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)110100100010000−80−60−40−20020?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 50000/((s + 500)(s + 20)). What is the slope n of the straight-line asymptote above 500 rad/s, in dB/decade?

G(s) = 50000/((s + 500)(s + 20))
n = dB/dec
2.Easy
|H| (dB)0.11101001000−40−200ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 46(s + 5)/((s + 20)(s + 50)) in decibels, |G(0)| in dB.

G(s) = 46(s + 5)/((s + 20)(s + 50))
|G(0)| = dB
3.Medium
|H| (dB)0.1110100−40−2002040ω (rad/s)ω = 5

Find the exact magnitude |G(jω)| of G(s) = 192/((s + 2)(s + 6)) at ω = 5 rad/s, in dB.

G(s) = 192/((s + 2)(s + 6))ω = 5 rad/s
|G(jω)| = dB
4.Medium
|H| (dB)0.10.111101010010010001000−40−200204060ω (rad/s)φ (°)ω (rad/s)−135−90−450ω = 3

Find the phase ∠G(jω) of G(s) = 32(s + 16)/(s(s + 9)) at ω = 3 rad/s, in degrees.

G(s) = 32(s + 16)/(s(s + 9))ω = 3 rad/s
∠G(jω) = °
5.Hard
|H| (dB)0.10.1111010100100−60−40−200204060ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​

A unity-feedback loop has the open-loop transfer function L(s) = 40/(s(s + 2)). Find the phase margin PM in degrees.

L(s) = 40/(s(s + 2))
PM = °
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) = 3/(s(s + 1)). Find the phase margin PM in degrees.

L(s) = 3/(s(s + 1))
PM = °

Answer key

  1. 1. n = −40 dB/dec
  2. 2. |G(0)| = −12.77 dB
  3. 3. |G(jω)| = 13.19 dB
  4. 4. ∠G(jω) = −97.82 °
  5. 5. PM = 17.96 °
  6. 6. PM = 32.1 °

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