Filter behavior using a tank: when a parallel resonant (tank) circuit is inserted in series with an output load resistor, what overall filter type does the network implement around the tank’s resonant frequency?

Introduction / Context:Resonant tanks (LC networks) are the building blocks of many passive filters. A “parallel tank” has a very high impedance at its resonant frequency and a much lower impedance away from resonance. The way it is placed with respect to the signal path determines whether it passes or rejects a band of frequencies.

Given Data / Assumptions:

• The tank is a parallel LC tuned to a resonant frequency f0.
• The tank is placed in series with the output load resistor.
• Components are ideal; we reason qualitatively around f0.

Concept / Approach:A parallel LC exhibits maximum impedance at f0. If this high-impedance element is in series with the load, the signal path “blocks” at f0, producing a deep attenuation (a notch). Frequencies far from f0 see a comparatively low impedance through the series path and are less attenuated. This is the defining behavior of a band-stop (notch) filter with the stopband centered on f0.

Step-by-Step Solution:

Verification / Alternative check:Plotting the transfer function magnitude shows a minimum (notch) at f0. Swapping the topology (placing the tank in shunt across the load) would produce a bandpass behavior, confirming the role of placement.

Why Other Options Are Wrong:

• Low-pass / High-pass: these pass one side of the spectrum and reject the other, not a narrow band around f0.
• Bandpass: would require low impedance at f0 in the series path (a series-resonant element), not a high impedance.
• All-pass: preserves magnitude while shifting phase; not applicable here.

Common Pitfalls:Confusing parallel vs series resonance; assuming any tank in the path yields bandpass; forgetting that parallel tanks have high impedance at resonance while series tanks have low impedance at resonance.

Final Answer:Band-stop