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 = 1 nFR = 22 kΩvout​

Find the corner (−3 dB) frequency fc of the RC high-pass filter shown, with R = 22 kΩ, C = 1 nF. Give it in Hz.

R = 22 kΩC = 1 nF
fc = Hz
2.Easy
|H| (dB)0.1110100100010000−60−40−200204060?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 100000/(s(s + 2)(s + 1000)). What is the slope n of the straight-line asymptote between 2 and 1000 rad/s, in dB/decade?

G(s) = 100000/(s(s + 2)(s + 1000))
n = dB/dec
3.Medium
|H| (dB)0.10.111101010010010001000−40−200204060ω (rad/s)φ (°)ω (rad/s)−90−450ω = 20

Find the phase ∠G(jω) of G(s) = 26(s + 2)/(s(s + 3)) at ω = 20 rad/s, in degrees.

G(s) = 26(s + 2)/(s(s + 3))ω = 20 rad/s
∠G(jω) = °
4.Medium
|H| (dB)0.11101001000−60−40−2002040ω (rad/s)ω = 3

Find the exact magnitude |G(jω)| of G(s) = 1512/((s + 6)(s + 18)) at ω = 3 rad/s, in dB.

G(s) = 1512/((s + 6)(s + 18))ω = 3 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) = 6/(s(s + 1)(s + 3)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 6/(s(s + 1)(s + 3))
ω180 = rad/s
6.Hard
|H| (dB)0.10.1111010100100−60−40−200204060ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​ = ?

A unity-feedback loop has the open-loop transfer function L(s) = 55/(s(s + 5)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 55/(s(s + 5))
ωc = rad/s

Answer key

  1. 1. fc = 7234 Hz
  2. 2. n = −40 dB/dec
  3. 3. ∠G(jω) = −87.18 °
  4. 4. |G(jω)| = 21.83 dB
  5. 5. ω180 = 1.732 rad/s
  6. 6. ωc = 6.626 rad/s

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