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)0.11101001000−80−60−40−2002040?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 800(s + 5)/(s(s + 20)(s + 100)). What is the slope n of the straight-line asymptote between 20 and 100 rad/s, in dB/decade?

G(s) = 800(s + 5)/(s(s + 20)(s + 100))
n = dB/dec
2.Easy
vin​L = 4.7 mHR = 47 Ωvout​

Find the corner (−3 dB) frequency fc of the RL low-pass filter shown, with R = 47 Ω, L = 4.7 mH. Give it in Hz.

R = 47 ΩL = 4.7 mH
fc = Hz
3.Medium
vin​R = 22 kΩC = 100 nFvout​

The RC low-pass filter shown has R = 22 kΩ, C = 100 nF. A sinusoidal input of 360 Hz is applied. Find the gain |H| = |vout/vin| in dB.

R = 22 kΩC = 100 nFf = 360 Hz
|H| = dB
4.Medium
vin​R = 22 kΩC = 1 nFvout​

The RC low-pass filter shown has R = 22 kΩ, C = 1 nF. A sinusoidal input of 3.6 kHz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 22 kΩC = 1 nFf = 3.6 kHz
φ = °
5.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) = 220/(s(s + 20)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 220/(s(s + 20))
ωc = rad/s
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) = 200/(s(s + 5)(s + 9)). Find the gain margin GM in dB.

L(s) = 200/(s(s + 5)(s + 9))
GM = dB

Answer key

  1. 1. n = −20 dB/dec
  2. 2. fc = 1592 Hz
  3. 3. |H| = −14.11 dB
  4. 4. φ = −26.46 °
  5. 5. ωc = 9.865 rad/s
  6. 6. GM = 9.966 dB

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