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)110100100010000−80−60−40−200?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 20000/((s + 1000)(s + 20)). What is the slope n of the straight-line asymptote between 20 and 1000 rad/s, in dB/decade?

G(s) = 20000/((s + 1000)(s + 20))
n = dB/dec
2.Easy
|H| (dB)10100100010000−100−80−60−40−20020?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 10000/(s(s + 500)). What is the slope n of the straight-line asymptote above 500 rad/s, in dB/decade?

G(s) = 10000/(s(s + 500))
n = dB/dec
3.Medium
vin​C = 4.7 nFR = 10 kΩvout​

The RC high-pass filter shown has R = 10 kΩ, C = 4.7 nF. A sinusoidal input of 1.7 kHz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 10 kΩC = 4.7 nFf = 1.7 kHz
φ = °
4.Medium
vin​R = 22 ΩL = 22 mHvout​

The RL high-pass filter shown has R = 22 Ω, L = 22 mH. A sinusoidal input of 320 Hz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 22 ΩL = 22 mHf = 320 Hz
φ = °
5.Hard
|H| (dB)0.10.111101010010010001000−80−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​

A unity-feedback loop has the open-loop transfer function L(s) = 200/(s(s + 20)). Find the phase margin PM in degrees.

L(s) = 200/(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) = 135/(s(s + 5)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 135/(s(s + 5))
ωc = rad/s

Answer key

  1. 1. n = −20 dB/dec
  2. 2. n = −40 dB/dec
  3. 3. φ = 63.34 °
  4. 4. φ = 26.44 °
  5. 5. PM = 65.53 °
  6. 6. ωc = 11.09 rad/s

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