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 = 470 Ωvout​

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

R = 470 ΩL = 1 mH
fc = Hz
2.Easy
vin​R = 10 ΩL = 4.7 mHvout​

Find the corner (−3 dB) frequency ωc of the RL high-pass filter shown, with R = 10 Ω, L = 4.7 mH. Give it in rad/s.

R = 10 ΩL = 4.7 mH
ωc = rad/s
3.Medium
vin​C = 1 nFR = 4.7 kΩvout​

The RC high-pass filter shown has R = 4.7 kΩ, C = 1 nF. A sinusoidal input of 68 kHz is applied. Find the gain |H| = |vout/vin| in dB.

R = 4.7 kΩC = 1 nFf = 68 kHz
|H| = dB
4.Medium
vin​R = 47 ΩL = 2.2 mHvout​

The RL high-pass filter shown has R = 47 Ω, L = 2.2 mH. A sinusoidal input of 10 kHz is applied. Find the gain |H| = |vout/vin| in dB.

R = 47 ΩL = 2.2 mHf = 10 kHz
|H| = dB
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) = 680/(s(s + 8)). Find the phase margin PM in degrees.

L(s) = 680/(s(s + 8))
PM = °
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) = 316/(s(s + 5)(s + 9)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 316/(s(s + 5)(s + 9))
ω180 = rad/s

Answer key

  1. 1. fc = 74803 Hz
  2. 2. ωc = 2128 rad/s
  3. 3. |H| = −0.9621 dB
  4. 4. |H| = −0.4751 dB
  5. 5. PM = 17.44 °
  6. 6. ω180 = 6.708 rad/s

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