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)0.11101001000−100−80−60−40−20020ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 42/((s + 1)(s + 30)) in decibels, |G(0)| in dB.

G(s) = 42/((s + 1)(s + 30))
|G(0)| = dB
2.Easy
vin​R = 4.7 kΩC = 4.7 nFvout​

Find the corner (−3 dB) frequency fc of the RC low-pass filter shown, with R = 4.7 kΩ, C = 4.7 nF. Give it in Hz.

R = 4.7 kΩC = 4.7 nF
fc = Hz
3.Medium
vin​R = 10 kΩC = 4.7 nFvout​

The RC low-pass filter shown has R = 10 kΩ, C = 4.7 nF. A sinusoidal input of 14 kHz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 10 kΩC = 4.7 nFf = 14 kHz
φ = °
4.Medium
vin​C = 2.2 nFR = 4.7 kΩvout​

The RC high-pass filter shown has R = 4.7 kΩ, C = 2.2 nF. A sinusoidal input of 7.7 kHz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 4.7 kΩC = 2.2 nFf = 7.7 kHz
φ = °
5.Hard
|H| (dB)11101010010010001000−60−40−200204060ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​ = ?

A unity-feedback loop has the open-loop transfer function L(s) = 2500/(s(s + 20)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 2500/(s(s + 20))
ωc = rad/s
6.Hard
|H| (dB)0.10.1111010100100−40−200204060ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​ = ?

A unity-feedback loop has the open-loop transfer function L(s) = 105/(s(s + 10)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 105/(s(s + 10))
ωc = rad/s

Answer key

  1. 1. |G(0)| = 2.923 dB
  2. 2. fc = 7205 Hz
  3. 3. φ = −76.4 °
  4. 4. φ = 63.42 °
  5. 5. ωc = 48.04 rad/s
  6. 6. ωc = 8.142 rad/s

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