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)0.11101001000−80−60−40−200ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 210/((s + 4)(s + 90)) in decibels, |G(0)| in dB.

G(s) = 210/((s + 4)(s + 90))
|G(0)| = dB
2.Easy
|H| (dB)0.010.1110100−60−40−2002040?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 100/((s + 0.5)(s + 2)). What is the slope n of the straight-line asymptote above 2 rad/s, in dB/decade?

G(s) = 100/((s + 0.5)(s + 2))
n = dB/dec
3.Medium
|H| (dB)0.11101001000−60−40−2002040ω (rad/s)ω = 20

Find the exact magnitude |G(jω)| of G(s) = 1512/((s + 7)(s + 12)) at ω = 20 rad/s, in dB.

G(s) = 1512/((s + 7)(s + 12))ω = 20 rad/s
|G(jω)| = dB
4.Medium
|H| (dB)1101001000−60−40−2002040ω (rad/s)ω = 15

Find the exact magnitude |G(jω)| of G(s) = 2800/((s + 10)(s + 20)) at ω = 15 rad/s, in dB.

G(s) = 2800/((s + 10)(s + 20))ω = 15 rad/s
|G(jω)| = dB
5.Hard
|H| (dB)0.10.111101010010010001000−60−40−200204060ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​ = ?

A unity-feedback loop has the open-loop transfer function L(s) = 150/(s(s + 5)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 150/(s(s + 5))
ωc = 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) = 10/(s(s + 2)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 10/(s(s + 2))
ωc = rad/s

Answer key

  1. 1. |G(0)| = −4.682 dB
  2. 2. n = −40 dB/dec
  3. 3. |G(jω)| = 9.713 dB
  4. 4. |G(jω)| = 15.87 dB
  5. 5. ωc = 11.75 rad/s
  6. 6. ωc = 2.863 rad/s

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