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)0.010.1110100100010000−40−20020406080?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 5000/(s(s + 0.5)(s + 500)). What is the slope n of the straight-line asymptote above 500 rad/s, in dB/decade?

G(s) = 5000/(s(s + 0.5)(s + 500))
n = dB/dec
2.Easy
vin​C = 22 nFR = 3.3 kΩvout​

Find the corner (−3 dB) frequency ωc of the RC high-pass filter shown, with R = 3.3 kΩ, C = 22 nF. Give it in rad/s.

R = 3.3 kΩC = 22 nF
ωc = rad/s
3.Medium
|H| (dB)0.10.111101010010010001000−40−200204060ω (rad/s)φ (°)ω (rad/s)−135−90−450ω = 15

Find the phase ∠G(jω) of G(s) = 27(s + 18)/(s(s + 7)) at ω = 15 rad/s, in degrees.

G(s) = 27(s + 18)/(s(s + 7))ω = 15 rad/s
∠G(jω) = °
4.Medium
vin​R = 47 kΩC = 1 nFvout​

The RC low-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)0.10.111101010010010001000−60−40−200204060ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​ = ?

A unity-feedback loop has the open-loop transfer function L(s) = 140/(s(s + 5)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 140/(s(s + 5))
ωc = rad/s
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) = 476/(s(s + 6)(s + 8)). Find the gain margin GM in dB.

L(s) = 476/(s(s + 6)(s + 8))
GM = dB

Answer key

  1. 1. n = −60 dB/dec
  2. 2. ωc = 13774 rad/s
  3. 3. ∠G(jω) = −115.2 °
  4. 4. φ = −11.35 °
  5. 5. ωc = 11.32 rad/s
  6. 6. GM = 2.995 dB

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