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)0.11101001000−40−20020ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 40(s + 13)/((s + 7)(s + 9)) in decibels, |G(0)| in dB.

G(s) = 40(s + 13)/((s + 7)(s + 9))
|G(0)| = dB
2.Easy
|H| (dB)0.1110100−40−2002040ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 220/((s + 3)(s + 6)) in decibels, |G(0)| in dB.

G(s) = 220/((s + 3)(s + 6))
|G(0)| = dB
3.Medium
|H| (dB)11101010010010001000−40−2002040ω (rad/s)φ (°)ω (rad/s)−135−90−450ω = 20

Find the phase ∠G(jω) of G(s) = 10(s + 19)/(s(s + 11)) at ω = 20 rad/s, in degrees.

G(s) = 10(s + 19)/(s(s + 11))ω = 20 rad/s
∠G(jω) = °
4.Medium
|H| (dB)0.10.111101010010010001000−40−20020406080ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ω = 8

Find the phase ∠G(jω) of G(s) = 8(s + 18)/(s(s + 1)) at ω = 8 rad/s, in degrees.

G(s) = 8(s + 18)/(s(s + 1))ω = 8 rad/s
∠G(jω) = °
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) = 212/(s(s + 7)(s + 10)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 212/(s(s + 7)(s + 10))
ω180 = rad/s
6.Hard
|H| (dB)0.10.1111010100100−80−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​

A unity-feedback loop has the open-loop transfer function L(s) = 6.8/(s(s + 2)). Find the phase margin PM in degrees.

L(s) = 6.8/(s(s + 2))
PM = °

Answer key

  1. 1. |G(0)| = 18.33 dB
  2. 2. |G(0)| = 21.74 dB
  3. 3. ∠G(jω) = −104.7 °
  4. 4. ∠G(jω) = −148.9 °
  5. 5. ω180 = 8.367 rad/s
  6. 6. PM = 41.56 °

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