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)1101001000−60−40−20020ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 1200/((s + 10)(s + 20)) in decibels, |G(0)| in dB.

G(s) = 1200/((s + 10)(s + 20))
|G(0)| = dB
2.Easy
|H| (dB)1101001000−40−200ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 50(s + 20)/((s + 30)(s + 80)) in decibels, |G(0)| in dB.

G(s) = 50(s + 20)/((s + 30)(s + 80))
|G(0)| = dB
3.Medium
|H| (dB)0.10.1111010100100−40−2002040ω (rad/s)φ (°)ω (rad/s)−90−450ω = 2

Find the phase ∠G(jω) of G(s) = 10(s + 5)/(s(s + 7)) at ω = 2 rad/s, in degrees.

G(s) = 10(s + 5)/(s(s + 7))ω = 2 rad/s
∠G(jω) = °
4.Medium
|H| (dB)0.11101001000−80−60−40−20020ω (rad/s)ω = 20

Find the exact magnitude |G(jω)| of G(s) = 768/((s + 8)(s + 12)) at ω = 20 rad/s, in dB.

G(s) = 768/((s + 8)(s + 12))ω = 20 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) = K/(s(s + 5)(s + 10)). Find the gain K that gives a gain margin of 20 dB.

L(s) = K/(s(s + 5)(s + 10))GM = 20 dB
K =
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) = K/(s(s + 2)(s + 8)). Find the gain K that gives a gain margin of 8 dB.

L(s) = K/(s(s + 2)(s + 8))GM = 8 dB
K =

Answer key

  1. 1. |G(0)| = 15.56 dB
  2. 2. |G(0)| = −7.604 dB
  3. 3. ∠G(jω) = −84.14 °
  4. 4. |G(jω)| = 3.686 dB
  5. 5. K = 75
  6. 6. K = 63.7

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