4-pole single opamp lopass filters

[Conrad Hoffman]

I've always been pleased at how well 4-pole filters work, especially for noise reduction and such. It's even nicer if you can do a single opamp version. The math for it is a PITA, though an excellent numeric solution was published by Burr-Brown in their old, and out of print, Function Circuits book, albeit in Fortran. Here's my minimalist conversion that hopefully will be of use to somebody. It's the 4th item down.

[jcx]

sensitivity to component tolerance is usually poor when you try to pile on poles, Q

even cascaded Sallen-Key biquad can become a problem holding tolerance in the higher Q's sections of high order filters

3rd order with passive RC in front of a biquad section is probably the best compromise with the input RC knocking down RF before the op amp input - the multiple feedback low pass biquad is esp good if signal inversion is OK

[Conrad Hoffman]

Certainly a valid concern, though I'd say it's an issue building any high order filter, regardless of topology, at least if one stays in the analog domain. Once the values are calculated it would be good advice to run some simulations and see what happens as components vary. IMO, getting close tolerance components isn't too difficult, or one can just measure. Where I'd really want to pay attention is if two high order filters had to sum correctly, say for a crossover.

[speakerman]

Dear Conrad and jcx -

You are both correct above re: component sensitivity. Douglas Self's "The Design of Active Crossovers" (out recently) is masterful in it's coverage of the above and so much more. Highly recommended reading.

Best, Speakerman

[Andrew Eckhardt]

Most of the time resistors an capacitors of "usual" tolerance from the same lot all measure very close, so it's not too bad to compensate so long as you know what the actual values are...

[AndrewT]

I have a small range of 0.3% and fewer 0.5% capacitors to use as references.
How would I minimise errors when used as a reference to calibrate a capacitance meter?
Temperature, humidity, handling, RF & other interferences? What else would/could have an effect on repeatability and absolute accuracy?

Would 1% absolute accuracy be within reach?
Would 1% absolute accuracy be sufficient for the higher Q filter that we are being told may be "off" by quite a bit?