I was just about to add that to my post #3. Papabravo beats me to it.I think your basic question was why is 3 dB so special?
Well it is because:
\(log_{10} (2) =0.3010\) which makes
\(10 \times log_{10} (2) \;\approx\;3\) and
\(10 \times log_{10} \left ( \frac{1}{2}\right)\;\approx\;-3\)
Hello,
A lot of information on decibels can be found in the links of this page of the EDUCYPEDIA:
http://educypedia.karadimov.info/electronics/decibels.htm
Bertus
I did not understandA bel is the logarithm (base-10) of the power ratio.
1:1 power ratio is 0 bel.
1:10 power ratio is 1 bel.
1:100 power ratio is 2 bel.
1:1000 power ratio is 3 bel.
There are 10 decibels in 1 bel.
Hence,
1:1 power ratio is 0dB.
1:10 power ratio is 10dB.
1:100 power ratio is 20dB.
1:1000 power ratio is 30dB.
1:2 power ratio is 3dB.
How did we arrive at this?
which makes
and
(with thanks to Papabravo, post #5)
In filter circuits, one wishes to identify the roll-off (cut-off, corner or knee point) frequency in the frequency response curve. When the power is reduced to 50% this is the -3dB point, i.e. the gain is -3dB (i.e. the signal is attenuated by 3dB).
View attachment 105993
For a voltage V into a load resistor R, the power into the load is calculated as
\(P = \frac{V^2}{R}\)
Hence the voltage drop at the cut-off frequency is 1/√2 = 0.707 or 70%
When the voltage drops to 50% this represents a power gain of -6dB.
(Note that we need to be careful with our choice of words. When someone says "-3dB attenuation" we know what they mean, i.e. a loss of 3dB. Semantically, "-3dB attenuation" means a "gain of 3dB". The person really means to say "3dB attenuation" or "-3dB gain".)
Thanks for your valuable time and information.For a basic RC low-pass filter, the -3dB point has some significant characteristics.
The corner frequency occurs at ω = 1/RC
i.e. \(2 \pi f = \frac{1}{RC}\)
At this point the impedance of C matches the impedance of R.
The resultant impedance
\(Z = \sqrt{R^2 + {X_c}^2}\)
\(V_{out} = V_{in} \frac{X_c}{Z}\)
From this you can see where the 70% voltage drop appears.
The phase shift is -45° at the -3dB point.
View attachment 106004
Reference: http://www.electronics-tutorials.ws/filter/filter_2.html
actually I was totally blank about this term 3db and it's meaning . I wanted to understand the complete theory of 3db whether it's in terms of gain or loss. I have frequently seen in explain it's Always written -3db that's why I wrote the same.We know what the writer means when they say "-3dB attenuation" but this is incorrect.
Two negatives make a positive. "-3dB attenuation" is literally translated to "3dB gain" but this is not what the writer is trying to express.
The writer should have said "-3dB gain" or "3dB attenuation".
Aha! That is a darn good question.I have no problem understanding the relative meaning of decibels, but I always struggle with the absolute. For instance my home theater receiver dutifully reports the volume setting in decibels. If the wife is out, I can watch a movie at -20dB and have it be gloriously loud. The AV gear heads talk about 0dB being "reference level". What the heck does that mean?