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​C = 22 nFR = 2.2 kΩvout​

Find the corner (−3 dB) frequency ωc of the RC high-pass filter shown, with R = 2.2 kΩ, C = 22 nF. Give it in rad/s.

R = 2.2 kΩC = 22 nF
ωc = rad/s
2.Easy
vin​L = 100 mHR = 10 Ωvout​

Find the corner (−3 dB) frequency fc of the RL low-pass filter shown, with R = 10 Ω, L = 100 mH. Give it in Hz.

R = 10 ΩL = 100 mH
fc = Hz
3.Medium
|H| (dB)11101010010010001000−40−2002040ω (rad/s)φ (°)ω (rad/s)−90−450ω = 30

Find the phase ∠G(jω) of G(s) = 47(s + 10)/(s(s + 11)) at ω = 30 rad/s, in degrees.

G(s) = 47(s + 10)/(s(s + 11))ω = 30 rad/s
∠G(jω) = °
4.Medium
vin​R = 2.2 kΩC = 10 nFvout​

The RC low-pass filter shown has R = 2.2 kΩ, C = 10 nF. A sinusoidal input of 3.6 kHz is applied. Find the gain |H| = |vout/vin| in dB.

R = 2.2 kΩC = 10 nFf = 3.6 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) = 7.4/(s(s + 2)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 7.4/(s(s + 2))
ωc = rad/s
6.Hard
|H| (dB)11101010010010001000−60−40−200204060ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​

A unity-feedback loop has the open-loop transfer function L(s) = 1400/(s(s + 10)). Find the phase margin PM in degrees.

L(s) = 1400/(s(s + 10))
PM = °

Answer key

  1. 1. ωc = 20661 rad/s
  2. 2. fc = 15.92 Hz
  3. 3. ∠G(jω) = −88.3 °
  4. 4. |H| = −0.9609 dB
  5. 5. ωc = 2.38 rad/s
  6. 6. PM = 15.22 °

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