# Maximise Q factor in low pass Sallen and Key Filter

How do I maximise the Q-factor of the low pass sallen and key design.

I have this equation: $Q = \sqrt{ \frac {(R1 \times R2 \times C1 \times C2)} {R1 \times C1 \times (1-A) + (R1 \times C2) + (R2 \times C2)}}$

but I'm not sure of the best way to maximise it!

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## 1 Answer

I'm not sure why you would want to do this - and presumably you have constraints such as the cutoff frequency and LF gain, but with an LF gain of 1 you can obtain an arbitrarily large Q (theoretically) by making C1 much larger than C2 whilst maintaining the product C1C2 to preserve the cutoff frequency. There will of course be a practical limit to both capacitor values.

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