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)0.111010010000204060ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 2900(s + 17)/((s + 7)(s + 8)) in decibels, |G(0)| in dB.

G(s) = 2900(s + 17)/((s + 7)(s + 8))
|G(0)| = dB
2.Easy
vin​L = 100 mHR = 100 Ωvout​

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

R = 100 ΩL = 100 mH
ωc = rad/s
3.Medium
vin​C = 4.7 nFR = 4.7 kΩvout​

The RC high-pass filter shown has R = 4.7 kΩ, C = 4.7 nF. A sinusoidal input of 36 kHz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 4.7 kΩC = 4.7 nFf = 36 kHz
φ = °
4.Medium
vin​R = 1 kΩC = 2.2 nFvout​

The RC low-pass filter shown has R = 1 kΩ, C = 2.2 nF. A sinusoidal input of 140 kHz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 1 kΩC = 2.2 nFf = 140 kHz
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) = 140/(s(s + 5)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 140/(s(s + 5))
ωc = rad/s
6.Hard
|H| (dB)0.10.1111010100100−100−80−60−40−20020ω (rad/s)φ (°)ω (rad/s)−270−180−900ω180​

A unity-feedback loop has the open-loop transfer function L(s) = 6/(s(s + 1)(s + 7)). Find the gain margin GM in dB.

L(s) = 6/(s(s + 1)(s + 7))
GM = dB

Answer key

  1. 1. |G(0)| = 58.89 dB
  2. 2. ωc = 1000 rad/s
  3. 3. φ = 11.32 °
  4. 4. φ = −62.67 °
  5. 5. ωc = 11.32 rad/s
  6. 6. GM = 19.4 dB

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