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)0.111010002040ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 220(s + 3)/((s + 2)(s + 8)) in decibels, |G(0)| in dB.

G(s) = 220(s + 3)/((s + 2)(s + 8))
|G(0)| = dB
2.Easy
vin​L = 22 mHR = 470 Ωvout​

Find the corner (−3 dB) frequency fc of the RL low-pass filter shown, with R = 470 Ω, L = 22 mH. Give it in Hz.

R = 470 ΩL = 22 mH
fc = Hz
3.Medium
|H| (dB)0.10.111101010010010001000−40−2002040ω (rad/s)φ (°)ω (rad/s)−90−450ω = 20

Find the phase ∠G(jω) of G(s) = 18(s + 3)/(s(s + 10)) at ω = 20 rad/s, in degrees.

G(s) = 18(s + 3)/(s(s + 10))ω = 20 rad/s
∠G(jω) = °
4.Medium
vin​L = 5 mHC = 2.2 µFR = 1 Ωvout​

In the series RLC band-pass filter shown the output is taken across R = 1 Ω, with L = 5 mH and C = 2.2 µF. Find the centre (resonant) frequency f0 in Hz.

R = 1 ΩL = 5 mHC = 2.2 µF
f0 = Hz
5.Hard
|H| (dB)11101010010010001000−60−40−200204060ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​

A unity-feedback loop has the open-loop transfer function L(s) = 1200/(s(s + 10)). Find the phase margin PM in degrees.

L(s) = 1200/(s(s + 10))
PM = °
6.Hard
|H| (dB)0.10.111101010010010001000−60−40−200204060ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​

A unity-feedback loop has the open-loop transfer function L(s) = 160/(s(s + 8)). Find the phase margin PM in degrees.

L(s) = 160/(s(s + 8))
PM = °

Answer key

  1. 1. |G(0)| = 32.31 dB
  2. 2. fc = 3400 Hz
  3. 3. ∠G(jω) = −71.97 °
  4. 4. f0 = 1517 Hz
  5. 5. PM = 16.42 °
  6. 6. PM = 34.93 °

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