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 = 22 ΩL = 4.7 mHvout​

Find the corner (−3 dB) frequency ωc of the RL high-pass filter shown, with R = 22 Ω, L = 4.7 mH. Give it in rad/s.

R = 22 ΩL = 4.7 mH
ωc = rad/s
2.Easy
vin​L = 4.7 mHR = 47 Ωvout​

Find the corner (−3 dB) frequency fc of the RL low-pass filter shown, with R = 47 Ω, L = 4.7 mH. Give it in Hz.

R = 47 ΩL = 4.7 mH
fc = Hz
3.Medium
vin​R = 22 kΩC = 2.2 nFvout​

The RC low-pass filter shown has R = 22 kΩ, C = 2.2 nF. A sinusoidal input of 16 kHz is applied. Find the gain |H| = |vout/vin| in dB.

R = 22 kΩC = 2.2 nFf = 16 kHz
|H| = dB
4.Medium
vin​R = 2.2 kΩC = 100 nFvout​

The RC low-pass filter shown has R = 2.2 kΩ, C = 100 nF. A sinusoidal input of 1.4 kHz is applied. Find the gain |H| = |vout/vin| in dB.

R = 2.2 kΩC = 100 nFf = 1.4 kHz
|H| = dB
5.Hard
|H| (dB)0.10.1111010100100−80−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​

A unity-feedback loop has the open-loop transfer function L(s) = 3.6/(s(s + 2)). Find the phase margin PM in degrees.

L(s) = 3.6/(s(s + 2))
PM = °
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) = 22/(s(s + 2)(s + 3)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 22/(s(s + 2)(s + 3))
ω180 = rad/s

Answer key

  1. 1. ωc = 4681 rad/s
  2. 2. fc = 1592 Hz
  3. 3. |H| = −13.92 dB
  4. 4. |H| = −6.762 dB
  5. 5. PM = 53.96 °
  6. 6. ω180 = 2.449 rad/s

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