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 = 22 kΩvout​

Find the corner (−3 dB) frequency fc of the RC high-pass filter shown, with R = 22 kΩ, C = 2.2 nF. Give it in Hz.

R = 22 kΩC = 2.2 nF
fc = Hz
2.Easy
vin​R = 100 ΩL = 10 mHvout​

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

R = 100 ΩL = 10 mH
fc = Hz
3.Medium
vin​L = 50 mHC = 0.1 µFR = 100 Ωvout​

In the series RLC band-pass filter shown the output is taken across R = 100 Ω, with L = 50 mH and C = 0.1 µF. Find the −3 dB bandwidth BW in Hz.

R = 100 ΩL = 50 mHC = 0.1 µF
BW = Hz
4.Medium
vin​L = 1 mHC = 1 µFR = 1 Ωvout​

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

R = 1 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) = K/(s(s + 4)(s + 7)). Find the gain K that gives a gain margin of 6 dB.

L(s) = K/(s(s + 4)(s + 7))GM = 6 dB
K =
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) = 26/(s(s + 3)(s + 8)). Find the gain margin GM in dB.

L(s) = 26/(s(s + 3)(s + 8))
GM = dB

Answer key

  1. 1. fc = 3288 Hz
  2. 2. fc = 1592 Hz
  3. 3. BW = 318.3 Hz
  4. 4. f0 = 5033 Hz
  5. 5. K = 154.4
  6. 6. GM = 20.13 dB

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