Sallen-Key LPF frequency scaling factor

[gehan_s]

Hi all,

I am trying to obtain Butterworth, Chebyshev and Bessal LPF responses with the Sallen-Key topology. I found this app-note from TI and it is very helpful. According to the document if I want a 2nd order Bessal LPF, I just use the equations on top of page 9 (first line) along with table 2 (in the same page). It is quite straight forward.

My questions are am I in the correct path and what is the effect of the frequency scaling factor (FSF)?
The FSF is 1 for Butterworth but for Bessel and Chebyshev it has an effect. Why is that?

Regards

[BTW I have asked a similar question a while back but apparently I had no idea about the subject at that time]

 

[LvW]

My questions are am I in the correct path and what is the effect of the frequency scaling factor (FSF)?
The FSF is 1 for Butterworth but for Bessel and Chebyshev it has an effect. Why is that?

The equations for filter dimensioning are based on pole locations (pole frequency Fp and pole Q).
However, the user normally specifies the 3dB cut-off frequency Fc rather than Fp.
For Butterworth response only: Fp=Fc with FSF=1.

For other low pass responses Fp is NOT identical to Fc. Therefore a scaling factor.

Remark: The S&K topology is very sensitive to the gain factor K.
Therefore, it is recommended to use K=1 (100% feedback) or K=2 with two equal resistors R3=R4.