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)0.010.11101001000−40−20020?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 25(s + 10)/((s + 0.5)(s + 100)). What is the slope n of the straight-line asymptote between 0.5 and 10 rad/s, in dB/decade?

G(s) = 25(s + 10)/((s + 0.5)(s + 100))
n = dB/dec
2.Easy
vin​L = 4.7 mHR = 1000 Ωvout​

Find the corner (−3 dB) frequency fc of the RL low-pass filter shown, with R = 1000 Ω, L = 4.7 mH. Give it in Hz.

R = 1000 ΩL = 4.7 mH
fc = Hz
3.Medium
vin​R = 4.7 kΩC = 22 nFvout​

The RC low-pass filter shown has R = 4.7 kΩ, C = 22 nF. A sinusoidal input of 3.1 kHz is applied. Find the gain |H| = |vout/vin| in dB.

R = 4.7 kΩC = 22 nFf = 3.1 kHz
|H| = dB
4.Medium
|H| (dB)0.010.010.10.111101010010010001000−40−200204060ω (rad/s)φ (°)ω (rad/s)−90−450ω = 0.5

Find the phase ∠G(jω) of G(s) = 24(s + 1)/(s(s + 15)) at ω = 0.5 rad/s, in degrees.

G(s) = 24(s + 1)/(s(s + 15))ω = 0.5 rad/s
∠G(jω) = °
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 gain margin GM in dB.

L(s) = 4/(s(s + 1)(s + 2))
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) = 398/(s(s + 5)(s + 9)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 398/(s(s + 5)(s + 9))
ω180 = rad/s

Answer key

  1. 1. n = −20 dB/dec
  2. 2. fc = 33863 Hz
  3. 3. |H| = −7.038 dB
  4. 4. ∠G(jω) = −65.34 °
  5. 5. GM = 3.522 dB
  6. 6. ω180 = 6.708 rad/s

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