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​R = 10 kΩC = 2.2 nFvout​

Find the corner (−3 dB) frequency ωc of the RC low-pass filter shown, with R = 10 kΩ, C = 2.2 nF. Give it in rad/s.

R = 10 kΩC = 2.2 nF
ωc = rad/s
2.Easy
|H| (dB)0.11101001000−40−20020ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 70(s + 20)/((s + 3)(s + 50)) in decibels, |G(0)| in dB.

G(s) = 70(s + 20)/((s + 3)(s + 50))
|G(0)| = dB
3.Medium
|H| (dB)0.10.111101010010010001000−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−135−90−450ω = 10

Find the phase ∠G(jω) of G(s) = (s + 19)/(s(s + 4)) at ω = 10 rad/s, in degrees.

G(s) = (s + 19)/(s(s + 4))ω = 10 rad/s
∠G(jω) = °
4.Medium
vin​R = 4.7 kΩC = 10 nFvout​

The RC low-pass filter shown has R = 4.7 kΩ, C = 10 nF. A sinusoidal input of 34 kHz is applied. Find the gain |H| = |vout/vin| in dB.

R = 4.7 kΩC = 10 nFf = 34 kHz
|H| = dB
5.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) = 145/(s(s + 10)). Find the phase margin PM in degrees.

L(s) = 145/(s(s + 10))
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) = 180/(s(s + 10)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 180/(s(s + 10))
ωc = rad/s

Answer key

  1. 1. ωc = 45455 rad/s
  2. 2. |G(0)| = 19.4 dB
  3. 3. ∠G(jω) = −130.4 °
  4. 4. |H| = −20.08 dB
  5. 5. PM = 44.52 °
  6. 6. ωc = 11.7 rad/s

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