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​L = 22 mHR = 1000 Ωvout​

Find the corner (−3 dB) frequency ωc of the RL low-pass filter shown, with R = 1000 Ω, L = 22 mH. Give it in rad/s.

R = 1000 ΩL = 22 mH
ωc = rad/s
2.Easy
vin​R = 470 ΩL = 10 mHvout​

Find the corner (−3 dB) frequency ωc of the RL high-pass filter shown, with R = 470 Ω, L = 10 mH. Give it in rad/s.

R = 470 ΩL = 10 mH
ωc = rad/s
3.Medium
|H| (dB)0.10.111101010010010001000−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−90−450ω = 10

Find the phase ∠G(jω) of G(s) = 10(s + 5)/(s(s + 12)) at ω = 10 rad/s, in degrees.

G(s) = 10(s + 5)/(s(s + 12))ω = 10 rad/s
∠G(jω) = °
4.Medium
vin​C = 22 nFR = 2.2 kΩvout​

The RC high-pass filter shown has R = 2.2 kΩ, C = 22 nF. A sinusoidal input of 1.6 kHz is applied. Find the gain |H| = |vout/vin| in dB.

R = 2.2 kΩC = 22 nFf = 1.6 kHz
|H| = dB
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) = 60/(s(s + 5)). Find the phase margin PM in degrees.

L(s) = 60/(s(s + 5))
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) = 40/(s(s + 1)(s + 8)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 40/(s(s + 1)(s + 8))
ω180 = rad/s

Answer key

  1. 1. ωc = 45455 rad/s
  2. 2. ωc = 47000 rad/s
  3. 3. ∠G(jω) = −66.37 °
  4. 4. |H| = −7.18 dB
  5. 5. PM = 35.6 °
  6. 6. ω180 = 2.828 rad/s

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