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)110100100002040ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 2500(s + 15)/((s + 30)(s + 70)) in decibels, |G(0)| in dB.

G(s) = 2500(s + 15)/((s + 30)(s + 70))
|G(0)| = dB
2.Easy
vin​C = 47 nFR = 4.7 kΩvout​

Find the corner (−3 dB) frequency ωc of the RC high-pass filter shown, with R = 4.7 kΩ, C = 47 nF. Give it in rad/s.

R = 4.7 kΩC = 47 nF
ωc = rad/s
3.Medium
|H| (dB)0.10.111101010010010001000−40−200204060ω (rad/s)φ (°)ω (rad/s)−135−90−450ω = 20

Find the phase ∠G(jω) of G(s) = 14(s + 5)/(s(s + 3)) at ω = 20 rad/s, in degrees.

G(s) = 14(s + 5)/(s(s + 3))ω = 20 rad/s
∠G(jω) = °
4.Medium
|H| (dB)0.10.111101010010010001000−40−20020406080ω (rad/s)φ (°)ω (rad/s)−135−90−450ω = 5

Find the phase ∠G(jω) of G(s) = 40(s + 13)/(s(s + 4)) at ω = 5 rad/s, in degrees.

G(s) = 40(s + 13)/(s(s + 4))ω = 5 rad/s
∠G(jω) = °
5.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) = 40/(s(s + 4)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 40/(s(s + 4))
ωc = rad/s
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) = 45/(s(s + 5)). Find the phase margin PM in degrees.

L(s) = 45/(s(s + 5))
PM = °

Answer key

  1. 1. |G(0)| = 25.04 dB
  2. 2. ωc = 4527 rad/s
  3. 3. ∠G(jω) = −95.51 °
  4. 4. ∠G(jω) = −120.3 °
  5. 5. ωc = 5.726 rad/s
  6. 6. PM = 40.53 °

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