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 = 22 kΩC = 1 nFvout​

Find the corner (−3 dB) frequency fc of the RC low-pass filter shown, with R = 22 kΩ, C = 1 nF. Give it in Hz.

R = 22 kΩC = 1 nF
fc = Hz
2.Easy
vin​R = 22 ΩL = 4.7 mHvout​

Find the corner (−3 dB) frequency fc of the RL high-pass filter shown, with R = 22 Ω, L = 4.7 mH. Give it in Hz.

R = 22 ΩL = 4.7 mH
fc = Hz
3.Medium
|H| (dB)0.11101001000−80−60−40−20020ω (rad/s)ω = 30

Find the exact magnitude |G(jω)| of G(s) = 160/((s + 4)(s + 20)) at ω = 30 rad/s, in dB.

G(s) = 160/((s + 4)(s + 20))ω = 30 rad/s
|G(jω)| = dB
4.Medium
vin​L = 20 mHC = 1 µFR = 10 Ωvout​

In the series RLC band-pass filter shown the output is taken across R = 10 Ω, with L = 20 mH and C = 1 µF. Find the quality factor Q.

R = 10 ΩL = 20 mHC = 1 µF
Q =
5.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) = 150/(s(s + 10)). Find the phase margin PM in degrees.

L(s) = 150/(s(s + 10))
PM = °
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) = 242/(s(s + 4)(s + 8)). Find the gain margin GM in dB.

L(s) = 242/(s(s + 4)(s + 8))
GM = dB

Answer key

  1. 1. fc = 7234 Hz
  2. 2. fc = 745 Hz
  3. 3. |G(jω)| = −16.68 dB
  4. 4. Q = 14.14
  5. 5. PM = 43.88 °
  6. 6. GM = 4.01 dB

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