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 = 22 kΩC = 4.7 nFvout​

Find the corner (−3 dB) frequency ωc of the RC low-pass filter shown, with R = 22 kΩ, C = 4.7 nF. Give it in rad/s.

R = 22 kΩC = 4.7 nF
ωc = rad/s
2.Easy
vin​R = 1 kΩC = 1 nFvout​

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

R = 1 kΩC = 1 nF
fc = Hz
3.Medium
vin​C = 4.7 nFR = 3.3 kΩvout​

The RC high-pass filter shown has R = 3.3 kΩ, C = 4.7 nF. A sinusoidal input of 2.6 kHz is applied. Find the gain |H| = |vout/vin| in dB.

R = 3.3 kΩC = 4.7 nFf = 2.6 kHz
|H| = dB
4.Medium
|H| (dB)0.11101001000−60−40−20020ω (rad/s)ω = 3

Find the exact magnitude |G(jω)| of G(s) = 2394/((s + 14)(s + 19)) at ω = 3 rad/s, in dB.

G(s) = 2394/((s + 14)(s + 19))ω = 3 rad/s
|G(jω)| = dB
5.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) = 20/(s(s + 1)(s + 10)). Find the gain margin GM in dB.

L(s) = 20/(s(s + 1)(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) = 540/(s(s + 9)(s + 10)). Find the gain margin GM in dB.

L(s) = 540/(s(s + 9)(s + 10))
GM = dB

Answer key

  1. 1. ωc = 9671 rad/s
  2. 2. fc = 159155 Hz
  3. 3. |H| = −12.19 dB
  4. 4. |G(jω)| = 18.78 dB
  5. 5. GM = 14.81 dB
  6. 6. GM = 10.01 dB

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