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​L = 100 mHR = 1000 Ωvout​

Find the corner (−3 dB) frequency ωc of the RL low-pass filter shown, with R = 1000 Ω, L = 100 mH. Give it in rad/s.

R = 1000 ΩL = 100 mH
ωc = rad/s
2.Easy
vin​R = 2.2 kΩC = 100 nFvout​

Find the corner (−3 dB) frequency fc of the RC low-pass filter shown, with R = 2.2 kΩ, C = 100 nF. Give it in Hz.

R = 2.2 kΩC = 100 nF
fc = Hz
3.Medium
|H| (dB)0.11101001000−80−60−40−20020ω (rad/s)ω = 4

Find the exact magnitude |G(jω)| of G(s) = 400/((s + 10)(s + 20)) at ω = 4 rad/s, in dB.

G(s) = 400/((s + 10)(s + 20))ω = 4 rad/s
|G(jω)| = dB
4.Medium
|H| (dB)0.10.111101010010010001000−40−200204060ω (rad/s)φ (°)ω (rad/s)−135−90−450ω = 4

Find the phase ∠G(jω) of G(s) = 29(s + 18)/(s(s + 10)) at ω = 4 rad/s, in degrees.

G(s) = 29(s + 18)/(s(s + 10))ω = 4 rad/s
∠G(jω) = °
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) = 12/(s(s + 2)(s + 5)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 12/(s(s + 2)(s + 5))
ω180 = rad/s
6.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) = 9/(s(s + 2)). Find the phase margin PM in degrees.

L(s) = 9/(s(s + 2))
PM = °

Answer key

  1. 1. ωc = 10000 rad/s
  2. 2. fc = 723.4 Hz
  3. 3. |G(jω)| = 5.206 dB
  4. 4. ∠G(jω) = −99.27 °
  5. 5. ω180 = 3.162 rad/s
  6. 6. PM = 36.66 °

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