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 = 4.7 mHR = 47 Ωvout​

Find the corner (−3 dB) frequency fc of the RL low-pass filter shown, with R = 47 Ω, L = 4.7 mH. Give it in Hz.

R = 47 ΩL = 4.7 mH
fc = Hz
2.Easy
vin​R = 10 kΩC = 1 nFvout​

Find the corner (−3 dB) frequency fc of the RC low-pass filter shown, with R = 10 kΩ, C = 1 nF. Give it in Hz.

R = 10 kΩC = 1 nF
fc = Hz
3.Medium
|H| (dB)0.10.111101010010010001000−40−200204060ω (rad/s)φ (°)ω (rad/s)−90−450ω = 15

Find the phase ∠G(jω) of G(s) = 31(s + 3)/(s(s + 9)) at ω = 15 rad/s, in degrees.

G(s) = 31(s + 3)/(s(s + 9))ω = 15 rad/s
∠G(jω) = °
4.Medium
|H| (dB)0.11101001000−80−60−40−2002040ω (rad/s)ω = 3

Find the exact magnitude |G(jω)| of G(s) = 912/((s + 4)(s + 12)) at ω = 3 rad/s, in dB.

G(s) = 912/((s + 4)(s + 12))ω = 3 rad/s
|G(jω)| = dB
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) = 158/(s(s + 2)(s + 9)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 158/(s(s + 2)(s + 9))
ω180 = rad/s
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) = 200/(s(s + 8)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 200/(s(s + 8))
ωc = rad/s

Answer key

  1. 1. fc = 1592 Hz
  2. 2. fc = 15915 Hz
  3. 3. ∠G(jω) = −70.35 °
  4. 4. |G(jω)| = 23.37 dB
  5. 5. ω180 = 4.243 rad/s
  6. 6. ωc = 13.06 rad/s

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