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|0.707110.7 MHzf1​f2​BW = ?

A tuned circuit resonates at 10.7 MHz and has a quality factor Q = 50. Find its bandwidth BW in kHz.

f0 = 10.7 MHzQ = 50
BW = kHz
2.Easy
f|I|0.707110.7 MHzf1​f2​BW = 1.07 MHz

A resonance curve peaks at 10.7 MHz, and its half-power points are 1.07 MHz apart. Find the quality factor Q.

f0 = 10.7 MHzBW = 1.07 MHz
Q =
3.Medium
V47 kΩ100 mH2.2 nF

A parallel RLC circuit has R = 47 kΩ, L = 100 mH and C = 2.2 nF. Find its quality factor Q.

R = 47 kΩL = 100 mHC = 2.2 nF
Q =
4.Medium
V10 Ω100 µH1 nF

A series RLC circuit has R = 10 Ω, L = 100 µH and C = 1 nF. Find its bandwidth BW in kHz.

R = 10 ΩL = 100 µHC = 1 nF
BW = kHz
5.Hard
C = 100 nFR = 2 ΩL = 22 mH

A charged 100 nF capacitor discharges through a 22 mH coil with a total series resistance of 2 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 = 22 mHC = 100 nFR = 2 Ω
n =
6.Hard
V5 ΩLC = ?

Design a series RLC filter with a total resistance of 5 Ω, a resonance frequency of 20 kHz and a bandwidth of 500 Hz. Find the capacitance C in nF.

R = 5 Ωf0 = 20 kHzBW = 500 Hz
C = nF

Answer key

  1. 1. BW = 214 kHz
  2. 2. Q = 10
  3. 3. Q = 6.971
  4. 4. BW = 15.92 kHz
  5. 5. n = 51.74
  6. 6. C = 39.79 nF

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