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 = 1 nFvout​

Find the corner (−3 dB) frequency ωc of the RC low-pass filter shown, with R = 10 kΩ, C = 1 nF. Give it in rad/s.

R = 10 kΩC = 1 nF
ωc = rad/s
2.Easy
vin​L = 22 mHR = 470 Ωvout​

Find the corner (−3 dB) frequency fc of the RL low-pass filter shown, with R = 470 Ω, L = 22 mH. Give it in Hz.

R = 470 ΩL = 22 mH
fc = Hz
3.Medium
vin​L = 100 mHR = 22 Ωvout​

The RL low-pass filter shown has R = 22 Ω, L = 100 mH. A sinusoidal input of 70 Hz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 22 ΩL = 100 mHf = 70 Hz
φ = °
4.Medium
|H| (dB)0.10.111101010010010001000−40−20020406080ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ω = 20

Find the phase ∠G(jω) of G(s) = 20(s + 18)/(s(s + 3)) at ω = 20 rad/s, in degrees.

G(s) = 20(s + 18)/(s(s + 3))ω = 20 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 + 3)(s + 6)). Find the gain K that gives a gain margin of 6 dB.

L(s) = K/(s(s + 3)(s + 6))GM = 6 dB
K =
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) = 440/(s(s + 20)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 440/(s(s + 20))
ωc = rad/s

Answer key

  1. 1. ωc = 100000 rad/s
  2. 2. fc = 3400 Hz
  3. 3. φ = −63.43 °
  4. 4. ∠G(jω) = −123.5 °
  5. 5. K = 81.19
  6. 6. ωc = 16.83 rad/s

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