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
vin​R = 100 ΩL = 1 mHvout​

Find the corner (−3 dB) frequency ωc of the RL high-pass filter shown, with R = 100 Ω, L = 1 mH. Give it in rad/s.

R = 100 ΩL = 1 mH
ωc = rad/s
2.Easy
vin​C = 22 nFR = 2.2 kΩvout​

Find the corner (−3 dB) frequency ωc of the RC high-pass filter shown, with R = 2.2 kΩ, C = 22 nF. Give it in rad/s.

R = 2.2 kΩC = 22 nF
ωc = rad/s
3.Medium
|H| (dB)1101001000−60−40−2002040ω (rad/s)ω = 30

Find the exact magnitude |G(jω)| of G(s) = 4104/((s + 12)(s + 18)) at ω = 30 rad/s, in dB.

G(s) = 4104/((s + 12)(s + 18))ω = 30 rad/s
|G(jω)| = dB
4.Medium
|H| (dB)0.10.111101010010010001000−40−200204060ω (rad/s)φ (°)ω (rad/s)−135−90−450ω = 1

Find the phase ∠G(jω) of G(s) = 37(s + 15)/(s(s + 6)) at ω = 1 rad/s, in degrees.

G(s) = 37(s + 15)/(s(s + 6))ω = 1 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) = 36/(s(s + 2)). Find the phase margin PM in degrees.

L(s) = 36/(s(s + 2))
PM = °
6.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) = K/(s(s + 1)(s + 7)). Find the gain K that gives a gain margin of 4 dB.

L(s) = K/(s(s + 1)(s + 7))GM = 4 dB
K =

Answer key

  1. 1. ωc = 100000 rad/s
  2. 2. ωc = 20661 rad/s
  3. 3. |G(jω)| = 11.2 dB
  4. 4. ∠G(jω) = −95.65 °
  5. 5. PM = 18.92 °
  6. 6. K = 35.33

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