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I'm designing a low pass active filter with a Butterworth response. The passband is DC to 1.5 kHz, so the -3 dB cut off frequency should be around 2-5 kHz to be safe.

The topology I've decided to use is a second order Sallen-Key, unity gain filter. The schematic can be found below.

I'm a bit confused on how to achieve a Butterworth response, though. From my understanding, the quality factor, Q, has to be 0.707 for a Butterworth response. However, I also read that A = 3 - 1/Q, where A is the gain and Q is the quality factor. With a unity gain topology (A = 1), this would give a quality factor of 0.5. It seems that my understanding of what determines the filter response is wrong.

I also used the coefficients derived from the transfer function of a second order Butterworth filter to design a circuit and simulate it. The circuit simulates well, but at higher frequencies begins to climb again to almost the original value. I used an ideal op amp for the simulation.

How do I choose suitable component values for a Butterworth response? What determines the characteristics of the frequency response? If I have a rough idea of how to achieve a Butterworth response, I can then do some parameter sweeps in my simulation to better understand how they impact the response.

enter image description here

enter image description here

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  • \$\begingroup\$ try giving your supply voltage a ground connection at its midpoint. \$\endgroup\$
    – tobalt
    Dec 29, 2021 at 17:13
  • \$\begingroup\$ RM429 - Hi, It seems you deleted the question immediately after it received an answer, but that's not how things are done here. Stack Exchange collects the Q&A for people to refer to in future, and questions with useful answers don't (usually) get deleted, so the topic has been undeleted. If you have questions about this, you can ask on Electrical Engineering Meta. Thanks. (Also, since your comment suggests the answer was useful, you can upvote and optionally accept it.) \$\endgroup\$
    – SamGibson ♦
    Dec 29, 2021 at 17:32
  • \$\begingroup\$ RM429 are we done here now? Is there anything else that needs advice on this circuit? \$\endgroup\$
    – Andy aka
    Dec 30, 2021 at 11:21

1 Answer 1

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The circuit simulates well, but at higher frequencies begins to climb again to almost the original value. I used an ideal op amp for the simulation.

I believe that the problem is here is that your op-amp supply is not adequately referenced to ground or 0 volts (the triangle symbol). Maybe use two series 2.5 volt supplies with the centre connection tied to ground. In effect it becomes a 5 volt supply with a centre-tap.

Butterworth has a Q of 0.7071 BTW. Here's an RLC low-pass filter example from my crappy website: -

enter image description here

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  • \$\begingroup\$ Of course!! The input is AC so it must be clipping the negative part of the output and causing a strange frequency response! It seems that my design was in fact correct. \$\endgroup\$
    – RM429
    Dec 29, 2021 at 17:19
  • \$\begingroup\$ Andy aka - Hi, Please reconsider referring to your website in that way. If you (or the mods) don't change that, it would make it much harder to disallow negative descriptions (perhaps more negative and unkind than you would like) of your website and other things (i.e. the start of a slippery slope). Even though you may feel that way about your website (though I can't think why you would), it still falls foul of the "unfriendly language" provision in the Code of Conduct and sets a negative tone. Can you please undo that? Thanks. \$\endgroup\$
    – SamGibson ♦
    Dec 29, 2021 at 17:44
  • \$\begingroup\$ @SamGibson I'm in between a rock and a hard place. On another answer I wrote some words that explained how tricky it was to fit the rules as I saw them. Is crappy such a bad word? It's my site and I'm quite happy to call it crappy. In fact, I like calling it "crappy" because I hate over-hyping stuff. \$\endgroup\$
    – Andy aka
    Dec 29, 2021 at 17:52
  • \$\begingroup\$ @Andyaka - Please just do what everyone else does across SE in similar situations, and refer to "my website" and that is completely fine. It isn't over-hyping, but it also doesn't cause us a problem because if we allow a negative word like "crappy" then where do we stop? It opens the door for even more negative words to be used which, if we challenge them, they can say "well you allowed Andy aka to use "crappy" and my word X is just another negative word so you must allow that too". \$\endgroup\$
    – SamGibson ♦
    Dec 29, 2021 at 19:33
  • \$\begingroup\$ [continued] So basically, "crappy" or other negative words are out - mod work is tough enough, without opening the door to even more of the "rules lawyering" that people already try to do to us, which takes time, is emotionally wearing, and adds to my stress level. As you have said before, you expect fairness, so I'm applying the "no negative language" rule fairly to everyone, including you. :-) Just refer to "my website" (as you used to do) and everything is fine. Thanks. \$\endgroup\$
    – SamGibson ♦
    Dec 29, 2021 at 19:34

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