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)0.111010010000204060ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 3700(s + 15)/((s + 20)(s + 9)) in decibels, |G(0)| in dB.

G(s) = 3700(s + 15)/((s + 20)(s + 9))
|G(0)| = dB
2.Easy
vin​L = 1 mHR = 220 Ωvout​

Find the corner (−3 dB) frequency ωc of the RL low-pass filter shown, with R = 220 Ω, L = 1 mH. Give it in rad/s.

R = 220 ΩL = 1 mH
ωc = rad/s
3.Medium
|H| (dB)0.11101001000−80−60−40−20020ω (rad/s)ω = 8

Find the exact magnitude |G(jω)| of G(s) = 448/((s + 8)(s + 14)) at ω = 8 rad/s, in dB.

G(s) = 448/((s + 8)(s + 14))ω = 8 rad/s
|G(jω)| = dB
4.Medium
vin​R = 3.3 kΩC = 10 nFvout​

The RC low-pass filter shown has R = 3.3 kΩ, C = 10 nF. A sinusoidal input of 48 kHz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 3.3 kΩC = 10 nFf = 48 kHz
φ = °
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) = 236/(s(s + 5)(s + 7)). Find the gain margin GM in dB.

L(s) = 236/(s(s + 5)(s + 7))
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) = 322/(s(s + 6)(s + 9)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 322/(s(s + 6)(s + 9))
ω180 = rad/s

Answer key

  1. 1. |G(0)| = 49.78 dB
  2. 2. ωc = 220000 rad/s
  3. 3. |G(jω)| = 7.804 dB
  4. 4. φ = −84.26 °
  5. 5. GM = 5.007 dB
  6. 6. ω180 = 7.348 rad/s

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