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​R = 22 ΩL = 47 mHvout​

Find the corner (−3 dB) frequency ωc of the RL high-pass filter shown, with R = 22 Ω, L = 47 mH. Give it in rad/s.

R = 22 ΩL = 47 mH
ωc = rad/s
2.Easy
|H| (dB)110100100010000−80−60−40−20020?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 5(s + 500)/((s + 10)(s + 50)). What is the slope n of the straight-line asymptote between 50 and 500 rad/s, in dB/decade?

G(s) = 5(s + 500)/((s + 10)(s + 50))
n = dB/dec
3.Medium
|H| (dB)0.11101001000−80−60−40−20020ω (rad/s)ω = 8

Find the exact magnitude |G(jω)| of G(s) = 684/((s + 9)(s + 19)) at ω = 8 rad/s, in dB.

G(s) = 684/((s + 9)(s + 19))ω = 8 rad/s
|G(jω)| = dB
4.Medium
|H| (dB)0.11101001000−60−40−2002040ω (rad/s)ω = 4

Find the exact magnitude |G(jω)| of G(s) = 1584/((s + 8)(s + 11)) at ω = 4 rad/s, in dB.

G(s) = 1584/((s + 8)(s + 11))ω = 4 rad/s
|G(jω)| = 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) = 4/(s(s + 1)(s + 2)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 4/(s(s + 1)(s + 2))
ω180 = rad/s
6.Hard
|H| (dB)0.10.1111010100100−60−40−200204060ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​

A unity-feedback loop has the open-loop transfer function L(s) = 88/(s(s + 8)). Find the phase margin PM in degrees.

L(s) = 88/(s(s + 8))
PM = °

Answer key

  1. 1. ωc = 468.1 rad/s
  2. 2. n = −40 dB/dec
  3. 3. |G(jω)| = 8.804 dB
  4. 4. |G(jω)| = 23.6 dB
  5. 5. ω180 = 1.414 rad/s
  6. 6. PM = 45.54 °

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