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 = 22 nFR = 4.7 kΩvout​

Find the corner (−3 dB) frequency fc of the RC high-pass filter shown, with R = 4.7 kΩ, C = 22 nF. Give it in Hz.

R = 4.7 kΩC = 22 nF
fc = Hz
2.Easy
vin​R = 4.7 kΩC = 47 nFvout​

Find the corner (−3 dB) frequency fc of the RC low-pass filter shown, with R = 4.7 kΩ, C = 47 nF. Give it in Hz.

R = 4.7 kΩC = 47 nF
fc = Hz
3.Medium
vin​L = 10 mHC = 0.47 µFR = 5 Ωvout​

In the series RLC band-pass filter shown the output is taken across R = 5 Ω, with L = 10 mH and C = 0.47 µF. Find the centre (resonant) frequency f0 in Hz.

R = 5 ΩL = 10 mHC = 0.47 µF
f0 = Hz
4.Medium
|H| (dB)0.10.1111010100100−200204060ω (rad/s)φ (°)ω (rad/s)−90−450ω = 10

Find the phase ∠G(jω) of G(s) = 33(s + 1)/(s(s + 3)) at ω = 10 rad/s, in degrees.

G(s) = 33(s + 1)/(s(s + 3))ω = 10 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) = 186/(s(s + 3)(s + 8)). Find the gain margin GM in dB.

L(s) = 186/(s(s + 3)(s + 8))
GM = dB
6.Hard
|H| (dB)0.10.1111010100100−40−200204060ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​ = ?

A unity-feedback loop has the open-loop transfer function L(s) = 116/(s(s + 8)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 116/(s(s + 8))
ωc = rad/s

Answer key

  1. 1. fc = 1539 Hz
  2. 2. fc = 720.5 Hz
  3. 3. f0 = 2322 Hz
  4. 4. ∠G(jω) = −79.01 °
  5. 5. GM = 3.042 dB
  6. 6. ωc = 9.399 rad/s

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