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
|H| (dB)0.1110100−40−20020ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 360/((s + 5)(s + 9)) in decibels, |G(0)| in dB.

G(s) = 360/((s + 5)(s + 9))
|G(0)| = dB
2.Easy
vin​L = 47 mHR = 47 Ωvout​

Find the corner (−3 dB) frequency ωc of the RL low-pass filter shown, with R = 47 Ω, L = 47 mH. Give it in rad/s.

R = 47 ΩL = 47 mH
ωc = rad/s
3.Medium
vin​R = 47 kΩC = 4.7 nFvout​

The RC low-pass filter shown has R = 47 kΩ, C = 4.7 nF. A sinusoidal input of 7.2 kHz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 47 kΩC = 4.7 nFf = 7.2 kHz
φ = °
4.Medium
vin​C = 47 nFR = 1 kΩvout​

The RC high-pass filter shown has R = 1 kΩ, C = 47 nF. A sinusoidal input of 1.7 kHz is applied. Find the gain |H| = |vout/vin| in dB.

R = 1 kΩC = 47 nFf = 1.7 kHz
|H| = 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) = 158/(s(s + 5)(s + 9)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 158/(s(s + 5)(s + 9))
ω180 = 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) = 250/(s(s + 10)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 250/(s(s + 10))
ωc = rad/s

Answer key

  1. 1. |G(0)| = 18.06 dB
  2. 2. ωc = 1000 rad/s
  3. 3. φ = −84.29 °
  4. 4. |H| = −6.962 dB
  5. 5. ω180 = 6.708 rad/s
  6. 6. ωc = 14.32 rad/s

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