Parallel resonant band-pass (lossy tank): With a 90 Ω series feed, a parallel tank L = 60 mH and C = 0.02 µF (inductor RW = 20 Ω), and output across the tank, what is the center frequency f0?

Introduction / Context:Resonant frequency in LC tanks is governed by L and C. Series feed and winding resistance mainly influence bandwidth and quality factor (Q) but not the ideal center frequency, which this question asks you to compute.

Given Data / Assumptions:

• L = 60 mH.
• C = 0.02 µF = 2.0 * 10^-8 F.
• Series feed resistor = 90 Ω; inductor winding resistance RW = 20 Ω.
• Assume sinusoidal steady state and small resistive effects on f0.

Concept / Approach:The resonant (center) frequency is f0 = 1 / (2 * pi * sqrt(L * C)). Resistances alter Q and amplitude but do not significantly shift f0 for small losses relative to reactances at resonance.

Step-by-Step Solution:

Verification / Alternative check:Rule-of-thumb: f0(kHz) ≈ 159 / sqrt(L(mH) * C(nF)) ⇒ 159 / sqrt(60 * 20) ≈ 159 / 34.64 ≈ 4.59 kHz, confirming the computation.

Why Other Options Are Wrong:

• 459 Hz and 999 Hz: Off by ~10× or wrong numerical handling.
• 2,176 Hz: About half the correct value; could come from misusing 4 * pi instead of 2 * pi.

Common Pitfalls:

• Unit mistakes (mH vs H, µF vs nF).
• Including resistances in the f0 formula for an LC tank (they mainly affect Q).

Final Answer:4,591 Hz