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 = 47 kΩC = 2.2 nFvout​

Find the corner (−3 dB) frequency fc of the RC low-pass filter shown, with R = 47 kΩ, C = 2.2 nF. Give it in Hz.

R = 47 kΩC = 2.2 nF
fc = Hz
2.Easy
vin​C = 1 nFR = 22 kΩvout​

Find the corner (−3 dB) frequency ωc of the RC high-pass filter shown, with R = 22 kΩ, C = 1 nF. Give it in rad/s.

R = 22 kΩC = 1 nF
ωc = rad/s
3.Medium
vin​L = 100 mHR = 47 Ωvout​

The RL low-pass filter shown has R = 47 Ω, L = 100 mH. A sinusoidal input of 750 Hz is applied. Find the gain |H| = |vout/vin| in dB.

R = 47 ΩL = 100 mHf = 750 Hz
|H| = dB
4.Medium
vin​R = 470 ΩL = 22 mHvout​

The RL high-pass filter shown has R = 470 Ω, L = 22 mH. A sinusoidal input of 850 Hz is applied. Find the gain |H| = |vout/vin| in dB.

R = 470 ΩL = 22 mHf = 850 Hz
|H| = dB
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) = 82/(s(s + 3)(s + 6)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 82/(s(s + 3)(s + 6))
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) = 118/(s(s + 3)(s + 7)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 118/(s(s + 3)(s + 7))
ω180 = rad/s

Answer key

  1. 1. fc = 1539 Hz
  2. 2. ωc = 45455 rad/s
  3. 3. |H| = −20.07 dB
  4. 4. |H| = −12.3 dB
  5. 5. ω180 = 4.243 rad/s
  6. 6. ω180 = 4.583 rad/s

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