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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
|H| (dB)0.1110100−20020ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 47(s + 6)/((s + 6)(s + 7)) in decibels, |G(0)| in dB.

G(s) = 47(s + 6)/((s + 6)(s + 7))
|G(0)| = dB
2.Easy
|H| (dB)0.010.1110100100010000−80−60−40−2002040?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 5(s + 1000)/((s + 0.5)(s + 200)). What is the slope n of the straight-line asymptote between 200 and 1000 rad/s, in dB/decade?

G(s) = 5(s + 1000)/((s + 0.5)(s + 200))
n = dB/dec
3.Medium
|H| (dB)0.10.111101010010010001000−40−20020406080ω (rad/s)φ (°)ω (rad/s)−135−90−450ω = 20

Find the phase ∠G(jω) of G(s) = 47(s + 15)/(s(s + 7)) at ω = 20 rad/s, in degrees.

G(s) = 47(s + 15)/(s(s + 7))ω = 20 rad/s
∠G(jω) = °
4.Medium
|H| (dB)0.10.111101010010010001000−40−20020406080ω (rad/s)φ (°)ω (rad/s)−135−90−450ω = 20

Find the phase ∠G(jω) of G(s) = 40(s + 17)/(s(s + 5)) at ω = 20 rad/s, in degrees.

G(s) = 40(s + 17)/(s(s + 5))ω = 20 rad/s
∠G(jω) = °
5.Hard
|H| (dB)0.10.1111010100100−40−200204060ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​

A unity-feedback loop has the open-loop transfer function L(s) = 140/(s(s + 10)). Find the phase margin PM in degrees.

L(s) = 140/(s(s + 10))
PM = °
6.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) = 85/(s(s + 5)). Find the phase margin PM in degrees.

L(s) = 85/(s(s + 5))
PM = °

Answer key

  1. 1. |G(0)| = 16.54 dB
  2. 2. n = −40 dB/dec
  3. 3. ∠G(jω) = −107.6 °
  4. 4. ∠G(jω) = −116.3 °
  5. 5. PM = 45.19 °
  6. 6. PM = 30.27 °

Full step-by-step solutions: practise this topic on examproblems.com.