Multiple feedback bandpass filter design question - Page 1
Forum section: electronics / beginners

author: SethGI
author_rank: Regular Contributor
timestamp: December 21, 2020, 07:27:22 pm
content: Hello,Sorry if this is a very simple question which should be answerable with a google search... I've been able to find nothing.I'm looking into multiple feedback filters, and came across this excellent app note explaining how to select component values:https://www.analog.com/media/en/training-seminars/tutorials/MT-218.pdf.They list that R2 = 1/(2Q-H)k. This seems to imply some limitations on the ratio between H and Q. Specifically, 2Q-H=0 would cause division by zero, and H > 2Q makes that value negative. In a few spice simulations, my circuit seemed to behave incorrectly when I chose a combination of values which led to R2 being negative (I just took the absolute value of the computed R2 value). With values that made 2Q > H, the filter behaved correctly.So, it seems to me like one of three things happened.1. This is a theoretical limitation on the ratio between H and Q. If I want more gain in a low-Q filter (as in, Q < 10), I should look into a different topology.2. This is a limitation of how the values are calculated. There is some other method of calculating components which doesn't run into this issue.3. I messed up. The method is fine, and taking the absolute value of the difference is fine. In this case, I'm still curious why this works. Although this doesn't resolve that when 2Q=H R2 is not a number...Any insights?Thanks for the help!

author: ejeffrey
author_rank: Super Contributor
timestamp: December 21, 2020, 07:37:15 pm
content: Yes, there is a relationship between gain and Q on a MFB bandpass filter. It's actually fixed for the core of the filter and R1 + R2 is just an input voltage divider.If you want more gain, just add a separate gain stage or two.

author: SethGI
author_rank: Regular Contributor
timestamp: December 21, 2020, 07:47:38 pm
content: Quote from: ejeffrey on December 21, 2020, 07:37:15 pmOk, thanks. I assumed this was the case. I'm just space-constrained so I was trying to get as much done in one stage as possible!

author: Benta
author_rank: Super Contributor
timestamp: December 21, 2020, 08:42:35 pm
content: If you drill down, you'll find that for this type of filter:Q = sqrt(Ho)So no, you cannot define Q and gain independently.

author: Benta
author_rank: Super Contributor
timestamp: December 21, 2020, 08:50:52 pm
content: Quote from: ejeffrey on December 21, 2020, 07:37:15 pmNot quite.2Ho = R5/R1This also implies that output impedance of the previous stage influences Ho and Q.

author: SethGI
author_rank: Regular Contributor
timestamp: December 21, 2020, 10:52:12 pm
content: Quote from: Benta on December 21, 2020, 08:42:35 pmInteresting thanks.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: December 21, 2020, 11:05:55 pm
content: Well yeah, you won't get the right results when you put in the wrong numbers.SPICE is perfectly happy with negative resistances, so you can test that and show it really is still working just the same -- the problem isn't the formula, the problem is we don't stock negative resistances anywhere.Tim