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​L = 1 mHR = 100 Ωvout​

Find the corner (−3 dB) frequency fc of the RL low-pass filter shown, with R = 100 Ω, L = 1 mH. Give it in Hz.

R = 100 ΩL = 1 mH
fc = Hz
2.Easy
vin​R = 470 ΩL = 1 mHvout​

Find the corner (−3 dB) frequency fc of the RL high-pass filter shown, with R = 470 Ω, L = 1 mH. Give it in Hz.

R = 470 ΩL = 1 mH
fc = Hz
3.Medium
vin​R = 47 kΩC = 10 nFvout​

The RC low-pass filter shown has R = 47 kΩ, C = 10 nF. A sinusoidal input of 170 Hz is applied. Find the gain |H| = |vout/vin| in dB.

R = 47 kΩC = 10 nFf = 170 Hz
|H| = dB
4.Medium
vin​L = 100 mHC = 0.47 µFR = 100 Ωvout​

In the series RLC band-pass filter shown the output is taken across R = 100 Ω, with L = 100 mH and C = 0.47 µF. Find the −3 dB bandwidth BW in Hz.

R = 100 ΩL = 100 mHC = 0.47 µF
BW = Hz
5.Hard
|H| (dB)0.010.010.10.1111010100100−80−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​

A unity-feedback loop has the open-loop transfer function L(s) = 5/(s(s + 5)). Find the phase margin PM in degrees.

L(s) = 5/(s(s + 5))
PM = °
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) = 39/(s(s + 2)). Find the phase margin PM in degrees.

L(s) = 39/(s(s + 2))
PM = °

Answer key

  1. 1. fc = 15915 Hz
  2. 2. fc = 74803 Hz
  3. 3. |H| = −0.9761 dB
  4. 4. BW = 159.2 Hz
  5. 5. PM = 78.9 °
  6. 6. PM = 18.19 °

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