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
vin​C = 4.7 nFR = 3.3 kΩvout​

Find the corner (−3 dB) frequency ωc of the RC high-pass filter shown, with R = 3.3 kΩ, C = 4.7 nF. Give it in rad/s.

R = 3.3 kΩC = 4.7 nF
ωc = rad/s
2.Easy
|H| (dB)101001000−60−40−20020?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 2000/(s(s + 100)). What is the slope n of the straight-line asymptote above 100 rad/s, in dB/decade?

G(s) = 2000/(s(s + 100))
n = dB/dec
3.Medium
vin​R = 470 ΩL = 22 mHvout​

The RL high-pass filter shown has R = 470 Ω, L = 22 mH. A sinusoidal input of 34 kHz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 470 ΩL = 22 mHf = 34 kHz
φ = °
4.Medium
|H| (dB)0.10.111101010010010001000−40−20020406080ω (rad/s)φ (°)ω (rad/s)−135−90−450ω = 5

Find the phase ∠G(jω) of G(s) = 50(s + 16)/(s(s + 5)) at ω = 5 rad/s, in degrees.

G(s) = 50(s + 16)/(s(s + 5))ω = 5 rad/s
∠G(jω) = °
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) = 132/(s(s + 8)). Find the phase margin PM in degrees.

L(s) = 132/(s(s + 8))
PM = °
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) = 240/(s(s + 20)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 240/(s(s + 20))
ωc = rad/s

Answer key

  1. 1. ωc = 64475 rad/s
  2. 2. n = −40 dB/dec
  3. 3. φ = 5.711 °
  4. 4. ∠G(jω) = −117.6 °
  5. 5. PM = 38.14 °
  6. 6. ωc = 10.6 rad/s

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