In an active notch filter, how do Q factor and notch depth relate, and which component adjustments influence Q?

In an active notch filter, how do Q factor and notch depth relate, and which component adjustments influence Q?

• A. Higher Q yields a broader notch; Q is largely determined by the op-amp’s supply voltage.
• B. Higher Q yields a sharper, deeper notch with narrower bandwidth; Q is influenced by ratios of feedback and notch network components (R and C).
• C. Notch depth is independent of Q; Q is fixed by the op-amp's bandwidth.
• D. Q has no practical impact on notch performance.

Answer: (B)

The main idea being tested is how the quality factor Q controls how selective the notch is and how the circuit’s component values set that Q. A higher Q means a sharper, more selective notch with a narrower bandwidth, and typically a deeper null, because the resonant path in the active notch becomes less damped and cancels the input more precisely at the center frequency. In an active notch, the op-amp provides gain and feedback that realize that resonance with gain control, so you can achieve a deep null. The notch depth—the amount of attenuation at the notch frequency—goes up as the selectivity (Q) increases, since the energy at the center frequency is canceled more effectively when the loop around ω0 is less damped. Which components set Q? It’s the ratios in the feedback path and the RC values in the notch network. Adjusting the feedback network resistors changes how much loop gain is around the resonant path, while the R and C values in the notch arms set the damping part of the response. Together these determine Q. Why the other statements aren’t accurate: increasing Q does not broaden the notch; it makes it narrower and typically deeper. The notch isn’t fixed by the op-amp’s supply voltage alone—supply affects headroom and linearity more than the intrinsic Q. Notch depth and Q are connected in practice, and Q has a real, practical impact on how deep and how sharp the notch is; saying Q has no practical impact or that the depth is independent of Q ignores the damping control provided by the component ratios and can mislead about how to tune the filter.

The main idea being tested is how the quality factor Q controls how selective the notch is and how the circuit’s component values set that Q. A higher Q means a sharper, more selective notch with a narrower bandwidth, and typically a deeper null, because the resonant path in the active notch becomes less damped and cancels the input more precisely at the center frequency.

In an active notch, the op-amp provides gain and feedback that realize that resonance with gain control, so you can achieve a deep null. The notch depth—the amount of attenuation at the notch frequency—goes up as the selectivity (Q) increases, since the energy at the center frequency is canceled more effectively when the loop around ω0 is less damped.

Which components set Q? It’s the ratios in the feedback path and the RC values in the notch network. Adjusting the feedback network resistors changes how much loop gain is around the resonant path, while the R and C values in the notch arms set the damping part of the response. Together these determine Q.

Why the other statements aren’t accurate: increasing Q does not broaden the notch; it makes it narrower and typically deeper. The notch isn’t fixed by the op-amp’s supply voltage alone—supply affects headroom and linearity more than the intrinsic Q. Notch depth and Q are connected in practice, and Q has a real, practical impact on how deep and how sharp the notch is; saying Q has no practical impact or that the depth is independent of Q ignores the damping control provided by the component ratios and can mislead about how to tune the filter.