Bode plots & margins worksheet with answers

Free printable Bode plots & margins 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
vin​R = 220 ΩL = 100 mHvout​

Find the corner (−3 dB) frequency fc of the RL high-pass filter shown, with R = 220 Ω, L = 100 mH. Give it in Hz.

R = 220 ΩL = 100 mH
fc = Hz
2.Easy
vin​L = 47 mHR = 22 Ωvout​

Find the corner (−3 dB) frequency fc of the RL low-pass filter shown, with R = 22 Ω, L = 47 mH. Give it in Hz.

R = 22 ΩL = 47 mH
fc = Hz
3.Medium
vin​C = 47 nFR = 47 kΩvout​

The RC high-pass filter shown has R = 47 kΩ, C = 47 nF. A sinusoidal input of 140 Hz is applied. Find the gain |H| = |vout/vin| in dB.

R = 47 kΩC = 47 nFf = 140 Hz
|H| = dB
4.Medium
vin​L = 50 mHC = 4.7 µFR = 5 Ωvout​

In the series RLC band-pass filter shown the output is taken across R = 5 Ω, with L = 50 mH and C = 4.7 µF. Find the centre (resonant) frequency f0 in Hz.

R = 5 ΩL = 50 mHC = 4.7 µF
f0 = Hz
5.Hard
|H| (dB)0.10.1111010100100−80−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−270−180−900ω180​ = ?

A unity-feedback loop has the open-loop transfer function L(s) = 28/(s(s + 1)(s + 9)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 28/(s(s + 1)(s + 9))
ω180 = rad/s
6.Hard
|H| (dB)0.10.1111010100100−80−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−270−180−900ω180​

A unity-feedback loop has the open-loop transfer function L(s) = 96/(s(s + 4)(s + 8)). Find the gain margin GM in dB.

L(s) = 96/(s(s + 4)(s + 8))
GM = dB

Answer key

  1. 1. fc = 350.1 Hz
  2. 2. fc = 74.5 Hz
  3. 3. |H| = −1.02 dB
  4. 4. f0 = 328.3 Hz
  5. 5. ω180 = 3 rad/s
  6. 6. GM = 12.04 dB

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