors are not pure resistance but a combination of out- of- phase resistances. Once say a resistor in a simple first-order filter shifts value or a capacitor changes value, however incrementally neither matches the at least 'notionally' pure resistor's value. Changes may be owing to say heat, age, construction even proximity-introduced factors. Those changes will affect the shape and slope of the signal. In designing filters one needs to have a starting point and an 'arbitrary' 3dB choice, whilst maybe conceived and born of good old electronics development tradition is of no use unless it provides a design relevance which will be universally adopted. The slope of the roll-off of a bandwidth offers a couple of influences on design and one is that it rapidly increases bandwidth, yet we need to form/create a picture in bandpass which somewhere below the knee of the waveform peak allows us to introduce controls whilst maintaining intelligibility.

Rather than join the "engineering waffle" here and on internet I've spent time redirecting, I hope, the focus of the engineers. Will my suggestions help the graduate engineers to now give answers appropriate and in precise filter engineering as to why 3dB is the chosen cut-off point, or... if you like ... starting point in bandwidth design? (lighthearted chuckles)...my regards