More Filter Design on a Budget

[garcho]

More Filter Design on a Budget

"This document describes filter design from the standpoint of cost. Filter design techniques that require the fewest possible op amps and passive components are described. Six types of filters are described—low pass, high pass, narrow bandpass, wide bandpass, notch, and band reject."

[Rob Strand]

A good addition to that would be the third-order filters.

http://sim.okawa-denshi.jp/Fkeisan.htm

Non-inverting S&K type (Called the Geffe circuit when the resistors are equal)
http://sim.okawa-denshi.jp/Sallenkey3Lowkeisan.htm

Inverting
http://sim.okawa-denshi.jp/MultipleFB3Lowkeisan.htm


Another angle for high-order filters is to choose filter responses with higher slopes (for the same order).  That means you can use a lower order filter to get the same amount of attenuation.   The penalty is the filter is more sensitive to component tolerances.

Here's some different filters which are all of order 10 (as an example).
You can see how you can get considerably more attenuation for the same order filter.

All filters have the same -3dB point. 
*** None of the filters have pass-band ripple, they are all monotonic ***.
Green:   Butterworth maximally flat
Cyan:    There's actually about three plots on top of one another here, all very close.
             These are some filters I developed.   Very flat and extended pass-band, monotonic.
             Attenuation is deliberately set between Butterworth (green) and Optimal Least Squares (Black).
             It is possible to tune the slope between the two extremes.
             These filters have very small steps. 
Black:    Optimal least squares filter.  Flattest passband and monotonic.
             While these are monotonic you can see a small step.
Red:      OptL filters.  Fastest roll-off yet still monotonic.
             Here the steps become more pronounced than the Black trace





Unfortunately the maths behind these filters is a bit complicated.