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)110100100010000−120−100−80−60−40−200?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 0.05(s + 1000)/(s(s + 50)). What is the slope n of the straight-line asymptote between 50 and 1000 rad/s, in dB/decade?

G(s) = 0.05(s + 1000)/(s(s + 50))
n = dB/dec
2.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
3.Medium
|H| (dB)0.11101001000−100−80−60−40−20020ω (rad/s)ω = 5

Find the exact magnitude |G(jω)| of G(s) = 80/((s + 2)(s + 20)) at ω = 5 rad/s, in dB.

G(s) = 80/((s + 2)(s + 20))ω = 5 rad/s
|G(jω)| = dB
4.Medium
|H| (dB)0.010.010.10.1111010100100−20020406080ω (rad/s)φ (°)ω (rad/s)−135−90−450ω = 0.5

Find the phase ∠G(jω) of G(s) = 38(s + 9)/(s(s + 7)) at ω = 0.5 rad/s, in degrees.

G(s) = 38(s + 9)/(s(s + 7))ω = 0.5 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) = 82/(s(s + 5)(s + 6)). Find the gain margin GM in dB.

L(s) = 82/(s(s + 5)(s + 6))
GM = dB
6.Hard
|H| (dB)0.10.1111010100100−80−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​

A unity-feedback loop has the open-loop transfer function L(s) = 6.4/(s(s + 4)). Find the phase margin PM in degrees.

L(s) = 6.4/(s(s + 4))
PM = °

Answer key

  1. 1. n = −40 dB/dec
  2. 2. fc = 7234 Hz
  3. 3. |G(jω)| = −2.846 dB
  4. 4. ∠G(jω) = −90.91 °
  5. 5. GM = 12.09 dB
  6. 6. PM = 69.46 °

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