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 = 2.2 nFR = 4.7 kΩvout​

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

R = 4.7 kΩC = 2.2 nF
ωc = rad/s
2.Easy
vin​R = 100 ΩL = 47 mHvout​

Find the corner (−3 dB) frequency fc of the RL high-pass filter shown, with R = 100 Ω, L = 47 mH. Give it in Hz.

R = 100 ΩL = 47 mH
fc = Hz
3.Medium
|H| (dB)0.010.010.10.1111010100100−20020406080ω (rad/s)φ (°)ω (rad/s)−90−450ω = 0.5

Find the phase ∠G(jω) of G(s) = 21(s + 8)/(s(s + 10)) at ω = 0.5 rad/s, in degrees.

G(s) = 21(s + 8)/(s(s + 10))ω = 0.5 rad/s
∠G(jω) = °
4.Medium
|H| (dB)0.11101001000−100−80−60−40−20020ω (rad/s)ω = 8

Find the exact magnitude |G(jω)| of G(s) = 60/((s + 1)(s + 12)) at ω = 8 rad/s, in dB.

G(s) = 60/((s + 1)(s + 12))ω = 8 rad/s
|G(jω)| = dB
5.Hard
|H| (dB)0.10.1111010100100−60−40−200204060ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​ = ?

A unity-feedback loop has the open-loop transfer function L(s) = 95/(s(s + 5)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 95/(s(s + 5))
ωc = rad/s
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) = 24/(s(s + 2)(s + 4)). Find the gain margin GM in dB.

L(s) = 24/(s(s + 2)(s + 4))
GM = dB

Answer key

  1. 1. ωc = 96712 rad/s
  2. 2. fc = 338.6 Hz
  3. 3. ∠G(jω) = −89.29 °
  4. 4. |G(jω)| = −5.747 dB
  5. 5. ωc = 9.128 rad/s
  6. 6. GM = 6.021 dB

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