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2-pole active filter question

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Hi audioguru,

The cutoff frequency is defined as the point where the normal passband gain drops to -3db. Thus you cant have a cutoff frequency 'fc' that is -6db.
........
I'm pretty sure you know this already so maybe you worded your post a little incorrect.
I tried to explain that a droopy lowpass Bessel filter type has two independent RC filters that are calculated to produce a -3db response EACH then both produce a total of -6dB.
Then I explained how a lowpass Butterworth filter provides boost from positive feedback so that the total response from both RC filters results in only -3dB at their calculated frequency.
 
Hi again,


Just thought i would add an extra note for this thread. In the Texas Instrument paper they quote values in Figure 5 and state that the cutoff frequency is 1kHz for each set of values.
Well, they show three sets, and the only one that comes out to very close to 1kHz is the Butterworth type. The "3-dB Chebyshev" comes out to 1158.3Hz, which for a paper like that i think is too far off when it is easy enough to select values that will come much closer to the stated frequency of 1kHz. And this has been checked using two different formulas.
I just wanted to mention this in case anyone else tries to compare their calculation results with the TI paper then they should beware that the TI paper may not be that accurate when it comes to the calculated values. They are not extremely far off, but far enough off i think to warrant some caution when using that paper as a reference guide, as your results will differ from theirs.

Also, the damping factor for the Multiple Feedback LP filter is:

[LATEX]d=\frac{\frac{1}{C2\,R3}+\frac{1}{C2\,R2}+\frac{1}{C2\,R1}}{2\,w_0}[/LATEX]

and so the FSF given previously can be used to calculate fc from f0 as before:

fc=FSF*f0

and again note that this 'FSF' is the reciprocal of the FSF given in the TI paper.

And now w0 is:

[LATEX]w_0=\frac{1}{\sqrt{C1\,C2\,R2\,R3}}[/LATEX]

It is also again interesting that the 3-dB Chebyshev frequency fc in the TI paper is off again by a substantial amount, calculating out to 1.3kHz rather than the stated 1kHz.
 
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