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)110100100010000−60−40−2002040?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 1 × 10⁶/((s + 1000)(s + 50)). What is the slope n of the straight-line asymptote above 1000 rad/s, in dB/decade?

G(s) = 1 × 10⁶/((s + 1000)(s + 50))
n = dB/dec
2.Easy
|H| (dB)0.11101001000−20020ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 480(s + 3)/((s + 2)(s + 80)) in decibels, |G(0)| in dB.

G(s) = 480(s + 3)/((s + 2)(s + 80))
|G(0)| = dB
3.Medium
|H| (dB)0.10.1111010100100−40−200204060ω (rad/s)φ (°)ω (rad/s)−135−90−450ω = 4

Find the phase ∠G(jω) of G(s) = 4(s + 10)/(s(s + 2)) at ω = 4 rad/s, in degrees.

G(s) = 4(s + 10)/(s(s + 2))ω = 4 rad/s
∠G(jω) = °
4.Medium
|H| (dB)0.1110100−40−20020ω (rad/s)ω = 1

Find the exact magnitude |G(jω)| of G(s) = 280/((s + 4)(s + 7)) at ω = 1 rad/s, in dB.

G(s) = 280/((s + 4)(s + 7))ω = 1 rad/s
|G(jω)| = dB
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) = 166/(s(s + 5)(s + 6)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 166/(s(s + 5)(s + 6))
ω180 = rad/s
6.Hard
|H| (dB)0.010.010.10.1111010100100−80−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​

A unity-feedback loop has the open-loop transfer function L(s) = 5/(s(s + 5)). Find the phase margin PM in degrees.

L(s) = 5/(s(s + 5))
PM = °

Answer key

  1. 1. n = −40 dB/dec
  2. 2. |G(0)| = 19.08 dB
  3. 3. ∠G(jω) = −131.6 °
  4. 4. |G(jω)| = 19.65 dB
  5. 5. ω180 = 5.477 rad/s
  6. 6. PM = 78.9 °

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