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​L = 4.7 mHR = 22 Ωvout​

Find the corner (−3 dB) frequency fc of the RL low-pass filter shown, with R = 22 Ω, L = 4.7 mH. Give it in Hz.

R = 22 ΩL = 4.7 mH
fc = Hz
2.Easy
vin​C = 100 nFR = 47 kΩvout​

Find the corner (−3 dB) frequency ωc of the RC high-pass filter shown, with R = 47 kΩ, C = 100 nF. Give it in rad/s.

R = 47 kΩC = 100 nF
ωc = rad/s
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 = 4.7 mHR = 22 Ωvout​

The RL low-pass filter shown has R = 22 Ω, L = 4.7 mH. A sinusoidal input of 370 Hz is applied. Find the gain |H| = |vout/vin| in dB.

R = 22 ΩL = 4.7 mHf = 370 Hz
|H| = dB
5.Hard
|H| (dB)0.010.010.10.1111010100100−80−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​

A unity-feedback loop has the open-loop transfer function L(s) = 1.8/(s(s + 2)). Find the phase margin PM in degrees.

L(s) = 1.8/(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) = 66/(s(s + 3)(s + 8)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 66/(s(s + 3)(s + 8))
ω180 = rad/s

Answer key

  1. 1. fc = 745 Hz
  2. 2. ωc = 212.8 rad/s
  3. 3. |H| = −1.02 dB
  4. 4. |H| = −0.9575 dB
  5. 5. PM = 67.43 °
  6. 6. ω180 = 4.899 rad/s

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