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 = 2.2 kΩvout​

Find the corner (−3 dB) frequency ωc of the RC high-pass filter shown, with R = 2.2 kΩ, C = 4.7 nF. Give it in rad/s.

R = 2.2 kΩC = 4.7 nF
ωc = rad/s
2.Easy
vin​L = 22 mHR = 22 Ωvout​

Find the corner (−3 dB) frequency fc of the RL low-pass filter shown, with R = 22 Ω, L = 22 mH. Give it in Hz.

R = 22 ΩL = 22 mH
fc = Hz
3.Medium
vin​C = 47 nFR = 1 kΩvout​

The RC high-pass filter shown has R = 1 kΩ, C = 47 nF. A sinusoidal input of 6.8 kHz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 1 kΩC = 47 nFf = 6.8 kHz
φ = °
4.Medium
|H| (dB)0.10.1111010100100−200204060ω (rad/s)φ (°)ω (rad/s)−135−90−450ω = 4

Find the phase ∠G(jω) of G(s) = 17(s + 4)/(s(s + 1)) at ω = 4 rad/s, in degrees.

G(s) = 17(s + 4)/(s(s + 1))ω = 4 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) = K/(s(s + 9)(s + 10)). Find the gain K that gives a gain margin of 20 dB.

L(s) = K/(s(s + 9)(s + 10))GM = 20 dB
K =
6.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) = 114/(s(s + 4)(s + 5)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 114/(s(s + 4)(s + 5))
ω180 = rad/s

Answer key

  1. 1. ωc = 96712 rad/s
  2. 2. fc = 159.2 Hz
  3. 3. φ = 26.47 °
  4. 4. ∠G(jω) = −121 °
  5. 5. K = 171
  6. 6. ω180 = 4.472 rad/s

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