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​L = 2.2 mHR = 1000 Ωvout​

Find the corner (−3 dB) frequency fc of the RL low-pass filter shown, with R = 1000 Ω, L = 2.2 mH. Give it in Hz.

R = 1000 ΩL = 2.2 mH
fc = Hz
2.Easy
|H| (dB)0.010.11101001000−80−60−40−2002040?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 1000/((s + 100)(s + 0.5)). What is the slope n of the straight-line asymptote above 100 rad/s, in dB/decade?

G(s) = 1000/((s + 100)(s + 0.5))
n = dB/dec
3.Medium
|H| (dB)0.10.111101010010010001000−40−20020406080ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ω = 8

Find the phase ∠G(jω) of G(s) = 23(s + 15)/(s(s + 2)) at ω = 8 rad/s, in degrees.

G(s) = 23(s + 15)/(s(s + 2))ω = 8 rad/s
∠G(jω) = °
4.Medium
|H| (dB)0.10.111101010010010001000−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−135−90−450ω = 5

Find the phase ∠G(jω) of G(s) = 5(s + 11)/(s(s + 10)) at ω = 5 rad/s, in degrees.

G(s) = 5(s + 11)/(s(s + 10))ω = 5 rad/s
∠G(jω) = °
5.Hard
|H| (dB)0.10.1111010100100−80−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​

A unity-feedback loop has the open-loop transfer function L(s) = 4.6/(s(s + 2)). Find the phase margin PM in degrees.

L(s) = 4.6/(s(s + 2))
PM = °
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) = 488/(s(s + 8)(s + 9)). Find the gain margin GM in dB.

L(s) = 488/(s(s + 8)(s + 9))
GM = dB

Answer key

  1. 1. fc = 72343 Hz
  2. 2. n = −40 dB/dec
  3. 3. ∠G(jω) = −137.9 °
  4. 4. ∠G(jω) = −92.12 °
  5. 5. PM = 49.03 °
  6. 6. GM = 7.987 dB

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