Series resonant band-stop (notch) filter: With R = 68 Ω in series, L = 110 mH (internal RW = 4 Ω), and C = 0.02 µF, input Vin = 200 mV, and output taken across the series LC branch, what is |Vout| at the center frequency f0?

Introduction / Context:
A series resonant band-stop (notch) filter uses a low-impedance series LC branch to shunt energy at the center frequency. Depending on where the output is taken, the notch behavior changes. Here, the output is measured directly across the series LC branch whose impedance is minimal at resonance but not strictly zero due to winding resistance.

Given Data / Assumptions:

• Series path: R = 68 Ω and an LC branch with inductor winding resistance RW = 4 Ω.
• At f0, XL = XC and the ideal reactive parts cancel.
• Input voltage Vin = 200 mV (rms).
• Output is taken across the series LC branch only.

Concept / Approach:
At resonance, the series LC branch reduces to its residual resistance, approximately RW. The overall loop is then a simple series divider between R and RW. The output across LC equals the drop across RW.

Step-by-Step Solution:

Verification / Alternative check:
The notch action implies most of the source voltage appears across the external series resistor at f0 while the LC looks like a near-short; a small but non-zero output remains due to RW, matching the calculated 11.1 mV.

Why Other Options Are Wrong:

• 200 mV: Would imply zero current or infinite LC impedance at f0, contrary to series resonance.
• 111 mV: About half the input; inconsistent with a low-resistance shunt branch.
• 1.1 mV: Ten times too small; would require RW ≈ 0.4 Ω.

Common Pitfalls:

• Forgetting the non-ideal winding resistance that limits the notch depth.
• Confusing band-stop topology and taking output at the wrong nodes.

Final Answer:
11.1 mV