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)0.11101001000−60−40−200ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 8(s + 3)/((s + 60)(s + 8)) in decibels, |G(0)| in dB.

G(s) = 8(s + 3)/((s + 60)(s + 8))
|G(0)| = dB
2.Easy
vin​R = 47 kΩC = 2.2 nFvout​

Find the corner (−3 dB) frequency ωc of the RC low-pass filter shown, with R = 47 kΩ, C = 2.2 nF. Give it in rad/s.

R = 47 kΩC = 2.2 nF
ωc = rad/s
3.Medium
vin​C = 22 nFR = 4.7 kΩvout​

The RC high-pass filter shown has R = 4.7 kΩ, C = 22 nF. A sinusoidal input of 4.6 kHz is applied. Find the gain |H| = |vout/vin| in dB.

R = 4.7 kΩC = 22 nFf = 4.6 kHz
|H| = dB
4.Medium
vin​C = 47 nFR = 47 kΩvout​

The RC high-pass filter shown has R = 47 kΩ, C = 47 nF. A sinusoidal input of 220 Hz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 47 kΩC = 47 nFf = 220 Hz
φ = °
5.Hard
|H| (dB)0.10.111101010010010001000−60−40−200204060ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​

A unity-feedback loop has the open-loop transfer function L(s) = 520/(s(s + 8)). Find the phase margin PM in degrees.

L(s) = 520/(s(s + 8))
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) = 90/(s(s + 2)(s + 7)). Find the gain margin GM in dB.

L(s) = 90/(s(s + 2)(s + 7))
GM = dB

Answer key

  1. 1. |G(0)| = −26.02 dB
  2. 2. ωc = 9671 rad/s
  3. 3. |H| = −0.4609 dB
  4. 4. φ = 18.13 °
  5. 5. PM = 19.89 °
  6. 6. GM = 2.923 dB

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