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​C = 4.7 nFR = 1 kΩvout​

Find the corner (−3 dB) frequency fc of the RC high-pass filter shown, with R = 1 kΩ, C = 4.7 nF. Give it in Hz.

R = 1 kΩC = 4.7 nF
fc = Hz
2.Easy
vin​L = 4.7 mHR = 1000 Ωvout​

Find the corner (−3 dB) frequency ωc of the RL low-pass filter shown, with R = 1000 Ω, L = 4.7 mH. Give it in rad/s.

R = 1000 ΩL = 4.7 mH
ωc = rad/s
3.Medium
|H| (dB)0.10.111101010010010001000−40−200204060ω (rad/s)φ (°)ω (rad/s)−135−90−450ω = 30

Find the phase ∠G(jω) of G(s) = 43(s + 11)/(s(s + 6)) at ω = 30 rad/s, in degrees.

G(s) = 43(s + 11)/(s(s + 6))ω = 30 rad/s
∠G(jω) = °
4.Medium
vin​L = 10 mHC = 2.2 µFR = 20 Ωvout​

In the series RLC band-pass filter shown the output is taken across R = 20 Ω, with L = 10 mH and C = 2.2 µF. Find the −3 dB bandwidth BW in Hz.

R = 20 ΩL = 10 mHC = 2.2 µF
BW = Hz
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 + 1)(s + 6)). Find the gain K that gives a gain margin of 4 dB.

L(s) = K/(s(s + 1)(s + 6))GM = 4 dB
K =
6.Hard
|H| (dB)0.10.1111010100100−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​

A unity-feedback loop has the open-loop transfer function L(s) = 12.4/(s(s + 4)). Find the phase margin PM in degrees.

L(s) = 12.4/(s(s + 4))
PM = °

Answer key

  1. 1. fc = 33863 Hz
  2. 2. ωc = 212766 rad/s
  3. 3. ∠G(jω) = −98.83 °
  4. 4. BW = 318.3 Hz
  5. 5. K = 26.5
  6. 6. PM = 56.98 °

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