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 = 47 ΩL = 1 mHvout​

Find the corner (−3 dB) frequency fc of the RL high-pass filter shown, with R = 47 Ω, L = 1 mH. Give it in Hz.

R = 47 ΩL = 1 mH
fc = Hz
2.Easy
|H| (dB)0.11101001000−80−60−40−2002040?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 200/(s(s + 5)(s + 20)). What is the slope n of the straight-line asymptote above 20 rad/s, in dB/decade?

G(s) = 200/(s(s + 5)(s + 20))
n = dB/dec
3.Medium
|H| (dB)0.10.1111010100100−40−20020ω (rad/s)φ (°)ω (rad/s)−90−450ω = 4

Find the phase ∠G(jω) of G(s) = 2(s + 3)/(s(s + 9)) at ω = 4 rad/s, in degrees.

G(s) = 2(s + 3)/(s(s + 9))ω = 4 rad/s
∠G(jω) = °
4.Medium
vin​R = 470 ΩL = 10 mHvout​

The RL high-pass filter shown has R = 470 Ω, L = 10 mH. A sinusoidal input of 22 kHz is applied. Find the gain |H| = |vout/vin| in dB.

R = 470 ΩL = 10 mHf = 22 kHz
|H| = dB
5.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) = 60/(s(s + 4)). Find the phase margin PM in degrees.

L(s) = 60/(s(s + 4))
PM = °
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 + 1)(s + 10)). Find the gain K that gives a gain margin of 12 dB.

L(s) = K/(s(s + 1)(s + 10))GM = 12 dB
K =

Answer key

  1. 1. fc = 7480 Hz
  2. 2. n = −60 dB/dec
  3. 3. ∠G(jω) = −60.83 °
  4. 4. |H| = −0.4751 dB
  5. 5. PM = 28.89 °
  6. 6. K = 27.63

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