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
|H| (dB)0.1110100100010000−60−40−200204060?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 4(s + 500)/(s(s + 2)(s + 50)). What is the slope n of the straight-line asymptote below 2 rad/s, in dB/decade?

G(s) = 4(s + 500)/(s(s + 2)(s + 50))
n = dB/dec
2.Easy
vin​R = 10 ΩL = 10 mHvout​

Find the corner (−3 dB) frequency fc of the RL high-pass filter shown, with R = 10 Ω, L = 10 mH. Give it in Hz.

R = 10 ΩL = 10 mH
fc = Hz
3.Medium
vin​C = 100 nFR = 47 kΩvout​

The RC high-pass filter shown has R = 47 kΩ, C = 100 nF. A sinusoidal input of 100 Hz is applied. Find the gain |H| = |vout/vin| in dB.

R = 47 kΩC = 100 nFf = 100 Hz
|H| = dB
4.Medium
|H| (dB)0.1110100−40−2002040ω (rad/s)ω = 8

Find the exact magnitude |G(jω)| of G(s) = 405/((s + 3)(s + 9)) at ω = 8 rad/s, in dB.

G(s) = 405/((s + 3)(s + 9))ω = 8 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) = 8/(s(s + 1)(s + 4)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 8/(s(s + 1)(s + 4))
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) = 56/(s(s + 2)). Find the phase margin PM in degrees.

L(s) = 56/(s(s + 2))
PM = °

Answer key

  1. 1. n = −20 dB/dec
  2. 2. fc = 159.2 Hz
  3. 3. |H| = −0.4715 dB
  4. 4. |G(jω)| = 11.9 dB
  5. 5. ω180 = 2 rad/s
  6. 6. PM = 15.22 °

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