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5th July 2019, 14:11 #1
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Why is Corner Frequency always 3db
During my electronic tutorials on filters, I was told that the corner frequency of RL filters and RC filters is where the gain deviates by 3db.
however, there was no stated reason why it had to always be 3db.
I would love to know the reason why it has to be 3db

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5th July 2019, 14:35 #2
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Re: Why is Corner Frequency always 3db
Hi,
a frequently asked question. There there are already discussion here in theis forum and even more in the internet.
Use the links in the box "Similar threads" below.
In short:
It´s not always 3dB.
 3dB means half the power:
Imagine a 2 way speaker box. There is a crossover installed. One is a HPF the other is a LPF. Say both filters have a cutoff at 2.5kHz. Now at exactly this frequency: half of the power comes from the low frequency speaker, the other half of power comes from the high frequency speaker (in ideal case).
Another cause:
Draw a chart (log Xaxis = frequency, linear dB axis) of an LPF (or HPF) there is a flat horizontal line from 0Hz close to fc...then there is a bent line around fc .. then it becomes again a straight line with constant slope.
Now extend the horizontal straight line in direction fc ... and extend the other straight line in direction to fc.
Where these both lines cross is fc (on most linear filters) ... and when you check the attenuation at this frequency: it will be 3dB. (on most linear filters)
(while the Y axis in dB is linear, the amplitude is logarithmic because of the mathematical calculation from amplitude to dB)
KlausPlease don´t contact me via PM, because there is no time to respond to them. No friend requests. Thank you.

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5th July 2019, 17:42 #3
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Re: Why is Corner Frequency always 3db
Excellent explanation by KlausST.
Just to add a tiny bit ... it's calculated from Log10( 1/ 2) = 0.3010299 dB

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5th July 2019, 18:06 #4
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Re: Why is Corner Frequency always 3db
however, there was no stated reason why it had to always be 3db...
It is typical to consider 1/2 value, e.g., half life, halfpower or half of some signal that decays exponentially.
For an exponentially decaying signal, one interesting property is that halfsignal value is constant; it does not depend on the original reference point.
If you have an exponentially decaying signal, and you plot that on a halflog paper (xlin and ylog), you get a straight line.
If you also convert the yaxis scale, 1/2 point will be log(1/2)=log(2)=0.3010 or 3db. That is where the 3db comes in the picture.
Hence, 3db point is the one where the signal becomes 1/2; at 6db point the signal becomes 1/4; at 12db point the signal becomes /16th of the original.
Next question will be the order of the filters. Well, that is another story.

5th July 2019, 18:40 #5

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5th July 2019, 18:59 #6
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Re: Why is Corner Frequency always 3db
Try not to obfuscate the issue...

5th July 2019, 19:27 #7
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