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)1101001000−40−200ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 33(s + 13)/((s + 50)(s + 60)) in decibels, |G(0)| in dB.

G(s) = 33(s + 13)/((s + 50)(s + 60))
|G(0)| = dB
2.Easy
|H| (dB)0.1110100−60−40−20020ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 30/((s + 3)(s + 5)) in decibels, |G(0)| in dB.

G(s) = 30/((s + 3)(s + 5))
|G(0)| = dB
3.Medium
|H| (dB)1101001000−60−40−2002040ω (rad/s)ω = 15

Find the exact magnitude |G(jω)| of G(s) = 4032/((s + 16)(s + 18)) at ω = 15 rad/s, in dB.

G(s) = 4032/((s + 16)(s + 18))ω = 15 rad/s
|G(jω)| = dB
4.Medium
vin​C = 1 nFR = 10 kΩvout​

The RC high-pass filter shown has R = 10 kΩ, C = 1 nF. A sinusoidal input of 160 kHz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 10 kΩC = 1 nFf = 160 kHz
φ = °
5.Hard
|H| (dB)0.10.1111010100100−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​

A unity-feedback loop has the open-loop transfer function L(s) = 19/(s(s + 2)). Find the phase margin PM in degrees.

L(s) = 19/(s(s + 2))
PM = °
6.Hard
|H| (dB)0.10.1111010100100−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​

A unity-feedback loop has the open-loop transfer function L(s) = 75/(s(s + 10)). Find the phase margin PM in degrees.

L(s) = 75/(s(s + 10))
PM = °

Answer key

  1. 1. |G(0)| = −16.89 dB
  2. 2. |G(0)| = 6.021 dB
  3. 3. |G(jω)| = 17.89 dB
  4. 4. φ = 5.681 °
  5. 5. PM = 25.81 °
  6. 6. PM = 57.64 °

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