When I was working on one of my projects I needed to filter analog signal above 10Hz... or above 1000Hz... whatever. Well I decided to add a second order low pass filter instead of simple first order to get rid of that ugly and nasty noise :)

General Sallen-Key low pass filter topology is nice, with some symmetry it is very easy to calculate gain, time constant and other stuff. It was working as expected until variable gain possibility was added.

Here Im going to mention filter quality factor Q which is a design parameter of filters. Q provides a measure of sharpness to the stage frequency response. High Q implies a very narrow sharp frequency response. Low Q provides a wide shallow frequency response. But high Q makes an oscillator from your filter, which I wasnt aware of :) See below what I have designed and constructed and the simulation in LTSpice (great piece of software - thank you guys) of a violent oscillations with higher gain :) Transient simulation of frist 250ms after startup, while stepping feedback resistor value to set gains to 1x, 2x, 3x, 4x, 5x, 6x. Anything above 2x oscillates.

Simulated frequency response of my filter should tell us more. Note that this is the same circuit but without opamp supply voltage limitation ( I had to add supply voltage limit so you can see something else than infinite oscillations on the picture above).

Frequency simulation from 0.1Hz to 100Hz for same gains reveals the reason. The filter with gain 2x tends to amplify extremely frequency about 10.5Hz, phase shift goes above 180° (not present on plot above) and positive feedback via C2 causes the oscillations.

Making the filter of first order (as I should have done from the beginning) just solves all the trouble. Making the C2 smaller and R1 higher works as well.

This was just an inspiration to see what can go wrong with active filters of higher order. I recommend you to read free document from Texas Instruments: Active Filter Design Techniques (excerpted from op amps for everyone).

https://focus.ti.com/lit/ml/sloa088/sloa088.pdf