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 = 47 nFR = 10 kΩvout​

Find the corner (−3 dB) frequency ωc of the RC high-pass filter shown, with R = 10 kΩ, C = 47 nF. Give it in rad/s.

R = 10 kΩC = 47 nF
ωc = rad/s
2.Easy
vin​L = 1 mHR = 22 Ωvout​

Find the corner (−3 dB) frequency ωc of the RL low-pass filter shown, with R = 22 Ω, L = 1 mH. Give it in rad/s.

R = 22 ΩL = 1 mH
ωc = rad/s
3.Medium
|H| (dB)0.010.11101001000−80−60−40−20020ω (rad/s)ω = 0.5

Find the exact magnitude |G(jω)| of G(s) = 684/((s + 18)(s + 19)) at ω = 0.5 rad/s, in dB.

G(s) = 684/((s + 18)(s + 19))ω = 0.5 rad/s
|G(jω)| = dB
4.Medium
|H| (dB)0.10.111101010010010001000−40−200204060ω (rad/s)φ (°)ω (rad/s)−135−90−450ω = 30

Find the phase ∠G(jω) of G(s) = 10(s + 18)/(s(s + 9)) at ω = 30 rad/s, in degrees.

G(s) = 10(s + 18)/(s(s + 9))ω = 30 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) = 216/(s(s + 8)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 216/(s(s + 8))
ωc = rad/s
6.Hard
|H| (dB)11101010010010001000−80−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​ = ?

A unity-feedback loop has the open-loop transfer function L(s) = 400/(s(s + 20)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 400/(s(s + 20))
ωc = rad/s

Answer key

  1. 1. ωc = 2128 rad/s
  2. 2. ωc = 22000 rad/s
  3. 3. |G(jω)| = 6.014 dB
  4. 4. ∠G(jω) = −104.3 °
  5. 5. ωc = 13.65 rad/s
  6. 6. ωc = 15.72 rad/s

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