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)0.1110100100010000−100−80−60−40−200?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 0.1(s + 200)/((s + 20)(s + 1)). What is the slope n of the straight-line asymptote between 1 and 20 rad/s, in dB/decade?

G(s) = 0.1(s + 200)/((s + 20)(s + 1))
n = dB/dec
2.Easy
|H| (dB)0.010.1110100−60−40−20020?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 50/((s + 10)(s + 0.5)). What is the slope n of the straight-line asymptote above 10 rad/s, in dB/decade?

G(s) = 50/((s + 10)(s + 0.5))
n = dB/dec
3.Medium
|H| (dB)0.11101001000−80−60−40−2002040ω (rad/s)ω = 30

Find the exact magnitude |G(jω)| of G(s) = 120/((s + 1)(s + 8)) at ω = 30 rad/s, in dB.

G(s) = 120/((s + 1)(s + 8))ω = 30 rad/s
|G(jω)| = dB
4.Medium
vin​C = 1 nFR = 1 kΩvout​

The RC high-pass filter shown has R = 1 kΩ, C = 1 nF. A sinusoidal input of 480 kHz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 1 kΩC = 1 nFf = 480 kHz
φ = °
5.Hard
|H| (dB)11101010010010001000−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​

A unity-feedback loop has the open-loop transfer function L(s) = 1440/(s(s + 20)). Find the phase margin PM in degrees.

L(s) = 1440/(s(s + 20))
PM = °
6.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) = 272/(s(s + 8)). Find the phase margin PM in degrees.

L(s) = 272/(s(s + 8))
PM = °

Answer key

  1. 1. n = −20 dB/dec
  2. 2. n = −40 dB/dec
  3. 3. |G(jω)| = −17.8 dB
  4. 4. φ = 18.34 °
  5. 5. PM = 29.46 °
  6. 6. PM = 27.22 °

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