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 = 10 mHvout​

Find the corner (−3 dB) frequency fc of the RL high-pass filter shown, with R = 220 Ω, L = 10 mH. Give it in Hz.

R = 220 ΩL = 10 mH
fc = Hz
2.Easy
vin​L = 47 mHR = 10 Ωvout​

Find the corner (−3 dB) frequency fc of the RL low-pass filter shown, with R = 10 Ω, L = 47 mH. Give it in Hz.

R = 10 ΩL = 47 mH
fc = Hz
3.Medium
vin​R = 2.2 kΩC = 1 nFvout​

The RC low-pass filter shown has R = 2.2 kΩ, C = 1 nF. A sinusoidal input of 360 kHz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 2.2 kΩC = 1 nFf = 360 kHz
φ = °
4.Medium
vin​C = 1 nFR = 10 kΩvout​

The RC high-pass filter shown has R = 10 kΩ, C = 1 nF. A sinusoidal input of 160 kHz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 10 kΩC = 1 nFf = 160 kHz
φ = °
5.Hard
|H| (dB)0.10.1111010100100−100−80−60−40−20020ω (rad/s)φ (°)ω (rad/s)−270−180−900ω180​

A unity-feedback loop has the open-loop transfer function L(s) = K/(s(s + 2)(s + 3)). Find the gain K that gives a gain margin of 20 dB.

L(s) = K/(s(s + 2)(s + 3))GM = 20 dB
K =
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) = 34/(s(s + 1)(s + 6)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 34/(s(s + 1)(s + 6))
ω180 = rad/s

Answer key

  1. 1. fc = 3501 Hz
  2. 2. fc = 33.86 Hz
  3. 3. φ = −78.64 °
  4. 4. φ = 5.681 °
  5. 5. K = 3
  6. 6. ω180 = 2.449 rad/s

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