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​L = 100 mHR = 47 Ωvout​

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

R = 47 ΩL = 100 mH
fc = Hz
2.Easy
vin​R = 22 ΩL = 47 mHvout​

Find the corner (−3 dB) frequency ωc of the RL high-pass filter shown, with R = 22 Ω, L = 47 mH. Give it in rad/s.

R = 22 ΩL = 47 mH
ωc = rad/s
3.Medium
|H| (dB)0.010.11101001000−80−60−40−20020ω (rad/s)ω = 0.5

Find the exact magnitude |G(jω)| of G(s) = 510/((s + 6)(s + 17)) at ω = 0.5 rad/s, in dB.

G(s) = 510/((s + 6)(s + 17))ω = 0.5 rad/s
|G(jω)| = dB
4.Medium
|H| (dB)0.10.1111010100100−40−2002040ω (rad/s)φ (°)ω (rad/s)−135−90−450ω = 2

Find the phase ∠G(jω) of G(s) = 2(s + 4)/(s(s + 3)) at ω = 2 rad/s, in degrees.

G(s) = 2(s + 4)/(s(s + 3))ω = 2 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 + 4)(s + 7)). Find the gain K that gives a gain margin of 8 dB.

L(s) = K/(s(s + 4)(s + 7))GM = 8 dB
K =
6.Hard
|H| (dB)0.10.1111010100100−60−40−200204060ω (rad/s)φ (°)ω (rad/s)−270−180−900ω180​

A unity-feedback loop has the open-loop transfer function L(s) = 1144/(s(s + 8)(s + 10)). Find the gain margin GM in dB.

L(s) = 1144/(s(s + 8)(s + 10))
GM = dB

Answer key

  1. 1. fc = 74.8 Hz
  2. 2. ωc = 468.1 rad/s
  3. 3. |G(jω)| = 13.95 dB
  4. 4. ∠G(jω) = −97.13 °
  5. 5. K = 122.6
  6. 6. GM = 1.999 dB

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