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)1101001000−80−60−40−200ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 490/((s + 20)(s + 60)) in decibels, |G(0)| in dB.

G(s) = 490/((s + 20)(s + 60))
|G(0)| = dB
2.Easy
|H| (dB)1101001000−100−80−60−40−200ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 50/((s + 60)(s + 70)) in decibels, |G(0)| in dB.

G(s) = 50/((s + 60)(s + 70))
|G(0)| = dB
3.Medium
vin​C = 10 nFR = 4.7 kΩvout​

The RC high-pass filter shown has R = 4.7 kΩ, C = 10 nF. A sinusoidal input of 1.7 kHz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 4.7 kΩC = 10 nFf = 1.7 kHz
φ = °
4.Medium
|H| (dB)0.11101001000−80−60−40−20020ω (rad/s)ω = 30

Find the exact magnitude |G(jω)| of G(s) = 228/((s + 6)(s + 19)) at ω = 30 rad/s, in dB.

G(s) = 228/((s + 6)(s + 19))ω = 30 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) = 300/(s(s + 10)). Find the phase margin PM in degrees.

L(s) = 300/(s(s + 10))
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) = 540/(s(s + 9)(s + 10)). Find the gain margin GM in dB.

L(s) = 540/(s(s + 9)(s + 10))
GM = dB

Answer key

  1. 1. |G(0)| = −7.78 dB
  2. 2. |G(0)| = −38.49 dB
  3. 3. φ = 63.34 °
  4. 4. |G(jω)| = −13.56 dB
  5. 5. PM = 32.1 °
  6. 6. GM = 10.01 dB

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