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 = 4.7 kΩC = 10 nFvout​

Find the corner (−3 dB) frequency fc of the RC low-pass filter shown, with R = 4.7 kΩ, C = 10 nF. Give it in Hz.

R = 4.7 kΩC = 10 nF
fc = Hz
2.Easy
vin​C = 22 nFR = 3.3 kΩvout​

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

R = 3.3 kΩC = 22 nF
fc = Hz
3.Medium
vin​C = 4.7 nFR = 22 kΩvout​

The RC high-pass filter shown has R = 22 kΩ, C = 4.7 nF. A sinusoidal input of 310 Hz is applied. Find the gain |H| = |vout/vin| in dB.

R = 22 kΩC = 4.7 nFf = 310 Hz
|H| = dB
4.Medium
vin​R = 4.7 kΩC = 1 nFvout​

The RC low-pass filter shown has R = 4.7 kΩ, C = 1 nF. A sinusoidal input of 140 kHz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 4.7 kΩC = 1 nFf = 140 kHz
φ = °
5.Hard
|H| (dB)11101010010010001000−80−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​

A unity-feedback loop has the open-loop transfer function L(s) = 300/(s(s + 20)). Find the phase margin PM in degrees.

L(s) = 300/(s(s + 20))
PM = °
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) = 34/(s(s + 4)). Find the phase margin PM in degrees.

L(s) = 34/(s(s + 4))
PM = °

Answer key

  1. 1. fc = 3386 Hz
  2. 2. fc = 2192 Hz
  3. 3. |H| = −14.09 dB
  4. 4. φ = −76.4 °
  5. 5. PM = 57.64 °
  6. 6. PM = 37.63 °

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