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)10100100010000−40−2002040?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 1 × 10⁷/((s + 100)(s + 1000)). What is the slope n of the straight-line asymptote between 100 and 1000 rad/s, in dB/decade?

G(s) = 1 × 10⁷/((s + 100)(s + 1000))
n = dB/dec
2.Easy
vin​L = 100 mHR = 22 Ωvout​

Find the corner (−3 dB) frequency fc of the RL low-pass filter shown, with R = 22 Ω, L = 100 mH. Give it in Hz.

R = 22 ΩL = 100 mH
fc = Hz
3.Medium
vin​R = 1000 ΩL = 10 mHvout​

The RL high-pass filter shown has R = 1000 Ω, L = 10 mH. A sinusoidal input of 48 kHz is applied. Find the gain |H| = |vout/vin| in dB.

R = 1000 ΩL = 10 mHf = 48 kHz
|H| = dB
4.Medium
|H| (dB)0.1110100−60−40−20020ω (rad/s)ω = 4

Find the exact magnitude |G(jω)| of G(s) = 90/((s + 1)(s + 10)) at ω = 4 rad/s, in dB.

G(s) = 90/((s + 1)(s + 10))ω = 4 rad/s
|G(jω)| = dB
5.Hard
|H| (dB)11101010010010001000−80−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​

A unity-feedback loop has the open-loop transfer function L(s) = 540/(s(s + 10)). Find the phase margin PM in degrees.

L(s) = 540/(s(s + 10))
PM = °
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) = 26/(s(s + 2)). Find the phase margin PM in degrees.

L(s) = 26/(s(s + 2))
PM = °

Answer key

  1. 1. n = −20 dB/dec
  2. 2. fc = 35.01 Hz
  3. 3. |H| = −0.453 dB
  4. 4. |G(jω)| = 6.136 dB
  5. 5. PM = 24.26 °
  6. 6. PM = 22.18 °

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