# Why does adding a gain to a Sallen-key second order HPF change the amplitude response?

As the title suggests, I have done all the necessary calculations to implement a gain into my second order stage of my 6th order high pass filter but for some odd reason, it would change the amplitude response of the circuit. I have recalculated the resistance that affect the filter by implementing K into their equations and I cross checked it with analog.com which proved that it was spot on so Im not really sure on why the response changes hence changing the cut-off frequency.

The difference in the cut-off frequency is huge, the original design is at 100Hz whilst the gain version reduces it to 180Hz.

The schematic without the gain:

The schematic with a gain:

And also if someone could explain why resistance of 150kOhms and above only work with the gain of the amplifier that would be appreciated!

• Adding gain reduces the gain margin available for the amplifier; the calculations assume there is sufficient gain in the amplifier. The rule of thumb is you need 40dB of gain margin (Open loop gain - closed loop gain). Jan 27, 2021 at 8:51
• Your "gain" does not implement a proper Sallen-Key topology (R7 and R8 are wrong). Jan 27, 2021 at 8:52
• What Peter means is that you're asking for too much gain. A factor 2 could be OK but you appear to want more than a factor 10 gain which influences the transfer function too much. And indeed, R7 and R8 "do nothing" so remove them. Jan 27, 2021 at 8:53