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 ΩL = 1 mHvout​

Find the corner (−3 dB) frequency fc of the RL high-pass filter shown, with R = 22 Ω, L = 1 mH. Give it in Hz.

R = 22 ΩL = 1 mH
fc = Hz
2.Easy
vin​R = 1 kΩC = 2.2 nFvout​

Find the corner (−3 dB) frequency fc of the RC low-pass filter shown, with R = 1 kΩ, C = 2.2 nF. Give it in Hz.

R = 1 kΩC = 2.2 nF
fc = Hz
3.Medium
vin​R = 47 ΩL = 22 mHvout​

The RL high-pass filter shown has R = 47 Ω, L = 22 mH. A sinusoidal input of 1 kHz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 47 ΩL = 22 mHf = 1 kHz
φ = °
4.Medium
|H| (dB)0.11101001000−80−60−40−2002040ω (rad/s)ω = 30

Find the exact magnitude |G(jω)| of G(s) = 240/((s + 2)(s + 8)) at ω = 30 rad/s, in dB.

G(s) = 240/((s + 2)(s + 8))ω = 30 rad/s
|G(jω)| = dB
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 + 1)(s + 8)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 58/(s(s + 1)(s + 8))
ω180 = rad/s
6.Hard
|H| (dB)0.10.1111010100100−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​

A unity-feedback loop has the open-loop transfer function L(s) = 60/(s(s + 10)). Find the phase margin PM in degrees.

L(s) = 60/(s(s + 10))
PM = °

Answer key

  1. 1. fc = 3501 Hz
  2. 2. fc = 72343 Hz
  3. 3. φ = 18.78 °
  4. 4. |G(jω)| = −11.8 dB
  5. 5. ω180 = 2.828 rad/s
  6. 6. PM = 62.07 °

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