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
|H| (dB)0.11101001000−60−40−200ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 2(s + 14)/((s + 80)(s + 9)) in decibels, |G(0)| in dB.

G(s) = 2(s + 14)/((s + 80)(s + 9))
|G(0)| = dB
2.Easy
|H| (dB)1101001000−40−200ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 31(s + 11)/((s + 40)(s + 70)) in decibels, |G(0)| in dB.

G(s) = 31(s + 11)/((s + 40)(s + 70))
|G(0)| = dB
3.Medium
|H| (dB)0.11101001000−80−60−40−2002040ω (rad/s)ω = 30

Find the exact magnitude |G(jω)| of G(s) = 196/((s + 2)(s + 7)) at ω = 30 rad/s, in dB.

G(s) = 196/((s + 2)(s + 7))ω = 30 rad/s
|G(jω)| = dB
4.Medium
|H| (dB)0.11101001000−60−40−2002040ω (rad/s)ω = 10

Find the exact magnitude |G(jω)| of G(s) = 1008/((s + 6)(s + 12)) at ω = 10 rad/s, in dB.

G(s) = 1008/((s + 6)(s + 12))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) = 68/(s(s + 3)(s + 5)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 68/(s(s + 3)(s + 5))
ω180 = rad/s
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) = 82/(s(s + 6)(s + 9)). Find the gain margin GM in dB.

L(s) = 82/(s(s + 6)(s + 9))
GM = dB

Answer key

  1. 1. |G(0)| = −28.2 dB
  2. 2. |G(0)| = −18.29 dB
  3. 3. |G(jω)| = −13.49 dB
  4. 4. |G(jω)| = 14.86 dB
  5. 5. ω180 = 3.873 rad/s
  6. 6. GM = 19.89 dB

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