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)0.1110100100002040ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 3600(s + 1)/((s + 60)(s + 8)) in decibels, |G(0)| in dB.

G(s) = 3600(s + 1)/((s + 60)(s + 8))
|G(0)| = dB
2.Easy
|H| (dB)110100100010000−80−60−40−200?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 20000/((s + 20)(s + 1000)). What is the slope n of the straight-line asymptote between 20 and 1000 rad/s, in dB/decade?

G(s) = 20000/((s + 20)(s + 1000))
n = dB/dec
3.Medium
|H| (dB)0.11101001000−60−40−2002040ω (rad/s)ω = 8

Find the exact magnitude |G(jω)| of G(s) = 3510/((s + 13)(s + 18)) at ω = 8 rad/s, in dB.

G(s) = 3510/((s + 13)(s + 18))ω = 8 rad/s
|G(jω)| = dB
4.Medium
|H| (dB)0.10.111101010010010001000−40−2002040ω (rad/s)φ (°)ω (rad/s)−90−450ω = 30

Find the phase ∠G(jω) of G(s) = 12(s + 5)/(s(s + 9)) at ω = 30 rad/s, in degrees.

G(s) = 12(s + 5)/(s(s + 9))ω = 30 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) = 304/(s(s + 9)(s + 10)). Find the gain margin GM in dB.

L(s) = 304/(s(s + 9)(s + 10))
GM = dB
6.Hard
|H| (dB)0.10.1111010100100−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​ = ?

A unity-feedback loop has the open-loop transfer function L(s) = 32/(s(s + 8)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 32/(s(s + 8))
ωc = rad/s

Answer key

  1. 1. |G(0)| = 17.5 dB
  2. 2. n = −20 dB/dec
  3. 3. |G(jω)| = 21.34 dB
  4. 4. ∠G(jω) = −82.76 °
  5. 5. GM = 15 dB
  6. 6. ωc = 3.641 rad/s

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