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 = 100 mHR = 220 Ωvout​

Find the corner (−3 dB) frequency fc of the RL low-pass filter shown, with R = 220 Ω, L = 100 mH. Give it in Hz.

R = 220 ΩL = 100 mH
fc = Hz
2.Easy
vin​R = 47 kΩC = 1 nFvout​

Find the corner (−3 dB) frequency fc of the RC low-pass filter shown, with R = 47 kΩ, C = 1 nF. Give it in Hz.

R = 47 kΩC = 1 nF
fc = Hz
3.Medium
vin​R = 470 ΩL = 2.2 mHvout​

The RL high-pass filter shown has R = 470 Ω, L = 2.2 mH. A sinusoidal input of 100 kHz is applied. Find the gain |H| = |vout/vin| in dB.

R = 470 ΩL = 2.2 mHf = 100 kHz
|H| = dB
4.Medium
vin​C = 100 nFR = 47 kΩvout​

The RC high-pass filter shown has R = 47 kΩ, C = 100 nF. A sinusoidal input of 170 Hz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 47 kΩC = 100 nFf = 170 Hz
φ = °
5.Hard
|H| (dB)0.10.1111010100100−60−40−200204060ω (rad/s)φ (°)ω (rad/s)−270−180−900ω180​

A unity-feedback loop has the open-loop transfer function L(s) = 680/(s(s + 6)(s + 10)). Find the gain margin GM in dB.

L(s) = 680/(s(s + 6)(s + 10))
GM = dB
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) = K/(s(s + 4)(s + 5)). Find the gain K that gives a gain margin of 15 dB.

L(s) = K/(s(s + 4)(s + 5))GM = 15 dB
K =

Answer key

  1. 1. fc = 350.1 Hz
  2. 2. fc = 3386 Hz
  3. 3. |H| = −0.4751 dB
  4. 4. φ = 11.27 °
  5. 5. GM = 2.995 dB
  6. 6. K = 32.01

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