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 = 3.3 kΩvout​

Find the corner (−3 dB) frequency fc of the RC high-pass filter shown, with R = 3.3 kΩ, C = 4.7 nF. Give it in Hz.

R = 3.3 kΩC = 4.7 nF
fc = Hz
2.Easy
vin​L = 4.7 mHR = 1000 Ωvout​

Find the corner (−3 dB) frequency ωc of the RL low-pass filter shown, with R = 1000 Ω, L = 4.7 mH. Give it in rad/s.

R = 1000 ΩL = 4.7 mH
ωc = rad/s
3.Medium
vin​R = 4.7 kΩC = 4.7 nFvout​

The RC low-pass filter shown has R = 4.7 kΩ, C = 4.7 nF. A sinusoidal input of 36 kHz is applied. Find the gain |H| = |vout/vin| in dB.

R = 4.7 kΩC = 4.7 nFf = 36 kHz
|H| = dB
4.Medium
|H| (dB)0.11101001000−80−60−40−20020ω (rad/s)ω = 5

Find the exact magnitude |G(jω)| of G(s) = 280/((s + 5)(s + 14)) at ω = 5 rad/s, in dB.

G(s) = 280/((s + 5)(s + 14))ω = 5 rad/s
|G(jω)| = dB
5.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) = 17.6/(s(s + 8)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 17.6/(s(s + 8))
ωc = rad/s
6.Hard
|H| (dB)11101010010010001000−80−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​ = ?

A unity-feedback loop has the open-loop transfer function L(s) = 155/(s(s + 10)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 155/(s(s + 10))
ωc = rad/s

Answer key

  1. 1. fc = 10261 Hz
  2. 2. ωc = 212766 rad/s
  3. 3. |H| = −14.14 dB
  4. 4. |G(jω)| = 8.51 dB
  5. 5. ωc = 2.126 rad/s
  6. 6. ωc = 10.62 rad/s

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