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 = 47 kΩC = 22 nFvout​

Find the corner (−3 dB) frequency fc of the RC low-pass filter shown, with R = 47 kΩ, C = 22 nF. Give it in Hz.

R = 47 kΩC = 22 nF
fc = Hz
2.Easy
vin​R = 220 ΩL = 100 mHvout​

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

R = 220 ΩL = 100 mH
fc = Hz
3.Medium
vin​L = 20 mHC = 0.1 µFR = 100 Ωvout​

In the series RLC band-pass filter shown the output is taken across R = 100 Ω, with L = 20 mH and C = 0.1 µF. Find the quality factor Q.

R = 100 ΩL = 20 mHC = 0.1 µF
Q =
4.Medium
|H| (dB)0.10.111101010010010001000−40−200204060ω (rad/s)φ (°)ω (rad/s)−135−90−450ω = 20

Find the phase ∠G(jω) of G(s) = 19(s + 10)/(s(s + 5)) at ω = 20 rad/s, in degrees.

G(s) = 19(s + 10)/(s(s + 5))ω = 20 rad/s
∠G(jω) = °
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) = 58/(s(s + 5)(s + 6)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 58/(s(s + 5)(s + 6))
ω180 = rad/s
6.Hard
|H| (dB)0.10.1111010100100−60−40−200204060ω (rad/s)φ (°)ω (rad/s)−270−180−900ω180​

A unity-feedback loop has the open-loop transfer function L(s) = 594/(s(s + 7)(s + 8)). Find the gain margin GM in dB.

L(s) = 594/(s(s + 7)(s + 8))
GM = dB

Answer key

  1. 1. fc = 153.9 Hz
  2. 2. fc = 350.1 Hz
  3. 3. Q = 4.472
  4. 4. ∠G(jω) = −102.5 °
  5. 5. ω180 = 5.477 rad/s
  6. 6. GM = 3.01 dB

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