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)0.1110100100002040?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 5000(s + 1)/((s + 50)(s + 5)). What is the slope n of the straight-line asymptote above 50 rad/s, in dB/decade?

G(s) = 5000(s + 1)/((s + 50)(s + 5))
n = dB/dec
2.Easy
|H| (dB)0.11101001000−100−80−60−40−20020?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 100/(s(s + 100)(s + 1)). What is the slope n of the straight-line asymptote between 1 and 100 rad/s, in dB/decade?

G(s) = 100/(s(s + 100)(s + 1))
n = dB/dec
3.Medium
vin​L = 22 mHR = 47 Ωvout​

The RL low-pass filter shown has R = 47 Ω, L = 22 mH. A sinusoidal input of 170 Hz is applied. Find the gain |H| = |vout/vin| in dB.

R = 47 ΩL = 22 mHf = 170 Hz
|H| = dB
4.Medium
vin​C = 4.7 nFR = 4.7 kΩvout​

The RC high-pass filter shown has R = 4.7 kΩ, C = 4.7 nF. A sinusoidal input of 1.4 kHz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 4.7 kΩC = 4.7 nFf = 1.4 kHz
φ = °
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) = 208/(s(s + 5)(s + 8)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 208/(s(s + 5)(s + 8))
ω180 = 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) = 22/(s(s + 1)(s + 6)). Find the gain margin GM in dB.

L(s) = 22/(s(s + 1)(s + 6))
GM = dB

Answer key

  1. 1. n = −20 dB/dec
  2. 2. n = −40 dB/dec
  3. 3. |H| = −0.969 dB
  4. 4. φ = 79 °
  5. 5. ω180 = 6.325 rad/s
  6. 6. GM = 5.617 dB

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