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​R = 22 ΩL = 47 mHvout​

Find the corner (−3 dB) frequency fc of the RL high-pass filter shown, with R = 22 Ω, L = 47 mH. Give it in Hz.

R = 22 ΩL = 47 mH
fc = Hz
2.Easy
vin​R = 22 kΩC = 4.7 nFvout​

Find the corner (−3 dB) frequency ωc of the RC low-pass filter shown, with R = 22 kΩ, C = 4.7 nF. Give it in rad/s.

R = 22 kΩC = 4.7 nF
ωc = rad/s
3.Medium
|H| (dB)0.10.1111010100100−200204060ω (rad/s)φ (°)ω (rad/s)−135−90−450ω = 1

Find the phase ∠G(jω) of G(s) = 29(s + 5)/(s(s + 3)) at ω = 1 rad/s, in degrees.

G(s) = 29(s + 5)/(s(s + 3))ω = 1 rad/s
∠G(jω) = °
4.Medium
|H| (dB)0.11101001000−60−40−20020ω (rad/s)ω = 10

Find the exact magnitude |G(jω)| of G(s) = 1064/((s + 7)(s + 19)) at ω = 10 rad/s, in dB.

G(s) = 1064/((s + 7)(s + 19))ω = 10 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) = 170/(s(s + 2)(s + 10)). Find the gain margin GM in dB.

L(s) = 170/(s(s + 2)(s + 10))
GM = dB
6.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) = 306/(s(s + 4)(s + 8)). Find the gain margin GM in dB.

L(s) = 306/(s(s + 4)(s + 8))
GM = dB

Answer key

  1. 1. fc = 74.5 Hz
  2. 2. ωc = 9671 rad/s
  3. 3. ∠G(jω) = −97.13 °
  4. 4. |G(jω)| = 12.17 dB
  5. 5. GM = 2.995 dB
  6. 6. GM = 1.972 dB

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