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) = 9(s + 3)/((s + 50)(s + 9)) in decibels, |G(0)| in dB.

G(s) = 9(s + 3)/((s + 50)(s + 9))
|G(0)| = dB
2.Easy
|H| (dB)1101001000−80−60−40−200ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 240/((s + 30)(s + 80)) in decibels, |G(0)| in dB.

G(s) = 240/((s + 30)(s + 80))
|G(0)| = dB
3.Medium
|H| (dB)0.11101001000−80−60−40−20020ω (rad/s)ω = 5

Find the exact magnitude |G(jω)| of G(s) = 912/((s + 16)(s + 19)) at ω = 5 rad/s, in dB.

G(s) = 912/((s + 16)(s + 19))ω = 5 rad/s
|G(jω)| = dB
4.Medium
|H| (dB)0.1110100−40−20020ω (rad/s)ω = 8

Find the exact magnitude |G(jω)| of G(s) = 168/((s + 4)(s + 6)) at ω = 8 rad/s, in dB.

G(s) = 168/((s + 4)(s + 6))ω = 8 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) = 314/(s(s + 4)(s + 10)). Find the gain margin GM in dB.

L(s) = 314/(s(s + 4)(s + 10))
GM = dB
6.Hard
|H| (dB)0.10.1111010100100−60−40−200204060ω (rad/s)φ (°)ω (rad/s)−270−180−900ω180​ = ?

A unity-feedback loop has the open-loop transfer function L(s) = 534/(s(s + 6)(s + 8)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 534/(s(s + 6)(s + 8))
ω180 = rad/s

Answer key

  1. 1. |G(0)| = −24.44 dB
  2. 2. |G(0)| = −20 dB
  3. 3. |G(jω)| = 8.847 dB
  4. 4. |G(jω)| = 5.475 dB
  5. 5. GM = 5.025 dB
  6. 6. ω180 = 6.928 rad/s

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