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)0.010.1110100100010000−40−20020406080?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 250(s + 100)/(s(s + 500)(s + 0.5)). What is the slope n of the straight-line asymptote between 0.5 and 100 rad/s, in dB/decade?

G(s) = 250(s + 100)/(s(s + 500)(s + 0.5))
n = dB/dec
2.Easy
vin​L = 22 mHR = 10 Ωvout​

Find the corner (−3 dB) frequency ωc of the RL low-pass filter shown, with R = 10 Ω, L = 22 mH. Give it in rad/s.

R = 10 ΩL = 22 mH
ωc = rad/s
3.Medium
vin​R = 4.7 kΩC = 2.2 nFvout​

The RC low-pass filter shown has R = 4.7 kΩ, C = 2.2 nF. A sinusoidal input of 150 kHz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 4.7 kΩC = 2.2 nFf = 150 kHz
φ = °
4.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 2.1 kHz is applied. Find the gain |H| = |vout/vin| in dB.

R = 3.3 kΩC = 4.7 nFf = 2.1 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) = 128/(s(s + 3)(s + 6)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 128/(s(s + 3)(s + 6))
ω180 = rad/s
6.Hard
|H| (dB)0.10.1111010100100−60−40−200204060ω (rad/s)φ (°)ω (rad/s)−270−180−900ω180​

A unity-feedback loop has the open-loop transfer function L(s) = 680/(s(s + 6)(s + 10)). Find the gain margin GM in dB.

L(s) = 680/(s(s + 6)(s + 10))
GM = dB

Answer key

  1. 1. n = −40 dB/dec
  2. 2. ωc = 454.5 rad/s
  3. 3. φ = −84.14 °
  4. 4. |H| = −13.96 dB
  5. 5. ω180 = 4.243 rad/s
  6. 6. GM = 2.995 dB

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