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17th March 2014, 23:29 #1
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sallen key active filter
why are resistor same values for sallen key filter when designing ?

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18th March 2014, 03:26 #2
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Re: sallen key active filter
Same values offer better possible matching but filter parameters are dependent on ratios.
A best design is easily achieved with good test specs™
A better question deserves a better answer. ™
... so include all your acceptance criteria ( values, % tolerance) and assumptions in your question or any design.
... Tony Stewart EE since 1975
 slightly north of Toronto

18th March 2014, 03:31 #3
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18th March 2014, 09:36 #4
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Re: sallen key active filter
Correct  however, does this justify the dimensioning with equal components?
I don`t think so  because this has severe disadvantages.
Selection of equal component values requires a fixed gain rater close to the stability limit (which is "3") and the filter parameter sensitivity upon tolerances is rather large.
A better design is based on unity gain or gain of "2"  with the consequence of unequal resistor values.

18th March 2014, 09:53 #5
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Re: sallen key active filter
Correct  however, does this justify the dimensioning with equal components?
I don`t think so  because this has severe disadvantages.
Selection of equal component values requires a fixed gain rater close to the stability limit (which is "3") and the filter parameter sensitivity upon tolerances is rather large.
A better design is based on unity gain or gain of "2"  with the consequence of unequal resistor values.
As opposite design method, you can chose an arbitrary gain for the Sallen Key filter and calculate R and C values for the intended filter prototype. The stability margin will be always reached with filter Q > infinity.

18th March 2014, 12:00 #6
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Re: sallen key active filter
Ok  I agree. The wording "near the stability limit" may sound a bit too "dramatic".
More than that, my answer was not related to lowpass filters only (the questioner did not speak of lowpass filters only).
What I mean is the following:
1.) For S&K lowpass filters, the "equal component" design (two equal R, two equal C) results in a pole Q of Qp=1/(3Acl) with Acl=closedloop gain.
Example: Chebyshev (1 dB ripple) with Qp=0.9565 and Acl=31/Qp=1.9545.
Hence, both gain determining resistors must have rather tight tolerances to meet this specific gain requirement.
2.) The situation is even more critical for bandpass filters. In this case, the equal component design results in Qp=SQRT(2)/4Acl).
Example: Q=Qp=5 with Acl=3.72. (Note that for Acl=4 the circuit oscillates already).
3.) Sensitivity calculations show that the pole Q is much more susceptible to the two gain determining resistors (active sensitivity) than to the two resistors in the passive network (which define the pole frequency).
Therefore, with regard to component tolerances it seems to be advantageous to use the unity gain concept Acl=1 (opamp with 100% feedback) for both lowpass and bandpass filters  even if we have to live with unequal components.

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18th March 2014, 14:14 #7
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Re: sallen key active filter
I am not sure when it was invented but the SK filter was in common use in 1945, an era of slide rules, nomographs and lined pads. Ease of computation was a major feature of the SK filter. Also in the age of 10% and 20% standard component tolerances only having to stock one or two special tight tolerance parts was a boon. Electrical performance is not always the biggest factor in filter design.
Nowadays, with more computing power than the Apollo space program available at your fingertips, there are many options that used to be impractical.

18th March 2014, 14:48 #8
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