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​C = 4.7 nFR = 10 kΩvout​

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

R = 10 kΩC = 4.7 nF
fc = Hz
2.Easy
vin​R = 22 ΩL = 1 mHvout​

Find the corner (−3 dB) frequency fc of the RL high-pass filter shown, with R = 22 Ω, L = 1 mH. Give it in Hz.

R = 22 ΩL = 1 mH
fc = Hz
3.Medium
|H| (dB)0.1110100−40−2002040ω (rad/s)ω = 4

Find the exact magnitude |G(jω)| of G(s) = 264/((s + 3)(s + 8)) at ω = 4 rad/s, in dB.

G(s) = 264/((s + 3)(s + 8))ω = 4 rad/s
|G(jω)| = dB
4.Medium
|H| (dB)0.11101001000−60−40−2002040ω (rad/s)ω = 8

Find the exact magnitude |G(jω)| of G(s) = 2280/((s + 8)(s + 19)) at ω = 8 rad/s, in dB.

G(s) = 2280/((s + 8)(s + 19))ω = 8 rad/s
|G(jω)| = dB
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) = 2/(s(s + 2)). Find the phase margin PM in degrees.

L(s) = 2/(s(s + 2))
PM = °
6.Hard
|H| (dB)0.10.1111010100100−80−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​

A unity-feedback loop has the open-loop transfer function L(s) = 9.2/(s(s + 4)). Find the phase margin PM in degrees.

L(s) = 9.2/(s(s + 4))
PM = °

Answer key

  1. 1. fc = 3386 Hz
  2. 2. fc = 3501 Hz
  3. 3. |G(jω)| = 15.42 dB
  4. 4. |G(jω)| = 19.8 dB
  5. 5. PM = 65.53 °
  6. 6. PM = 62.89 °

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