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 = 10 ΩL = 22 mHvout​

Find the corner (−3 dB) frequency fc of the RL high-pass filter shown, with R = 10 Ω, L = 22 mH. Give it in Hz.

R = 10 ΩL = 22 mH
fc = Hz
2.Easy
|H| (dB)110100100010000−80−60−40−20020?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 100000/((s + 50)(s + 200)). What is the slope n of the straight-line asymptote between 50 and 200 rad/s, in dB/decade?

G(s) = 100000/((s + 50)(s + 200))
n = dB/dec
3.Medium
vin​C = 2.2 nFR = 4.7 kΩvout​

The RC high-pass filter shown has R = 4.7 kΩ, C = 2.2 nF. A sinusoidal input of 3.8 kHz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 4.7 kΩC = 2.2 nFf = 3.8 kHz
φ = °
4.Medium
|H| (dB)0.10.111101010010010001000−40−200204060ω (rad/s)φ (°)ω (rad/s)−135−90−450ω = 5

Find the phase ∠G(jω) of G(s) = 13(s + 11)/(s(s + 2)) at ω = 5 rad/s, in degrees.

G(s) = 13(s + 11)/(s(s + 2))ω = 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) = 472/(s(s + 7)(s + 8)). Find the gain margin GM in dB.

L(s) = 472/(s(s + 7)(s + 8))
GM = dB
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) = K/(s(s + 3)(s + 9)). Find the gain K that gives a gain margin of 8 dB.

L(s) = K/(s(s + 3)(s + 9))GM = 8 dB
K =

Answer key

  1. 1. fc = 72.34 Hz
  2. 2. n = −20 dB/dec
  3. 3. φ = 76.13 °
  4. 4. ∠G(jω) = −133.8 °
  5. 5. GM = 5.007 dB
  6. 6. K = 129

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