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 = 4.7 nFR = 10 kΩvout​

Find the corner (−3 dB) frequency ωc of the RC high-pass filter shown, with R = 10 kΩ, C = 4.7 nF. Give it in rad/s.

R = 10 kΩC = 4.7 nF
ωc = rad/s
2.Easy
vin​C = 47 nFR = 47 kΩvout​

Find the corner (−3 dB) frequency fc of the RC high-pass filter shown, with R = 47 kΩ, C = 47 nF. Give it in Hz.

R = 47 kΩC = 47 nF
fc = Hz
3.Medium
vin​C = 100 nFR = 22 kΩvout​

The RC high-pass filter shown has R = 22 kΩ, C = 100 nF. A sinusoidal input of 14 Hz is applied. Find the gain |H| = |vout/vin| in dB.

R = 22 kΩC = 100 nFf = 14 Hz
|H| = dB
4.Medium
vin​L = 50 mHC = 1 µFR = 20 Ωvout​

In the series RLC band-pass filter shown the output is taken across R = 20 Ω, with L = 50 mH and C = 1 µF. Find the −3 dB bandwidth BW in Hz.

R = 20 ΩL = 50 mHC = 1 µF
BW = 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) = 22/(s(s + 2)(s + 5)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 22/(s(s + 2)(s + 5))
ω180 = rad/s
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) = 68/(s(s + 6)(s + 8)). Find the gain margin GM in dB.

L(s) = 68/(s(s + 6)(s + 8))
GM = dB

Answer key

  1. 1. ωc = 21277 rad/s
  2. 2. fc = 72.05 Hz
  3. 3. |H| = −14.43 dB
  4. 4. BW = 63.66 Hz
  5. 5. ω180 = 3.162 rad/s
  6. 6. GM = 19.9 dB

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