In a Sallen-Key low-pass filter, what role does the feedback path play in setting Q and gain?

In a Sallen-Key low-pass filter, what role does the feedback path play in setting Q and gain?

• A. Feedback sets only the gain.
• B. Feedback ratio determines Q.
• C. There is no feedback in this topology.
• D. Feedback path determines input impedance.

Answer: (B)

The key idea is that the Sallen-Key filter uses the op-amp as a noninverting amplifier whose gain is set by the feedback path. That same feedback fraction shapes how much of the output is fed back into the RC ladder, and this feedback directly determines the damping of the second-order response, i.e., the quality factor Q. For equal RC values, the damping term in the denominator ends up proportional to (3 − K), where K is the noninverting gain from the op-amp. Since Q = 1/(3 − K) in that case, changing the feedback gain alters Q: increasing the feedback (raising K) reduces damping and raises Q, up to the point where the system becomes unstable as K approaches 3. So the feedback path is what sets the gain and, at the same time, controls Q. This is why the statement that the feedback ratio determines Q is the best description.

The key idea is that the Sallen-Key filter uses the op-amp as a noninverting amplifier whose gain is set by the feedback path. That same feedback fraction shapes how much of the output is fed back into the RC ladder, and this feedback directly determines the damping of the second-order response, i.e., the quality factor Q. For equal RC values, the damping term in the denominator ends up proportional to (3 − K), where K is the noninverting gain from the op-amp. Since Q = 1/(3 − K) in that case, changing the feedback gain alters Q: increasing the feedback (raising K) reduces damping and raises Q, up to the point where the system becomes unstable as K approaches 3. So the feedback path is what sets the gain and, at the same time, controls Q. This is why the statement that the feedback ratio determines Q is the best description.