Details

The transfer function, cutoff frequency, and for low-pass and high-pass filters (with non-unity gain) are

1. ;

2. ;

3. ;

4. ;

5. ;

where and , , , , , are the resistances and capacitances.

For higher-order filters, the transfer funtions 1 and 2 are raised to the order of the filter. For a high-pass (low-pass) filter, set the order of the low-pass (high-pass) filter to "0".

Reference

[1] "Analysis of the Sallen–Key Architecture." Texas Instruments. (Sep 2002) http://www.ti.com/lit/an/sloa024b/sloa024b.pdf.