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)0.010.1110100−60−40−200204060?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 50/(s(s + 10)(s + 0.5)). What is the slope n of the straight-line asymptote below 0.5 rad/s, in dB/decade?

G(s) = 50/(s(s + 10)(s + 0.5))
n = dB/dec
2.Easy
vin​R = 1000 ΩL = 10 mHvout​

Find the corner (−3 dB) frequency fc of the RL high-pass filter shown, with R = 1000 Ω, L = 10 mH. Give it in Hz.

R = 1000 ΩL = 10 mH
fc = Hz
3.Medium
|H| (dB)0.11101001000−60−40−20020ω (rad/s)ω = 8

Find the exact magnitude |G(jω)| of G(s) = 1008/((s + 8)(s + 14)) at ω = 8 rad/s, in dB.

G(s) = 1008/((s + 8)(s + 14))ω = 8 rad/s
|G(jω)| = dB
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 31 kHz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 3.3 kΩC = 4.7 nFf = 31 kHz
φ = °
5.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) = 540/(s(s + 20)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 540/(s(s + 20))
ωc = rad/s
6.Hard
|H| (dB)0.10.111101010010010001000−60−40−200204060ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​ = ?

A unity-feedback loop has the open-loop transfer function L(s) = 448/(s(s + 8)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 448/(s(s + 8))
ωc = rad/s

Answer key

  1. 1. n = −20 dB/dec
  2. 2. fc = 15915 Hz
  3. 3. |G(jω)| = 14.85 dB
  4. 4. φ = 18.32 °
  5. 5. ωc = 19.39 rad/s
  6. 6. ωc = 20.42 rad/s

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