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)1101001000−80−60−40−2002040?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 400/(s(s + 20)). What is the slope n of the straight-line asymptote above 20 rad/s, in dB/decade?

G(s) = 400/(s(s + 20))
n = dB/dec
2.Easy
vin​R = 22 kΩC = 4.7 nFvout​

Find the corner (−3 dB) frequency ωc of the RC low-pass filter shown, with R = 22 kΩ, C = 4.7 nF. Give it in rad/s.

R = 22 kΩC = 4.7 nF
ωc = rad/s
3.Medium
|H| (dB)0.10.111101010010010001000−60−40−200204060ω (rad/s)φ (°)ω (rad/s)−135−90−450ω = 4

Find the phase ∠G(jω) of G(s) = 9(s + 16)/(s(s + 11)) at ω = 4 rad/s, in degrees.

G(s) = 9(s + 16)/(s(s + 11))ω = 4 rad/s
∠G(jω) = °
4.Medium
vin​R = 4.7 kΩC = 22 nFvout​

The RC low-pass filter shown has R = 4.7 kΩ, C = 22 nF. A sinusoidal input of 7.7 kHz is applied. Find the gain |H| = |vout/vin| in dB.

R = 4.7 kΩC = 22 nFf = 7.7 kHz
|H| = dB
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) = 30/(s(s + 10)). Find the phase margin PM in degrees.

L(s) = 30/(s(s + 10))
PM = °
6.Hard
|H| (dB)11101010010010001000−80−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​ = ?

A unity-feedback loop has the open-loop transfer function L(s) = 500/(s(s + 10)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 500/(s(s + 10))
ωc = rad/s

Answer key

  1. 1. n = −40 dB/dec
  2. 2. ωc = 9671 rad/s
  3. 3. ∠G(jω) = −95.95 °
  4. 4. |H| = −14.15 dB
  5. 5. PM = 73.92 °
  6. 6. ωc = 21.27 rad/s

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