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 = 100 nFvout​

Find the corner (−3 dB) frequency fc of the RC low-pass filter shown, with R = 10 kΩ, C = 100 nF. Give it in Hz.

R = 10 kΩC = 100 nF
fc = Hz
2.Easy
vin​R = 220 ΩL = 100 mHvout​

Find the corner (−3 dB) frequency ωc of the RL high-pass filter shown, with R = 220 Ω, L = 100 mH. Give it in rad/s.

R = 220 ΩL = 100 mH
ωc = rad/s
3.Medium
|H| (dB)0.1110100−60−40−20020ω (rad/s)ω = 5

Find the exact magnitude |G(jω)| of G(s) = 96/((s + 2)(s + 8)) at ω = 5 rad/s, in dB.

G(s) = 96/((s + 2)(s + 8))ω = 5 rad/s
|G(jω)| = dB
4.Medium
|H| (dB)0.11101001000−60−40−20020ω (rad/s)ω = 1

Find the exact magnitude |G(jω)| of G(s) = 1105/((s + 13)(s + 17)) at ω = 1 rad/s, in dB.

G(s) = 1105/((s + 13)(s + 17))ω = 1 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) = 80/(s(s + 4)). Find the phase margin PM in degrees.

L(s) = 80/(s(s + 4))
PM = °
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) = 560/(s(s + 10)). Find the phase margin PM in degrees.

L(s) = 560/(s(s + 10))
PM = °

Answer key

  1. 1. fc = 159.2 Hz
  2. 2. ωc = 2200 rad/s
  3. 3. |G(jω)| = 5.528 dB
  4. 4. |G(jω)| = 13.94 dB
  5. 5. PM = 25.18 °
  6. 6. PM = 23.84 °

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