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 = 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
2.Easy
vin​C = 4.7 nFR = 3.3 kΩvout​

Find the corner (−3 dB) frequency fc of the RC high-pass filter shown, with R = 3.3 kΩ, C = 4.7 nF. Give it in Hz.

R = 3.3 kΩC = 4.7 nF
fc = Hz
3.Medium
|H| (dB)0.10.111101010010010001000−40−2002040ω (rad/s)φ (°)ω (rad/s)−90−450ω = 1

Find the phase ∠G(jω) of G(s) = 42(s + 2)/(s(s + 12)) at ω = 1 rad/s, in degrees.

G(s) = 42(s + 2)/(s(s + 12))ω = 1 rad/s
∠G(jω) = °
4.Medium
|H| (dB)0.010.010.10.1111010100100−20020406080ω (rad/s)φ (°)ω (rad/s)−135−90−450ω = 0.5

Find the phase ∠G(jω) of G(s) = 13(s + 6)/(s(s + 4)) at ω = 0.5 rad/s, in degrees.

G(s) = 13(s + 6)/(s(s + 4))ω = 0.5 rad/s
∠G(jω) = °
5.Hard
|H| (dB)0.10.111101010010010001000−60−40−200204060ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​ = ?

A unity-feedback loop has the open-loop transfer function L(s) = 496/(s(s + 8)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 496/(s(s + 8))
ωc = rad/s
6.Hard
|H| (dB)0.10.1111010100100−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​ = ?

A unity-feedback loop has the open-loop transfer function L(s) = 40/(s(s + 10)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 40/(s(s + 10))
ωc = rad/s

Answer key

  1. 1. ωc = 212.8 rad/s
  2. 2. fc = 10261 Hz
  3. 3. ∠G(jω) = −68.2 °
  4. 4. ∠G(jω) = −92.36 °
  5. 5. ωc = 21.56 rad/s
  6. 6. ωc = 3.746 rad/s

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