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 = 22 mHR = 1000 Ωvout​

Find the corner (−3 dB) frequency fc of the RL low-pass filter shown, with R = 1000 Ω, L = 22 mH. Give it in Hz.

R = 1000 ΩL = 22 mH
fc = Hz
2.Easy
vin​L = 10 mHR = 22 Ωvout​

Find the corner (−3 dB) frequency fc of the RL low-pass filter shown, with R = 22 Ω, L = 10 mH. Give it in Hz.

R = 22 ΩL = 10 mH
fc = Hz
3.Medium
|H| (dB)0.10.1111010100100−20020406080ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ω = 5

Find the phase ∠G(jω) of G(s) = 28(s + 8)/(s(s + 1)) at ω = 5 rad/s, in degrees.

G(s) = 28(s + 8)/(s(s + 1))ω = 5 rad/s
∠G(jω) = °
4.Medium
|H| (dB)0.10.1111010100100−2002040ω (rad/s)φ (°)ω (rad/s)−90−450ω = 1

Find the phase ∠G(jω) of G(s) = 15(s + 1)/(s(s + 6)) at ω = 1 rad/s, in degrees.

G(s) = 15(s + 1)/(s(s + 6))ω = 1 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) = K/(s(s + 7)(s + 8)). Find the gain K that gives a gain margin of 8 dB.

L(s) = K/(s(s + 7)(s + 8))GM = 8 dB
K =
6.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 phase margin PM in degrees.

L(s) = 496/(s(s + 8))
PM = °

Answer key

  1. 1. fc = 7234 Hz
  2. 2. fc = 350.1 Hz
  3. 3. ∠G(jω) = −136.7 °
  4. 4. ∠G(jω) = −54.46 °
  5. 5. K = 334.4
  6. 6. PM = 20.35 °

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