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.

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1.Easy
vin​R = 22 ΩL = 2.2 mHvout​

Find the corner (−3 dB) frequency fc of the RL high-pass filter shown, with R = 22 Ω, L = 2.2 mH. Give it in Hz.

R = 22 ΩL = 2.2 mH
fc = Hz
2.Easy
vin​L = 47 mHR = 220 Ωvout​

Find the corner (−3 dB) frequency fc of the RL low-pass filter shown, with R = 220 Ω, L = 47 mH. Give it in Hz.

R = 220 ΩL = 47 mH
fc = Hz
3.Medium
vin​L = 1 mHC = 0.47 µFR = 1 Ωvout​

In the series RLC band-pass filter shown the output is taken across R = 1 Ω, with L = 1 mH and C = 0.47 µF. Find the −3 dB bandwidth BW in Hz.

R = 1 ΩL = 1 mHC = 0.47 µF
BW = Hz
4.Medium
vin​L = 5 mHC = 4.7 µFR = 10 Ωvout​

In the series RLC band-pass filter shown the output is taken across R = 10 Ω, with L = 5 mH and C = 4.7 µF. Find the −3 dB bandwidth BW in Hz.

R = 10 ΩL = 5 mHC = 4.7 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) = 482/(s(s + 6)(s + 10)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 482/(s(s + 6)(s + 10))
ω180 = rad/s
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) = 35/(s(s + 5)). Find the phase margin PM in degrees.

L(s) = 35/(s(s + 5))
PM = °

Answer key

  1. 1. fc = 1592 Hz
  2. 2. fc = 745 Hz
  3. 3. BW = 159.2 Hz
  4. 4. BW = 318.3 Hz
  5. 5. ω180 = 7.746 rad/s
  6. 6. PM = 45.19 °

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