Consider the active filter shown (an operational-amplifier based network). Evaluate the following claims about the filter: (1) it is an active low-pass filter, (2) it is second order, and (3) its magnitude slope changes by 40 dB per decade beyond cutoff. Which statements are correct?

Introduction / Context:Active filters employ operational amplifiers with resistors and capacitors to realize frequency-selective responses without using inductors. A classic low-pass topology (such as Sallen–Key or multiple-feedback) provides a second-order transfer function, giving a −40 dB/decade roll-off in the stopband. This question checks your ability to match qualitative statements to a standard active low-pass response.

Given Data / Assumptions:

• The depicted circuit is a common op-amp active filter topology.
• Component choices yield a low-pass response (DC gain finite, high-frequency attenuation).
• Order is determined by the highest power of s in the denominator (two reactive elements ⇒ second order).

Concept / Approach:A second-order low-pass filter has transfer function magnitude that is flat near DC (passband), transitions around the natural frequency or cutoff, and then attenuates with a slope of 40 dB/decade (12 dB/octave) as frequency increases past the corner. Whether implemented by Sallen–Key or multiple-feedback, two capacitors (or two independent energy storage elements) confirm the second order.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

Common Pitfalls:

Final Answer: