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 = 470 ΩL = 4.7 mHvout​

Find the corner (−3 dB) frequency fc of the RL high-pass filter shown, with R = 470 Ω, L = 4.7 mH. Give it in Hz.

R = 470 ΩL = 4.7 mH
fc = Hz
2.Easy
vin​R = 10 kΩC = 10 nFvout​

Find the corner (−3 dB) frequency fc of the RC low-pass filter shown, with R = 10 kΩ, C = 10 nF. Give it in Hz.

R = 10 kΩC = 10 nF
fc = Hz
3.Medium
|H| (dB)0.10.1111010100100−200204060ω (rad/s)φ (°)ω (rad/s)−135−90−450ω = 1

Find the phase ∠G(jω) of G(s) = 48(s + 6)/(s(s + 4)) at ω = 1 rad/s, in degrees.

G(s) = 48(s + 6)/(s(s + 4))ω = 1 rad/s
∠G(jω) = °
4.Medium
|H| (dB)0.010.010.10.1111010100100−20020406080100ω (rad/s)φ (°)ω (rad/s)−135−90−450ω = 0.5

Find the phase ∠G(jω) of G(s) = 45(s + 3)/(s(s + 1)) at ω = 0.5 rad/s, in degrees.

G(s) = 45(s + 3)/(s(s + 1))ω = 0.5 rad/s
∠G(jω) = °
5.Hard
|H| (dB)0.10.1111010100100−60−40−200204060ω (rad/s)φ (°)ω (rad/s)−270−180−900ω180​

A unity-feedback loop has the open-loop transfer function L(s) = K/(s(s + 7)(s + 9)). Find the gain K that gives a gain margin of 4 dB.

L(s) = K/(s(s + 7)(s + 9))GM = 4 dB
K =
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 + 4)(s + 10)). Find the gain K that gives a gain margin of 5 dB.

L(s) = K/(s(s + 4)(s + 10))GM = 5 dB
K =

Answer key

  1. 1. fc = 15915 Hz
  2. 2. fc = 1592 Hz
  3. 3. ∠G(jω) = −94.57 °
  4. 4. ∠G(jω) = −107.1 °
  5. 5. K = 636
  6. 6. K = 314.9

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