the transformation from power units - Watts to dB are done by:
10*log(Watts)=[dB]
and 3 dB is the half of the whole power.
for example: lets take 5000 [Watts]
10*log(5000)=36.989 [dB]
and now let take only a half of that 2500[Watts]
10*log(2500)=33.979[dB]
as you can see we lost half of our power, and its worth to 3 dB
the importance of the 3dB frequency is for example:
Low Pass Filter - you say tht the cutoff frequency of the filter it's where it stops at least half of the power - this is the 3dB frequency.
the importance of the 3dB frequency is for example:
Low Pass Filter - you say tht the cutoff frequency of the filter it's where it stops at least half of the power - this is the 3dB frequency.
3dB means 0.707 of Maximum Amplitude or half of power (A: amplitude and A^2ower)
\[0.707=\frac{\sqrt{2}}{2}\]
\[\left(\frac{\sqrt{2}}{2}\right)^2=\frac{1}{2}\]
asafbit has written the formulas
For amplifier, u can consider as the frequency at which gain is reduced by 0.707 of its maximum value.
in terms of power its half of maximum value i.e 3db down from maximum value.
I have a doubt regarding the 3dB. Why is it that the 50% or half power point is chosen and why not 75% or any other ratio? What makes 3dB point /half power point important?
You can pick all kinds of arbitrary definitions of bandwidths, just like you can pick all kinds of arbitrary definitions of beamwidths for antennas. 3dB is commonly used and understood.
1. Most of the people feel 50% lost of output power of an audio amplifier.
2. Most of the tests are made with sinusoidal signal.
In that case it is easy to calculate 50% lost of power.
Also 0.707*0.707=0.5
Etc.
As you see there are a lot of real reasons for that level.
But in some cases different levels are imposed depending on the case.