A circuit that combines an active device (such as an op-amp) with resistors and capacitors to realize a frequency-selective response is referred to as what type of filter?

Introduction:
Filters are used to shape spectra by passing desired frequency bands and attenuating others. When a filter uses an active element such as an operational amplifier together with passive resistors and capacitors, it is called an active filter. These are ubiquitous in audio, instrumentation, and communications front-ends due to their predictable response and ability to provide gain and buffering.

Given Data / Assumptions:

• Presence of an amplifier (op-amp, BJT, FET) in combination with RC networks.
• Goal is to realize a frequency-selective transfer function (low-pass, high-pass, band-pass, or band-stop).
• No inductors are required; the active device can synthesize inductor-like behavior when needed.

Concept / Approach:
Active filters use negative feedback around an amplifier to implement precise poles and zeros. By choosing component values, one can realize standard responses (Butterworth, Bessel, Chebyshev, multiple feedback, Sallen–Key) with controllable cutoff frequency, quality factor, and gain. The amplifier also isolates stages, presenting high input impedance and low output impedance.

Step-by-Step Solution:
Identify components: op-amp + R and C form the building block.Select topology: e.g., Sallen–Key for low-pass/high-pass or multiple-feedback for band-pass.Set design targets: choose fc, Q, and passband gain by calculating resistor and capacitor values.Implement and verify: simulate or measure magnitude and phase to confirm the intended frequency response.

Verification / Alternative check:
Active filters provide gain (unlike purely passive RC filters), maintain load isolation, and allow precise tuning. Replacing the amplifier with a passive network would remove these advantages and change the classification to a passive filter.

Why Other Options Are Wrong:

• Relaxation or harmonic oscillator: These generate periodic signals rather than selective filtering of an input.
• Signal generator: Broad term for sources, not selective networks.
• Differential amplifier: A building block that amplifies differences; not itself a filter unless combined with RC networks in a feedback configuration.

Common Pitfalls:

• Assuming an op-amp alone makes a circuit an active filter; the RC network and feedback define the filtering.
• Ignoring op-amp bandwidth and slew-rate limits that can distort high-frequency responses.
• Loading effects between cascaded stages when buffering is omitted.

Final Answer:
active filter