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
|H| (dB)0.11101001000−40−20020ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 10(s + 14)/((s + 5)(s + 9)) in decibels, |G(0)| in dB.

G(s) = 10(s + 14)/((s + 5)(s + 9))
|G(0)| = dB
2.Easy
vin​L = 10 mHR = 100 Ωvout​

Find the corner (−3 dB) frequency fc of the RL low-pass filter shown, with R = 100 Ω, L = 10 mH. Give it in Hz.

R = 100 ΩL = 10 mH
fc = Hz
3.Medium
vin​C = 10 nFR = 22 kΩvout​

The RC high-pass filter shown has R = 22 kΩ, C = 10 nF. A sinusoidal input of 180 Hz is applied. Find the gain |H| = |vout/vin| in dB.

R = 22 kΩC = 10 nFf = 180 Hz
|H| = dB
4.Medium
vin​L = 1 mHC = 1 µFR = 5 Ωvout​

In the series RLC band-pass filter shown the output is taken across R = 5 Ω, with L = 1 mH and C = 1 µF. Find the centre (resonant) frequency f0 in Hz.

R = 5 ΩL = 1 mHC = 1 µF
f0 = Hz
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) = 54/(s(s + 3)(s + 4)). Find the gain margin GM in dB.

L(s) = 54/(s(s + 3)(s + 4))
GM = dB
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) = 566/(s(s + 7)(s + 9)). Find the gain margin GM in dB.

L(s) = 566/(s(s + 7)(s + 9))
GM = dB

Answer key

  1. 1. |G(0)| = 9.858 dB
  2. 2. fc = 1592 Hz
  3. 3. |H| = −12.34 dB
  4. 4. f0 = 5033 Hz
  5. 5. GM = 3.838 dB
  6. 6. GM = 5.013 dB

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