LC resonance, Q factor & bandwidth worksheet with answers

Free printable LC resonance, Q factor & bandwidth worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
f|I|0.70711.6 MHzf1​f2​BW = 320 kHz

A resonance curve peaks at 1.6 MHz, and its half-power points are 320 kHz apart. Find the quality factor Q.

f0 = 1.6 MHzBW = 320 kHz
Q =
2.Easy
f|I|0.7071500 kHzf1​f2​BW = 62.5 kHz

A resonance curve peaks at 500 kHz, and its half-power points are 62.5 kHz apart. Find the quality factor Q.

f0 = 500 kHzBW = 62.5 kHz
Q =
3.Medium
C = 1 µF+−3 VL = 2.2 µHiL​

A 1 µF capacitor charged to 5 V oscillates with an ideal 2.2 µH inductor. Find the energy WL stored in the inductor at the moment the capacitor voltage is 3 V, in µJ.

C = 1 µFV0 = 5 VvC = 3 V
WL = µJ
4.Medium
V22 Ω10 mH10 nF

A series RLC circuit has R = 22 Ω, L = 10 mH and C = 10 nF. Find its bandwidth BW in Hz.

R = 22 ΩL = 10 mHC = 10 nF
BW = Hz
5.Hard
C = 22 nFR = 0.5 ΩL = 2.2 µH

A charged 22 nF capacitor discharges through a 2.2 µH coil with a total series resistance of 0.5 Ω, so the oscillation slowly dies out. Its amplitude decays as e−Rt/(2L). How many oscillation cycles n pass before the amplitude has halved? (The losses are small, so the frequency is f₀.)

L = 2.2 µHC = 22 nFR = 0.5 Ω
n =
6.Hard
V100 ΩLC = ?

Design a series RLC filter with a total resistance of 100 Ω, a resonance frequency of 200 kHz and a bandwidth of 8 kHz. Find the capacitance C in nF.

R = 100 Ωf0 = 200 kHzBW = 8 kHz
C = nF

Answer key

  1. 1. Q = 5
  2. 2. Q = 8
  3. 3. WL = 8 µJ
  4. 4. BW = 350.1 Hz
  5. 5. n = 4.413
  6. 6. C = 0.3183 nF

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