I'm designing a low pass active filter with a Butterworth response. The passband is DC to 1.5 kHz, so the -3 dB cut off frequency should be around 2-5 kHz to be safe.
The topology I've decided to use is a second order Sallen-Key, unity gain filter. The schematic can be found below.
I'm a bit confused on how to achieve a Butterworth response, though. From my understanding, the quality factor, Q, has to be 0.707 for a Butterworth response. However, I also read that A = 3 - 1/Q, where A is the gain and Q is the quality factor. With a unity gain topology (A = 1), this would give a quality factor of 0.5. It seems that my understanding of what determines the filter response is wrong.
I also used the coefficients derived from the transfer function of a second order Butterworth filter to design a circuit and simulate it. The circuit simulates well, but at higher frequencies begins to climb again to almost the original value. I used an ideal op amp for the simulation.
How do I choose suitable component values for a Butterworth response? What determines the characteristics of the frequency response? If I have a rough idea of how to achieve a Butterworth response, I can then do some parameter sweeps in my simulation to better understand how they impact the response.