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)0.1110100−40−2002040ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 290/((s + 3)(s + 4)) in decibels, |G(0)| in dB.

G(s) = 290/((s + 3)(s + 4))
|G(0)| = dB
2.Easy
|H| (dB)0.1110100100010000−60−40−20020?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 12.5(s + 200)/((s + 50)(s + 5)). What is the slope n of the straight-line asymptote between 5 and 50 rad/s, in dB/decade?

G(s) = 12.5(s + 200)/((s + 50)(s + 5))
n = dB/dec
3.Medium
vin​C = 47 nFR = 4.7 kΩvout​

The RC high-pass filter shown has R = 4.7 kΩ, C = 47 nF. A sinusoidal input of 140 Hz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 4.7 kΩC = 47 nFf = 140 Hz
φ = °
4.Medium
|H| (dB)0.10.1111010100100−200204060ω (rad/s)φ (°)ω (rad/s)−135−90−450ω = 1

Find the phase ∠G(jω) of G(s) = 19(s + 9)/(s(s + 5)) at ω = 1 rad/s, in degrees.

G(s) = 19(s + 9)/(s(s + 5))ω = 1 rad/s
∠G(jω) = °
5.Hard
|H| (dB)0.010.010.10.1111010−40−200204060ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​ = ?

A unity-feedback loop has the open-loop transfer function L(s) = 1.2/(s(s + 1)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 1.2/(s(s + 1))
ωc = rad/s
6.Hard
|H| (dB)11101010010010001000−80−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​

A unity-feedback loop has the open-loop transfer function L(s) = 370/(s(s + 10)). Find the phase margin PM in degrees.

L(s) = 370/(s(s + 10))
PM = °

Answer key

  1. 1. |G(0)| = 27.66 dB
  2. 2. n = −20 dB/dec
  3. 3. φ = 79 °
  4. 4. ∠G(jω) = −94.97 °
  5. 5. ωc = 0.8944 rad/s
  6. 6. PM = 29.08 °

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