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 ΩL = 47 mHvout​

Find the corner (−3 dB) frequency ωc of the RL high-pass filter shown, with R = 22 Ω, L = 47 mH. Give it in rad/s.

R = 22 ΩL = 47 mH
ωc = rad/s
2.Easy
|H| (dB)0.11101001000−80−60−40−200ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 240/((s + 7)(s + 80)) in decibels, |G(0)| in dB.

G(s) = 240/((s + 7)(s + 80))
|G(0)| = dB
3.Medium
vin​L = 22 mHR = 1000 Ωvout​

The RL low-pass filter shown has R = 1000 Ω, L = 22 mH. A sinusoidal input of 14 kHz is applied. Find the gain |H| = |vout/vin| in dB.

R = 1000 ΩL = 22 mHf = 14 kHz
|H| = dB
4.Medium
vin​L = 5 mHC = 4.7 µFR = 5 Ωvout​

In the series RLC band-pass filter shown the output is taken across R = 5 Ω, with L = 5 mH and C = 4.7 µF. Find the quality factor Q.

R = 5 ΩL = 5 mHC = 4.7 µF
Q =
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 + 2)(s + 8)). Find the gain K that gives a gain margin of 15 dB.

L(s) = K/(s(s + 2)(s + 8))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) = 474/(s(s + 5)(s + 10)). Find the gain margin GM in dB.

L(s) = 474/(s(s + 5)(s + 10))
GM = dB

Answer key

  1. 1. ωc = 468.1 rad/s
  2. 2. |G(0)| = −7.36 dB
  3. 3. |H| = −6.762 dB
  4. 4. Q = 6.523
  5. 5. K = 28.45
  6. 6. GM = 3.986 dB

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