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 = 47 kΩC = 2.2 nFvout​

Find the corner (−3 dB) frequency fc of the RC low-pass filter shown, with R = 47 kΩ, C = 2.2 nF. Give it in Hz.

R = 47 kΩC = 2.2 nF
fc = Hz
2.Easy
vin​R = 22 kΩC = 2.2 nFvout​

Find the corner (−3 dB) frequency ωc of the RC low-pass filter shown, with R = 22 kΩ, C = 2.2 nF. Give it in rad/s.

R = 22 kΩC = 2.2 nF
ωc = rad/s
3.Medium
|H| (dB)0.10.111101010010010001000−40−200204060ω (rad/s)φ (°)ω (rad/s)−135−90−450ω = 1

Find the phase ∠G(jω) of G(s) = 36(s + 15)/(s(s + 9)) at ω = 1 rad/s, in degrees.

G(s) = 36(s + 15)/(s(s + 9))ω = 1 rad/s
∠G(jω) = °
4.Medium
|H| (dB)0.10.111101010010010001000−60−40−20020ω (rad/s)φ (°)ω (rad/s)−90−450ω = 15

Find the phase ∠G(jω) of G(s) = 3(s + 1)/(s(s + 5)) at ω = 15 rad/s, in degrees.

G(s) = 3(s + 1)/(s(s + 5))ω = 15 rad/s
∠G(jω) = °
5.Hard
|H| (dB)0.10.1111010100100−80−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−270−180−900ω180​

A unity-feedback loop has the open-loop transfer function L(s) = 122/(s(s + 4)(s + 8)). Find the gain margin GM in dB.

L(s) = 122/(s(s + 4)(s + 8))
GM = dB
6.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) = 120/(s(s + 20)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 120/(s(s + 20))
ωc = rad/s

Answer key

  1. 1. fc = 1539 Hz
  2. 2. ωc = 20661 rad/s
  3. 3. ∠G(jω) = −92.53 °
  4. 4. ∠G(jω) = −75.38 °
  5. 5. GM = 9.959 dB
  6. 6. ωc = 5.765 rad/s

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