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 = 220 ΩL = 100 mHvout​

Find the corner (−3 dB) frequency ωc of the RL high-pass filter shown, with R = 220 Ω, L = 100 mH. Give it in rad/s.

R = 220 ΩL = 100 mH
ωc = rad/s
2.Easy
vin​R = 1 kΩC = 10 nFvout​

Find the corner (−3 dB) frequency fc of the RC low-pass filter shown, with R = 1 kΩ, C = 10 nF. Give it in Hz.

R = 1 kΩC = 10 nF
fc = Hz
3.Medium
vin​R = 10 kΩC = 2.2 nFvout​

The RC low-pass filter shown has R = 10 kΩ, C = 2.2 nF. A sinusoidal input of 3.6 kHz is applied. Find the gain |H| = |vout/vin| in dB.

R = 10 kΩC = 2.2 nFf = 3.6 kHz
|H| = dB
4.Medium
|H| (dB)0.11101001000−60−40−2002040ω (rad/s)ω = 8

Find the exact magnitude |G(jω)| of G(s) = 1064/((s + 4)(s + 14)) at ω = 8 rad/s, in dB.

G(s) = 1064/((s + 4)(s + 14))ω = 8 rad/s
|G(jω)| = dB
5.Hard
|H| (dB)0.10.1111010100100−40−200204060ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​

A unity-feedback loop has the open-loop transfer function L(s) = 110/(s(s + 10)). Find the phase margin PM in degrees.

L(s) = 110/(s(s + 10))
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) = 40/(s(s + 4)). Find the phase margin PM in degrees.

L(s) = 40/(s(s + 4))
PM = °

Answer key

  1. 1. ωc = 2200 rad/s
  2. 2. fc = 15915 Hz
  3. 3. |H| = −0.9609 dB
  4. 4. |G(jω)| = 17.36 dB
  5. 5. PM = 49.92 °
  6. 6. PM = 34.93 °

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