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)0.1110100100010000−60−40−200204060?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 25000(s + 2)/(s(s + 500)(s + 10)). What is the slope n of the straight-line asymptote between 10 and 500 rad/s, in dB/decade?

G(s) = 25000(s + 2)/(s(s + 500)(s + 10))
n = dB/dec
2.Easy
vin​C = 1 nFR = 4.7 kΩvout​

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

R = 4.7 kΩC = 1 nF
fc = Hz
3.Medium
|H| (dB)0.10.1111010100100−20020406080ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ω = 10

Find the phase ∠G(jω) of G(s) = 27(s + 7)/(s(s + 1)) at ω = 10 rad/s, in degrees.

G(s) = 27(s + 7)/(s(s + 1))ω = 10 rad/s
∠G(jω) = °
4.Medium
vin​C = 1 nFR = 47 kΩvout​

The RC high-pass filter shown has R = 47 kΩ, C = 1 nF. A sinusoidal input of 680 Hz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 47 kΩC = 1 nFf = 680 Hz
φ = °
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) = 134/(s(s + 5)(s + 10)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 134/(s(s + 5)(s + 10))
ω180 = rad/s
6.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) = 80/(s(s + 5)). Find the phase margin PM in degrees.

L(s) = 80/(s(s + 5))
PM = °

Answer key

  1. 1. n = −20 dB/dec
  2. 2. fc = 33863 Hz
  3. 3. ∠G(jω) = −119.3 °
  4. 4. φ = 78.65 °
  5. 5. ω180 = 7.071 rad/s
  6. 6. PM = 31.14 °

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