Describe a Sallen–Key biquad structure. Which statement is true about its natural frequency and Q?

• A. ω0 ≈ 1/√(R1R2C1C2) and Q is fixed by the op-amp gain
• B. ω0 ≈ 1/√(R1R2C1C2) and Q depends on gain and component ratios
• C. ω0 is determined by capacitors only and Q is independent of resistor values
• D. ω0 depends on the op-amp supply voltage and Q on input impedance

Answer: (C)

In a Sallen–Key biquad, the second-order behavior comes from the RC network that the input and the buffered output form. The natural frequency is set by the time constants of both resistors and both capacitors, giving the familiar result ω0 ≈ 1/√(R1 R2 C1 C2). That means you can shift the resonance by changing any of the four components; none of them can be ignored if you’re aiming for a specific ω0.

The quality factor, or Q, describes how steep or damped the resonance is. In this topology, Q is controlled by the op-amp’s non-inverting gain (the amount of positive feedback) and the ratios of the components. Adjusting the gain changes the damping of the second-order response, and tweaking R and C ratios allows further fine-tuning of Q. So ω0 depends on all four components, and Q depends on the gain and the component ratios, not just one or the other.

The other statements miss key pieces: ω0 is not determined by capacitors alone (the resistors matter too), Q is not independent of resistor values, and the op-amp’s supply voltage does not set ω0 or Q in the ideal model (non-idealities like bandwidth can modify behavior, but that’s separate from the basic design equations).