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 = 1 kΩC = 1 nFvout​

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

R = 1 kΩC = 1 nF
fc = Hz
2.Easy
vin​R = 47 kΩC = 2.2 nFvout​

Find the corner (−3 dB) frequency ωc of the RC low-pass filter shown, with R = 47 kΩ, C = 2.2 nF. Give it in rad/s.

R = 47 kΩC = 2.2 nF
ωc = rad/s
3.Medium
vin​R = 2.2 kΩC = 2.2 nFvout​

The RC low-pass filter shown has R = 2.2 kΩ, C = 2.2 nF. A sinusoidal input of 16 kHz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 2.2 kΩC = 2.2 nFf = 16 kHz
φ = °
4.Medium
|H| (dB)0.1110100−40−2002040ω (rad/s)ω = 10

Find the exact magnitude |G(jω)| of G(s) = 272/((s + 2)(s + 8)) at ω = 10 rad/s, in dB.

G(s) = 272/((s + 2)(s + 8))ω = 10 rad/s
|G(jω)| = dB
5.Hard
|H| (dB)11101010010010001000−80−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​ = ?

A unity-feedback loop has the open-loop transfer function L(s) = 760/(s(s + 20)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 760/(s(s + 20))
ωc = 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) = 472/(s(s + 7)(s + 8)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 472/(s(s + 7)(s + 8))
ω180 = rad/s

Answer key

  1. 1. fc = 159155 Hz
  2. 2. ωc = 9671 rad/s
  3. 3. φ = −25.95 °
  4. 4. |G(jω)| = 6.373 dB
  5. 5. ωc = 24.2 rad/s
  6. 6. ω180 = 7.483 rad/s

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