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 = 22 kΩC = 10 nFvout​

Find the corner (−3 dB) frequency ωc of the RC low-pass filter shown, with R = 22 kΩ, C = 10 nF. Give it in rad/s.

R = 22 kΩC = 10 nF
ωc = rad/s
2.Easy
|H| (dB)1101001000−40−200ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 29(s + 14)/((s + 10)(s + 50)) in decibels, |G(0)| in dB.

G(s) = 29(s + 14)/((s + 10)(s + 50))
|G(0)| = dB
3.Medium
|H| (dB)1101001000−60−40−2002040ω (rad/s)ω = 20

Find the exact magnitude |G(jω)| of G(s) = 4590/((s + 15)(s + 18)) at ω = 20 rad/s, in dB.

G(s) = 4590/((s + 15)(s + 18))ω = 20 rad/s
|G(jω)| = dB
4.Medium
|H| (dB)0.010.1110100−40−2002040ω (rad/s)ω = 0.5

Find the exact magnitude |G(jω)| of G(s) = 110/((s + 1)(s + 10)) at ω = 0.5 rad/s, in dB.

G(s) = 110/((s + 1)(s + 10))ω = 0.5 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) = K/(s(s + 8)(s + 9)). Find the gain K that gives a gain margin of 15 dB.

L(s) = K/(s(s + 8)(s + 9))GM = 15 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) = 68/(s(s + 6)(s + 8)). Find the gain margin GM in dB.

L(s) = 68/(s(s + 6)(s + 8))
GM = dB

Answer key

  1. 1. ωc = 4545 rad/s
  2. 2. |G(0)| = −1.809 dB
  3. 3. |G(jω)| = 16.68 dB
  4. 4. |G(jω)| = 19.85 dB
  5. 5. K = 217.7
  6. 6. GM = 19.9 dB

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