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)0.11101001000−80−60−40−200ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 140/((s + 50)(s + 9)) in decibels, |G(0)| in dB.

G(s) = 140/((s + 50)(s + 9))
|G(0)| = dB
2.Easy
|H| (dB)0.11101001000−40−2002040ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 46(s + 17)/((s + 1)(s + 60)) in decibels, |G(0)| in dB.

G(s) = 46(s + 17)/((s + 1)(s + 60))
|G(0)| = dB
3.Medium
vin​C = 1 nFR = 22 kΩvout​

The RC high-pass filter shown has R = 22 kΩ, C = 1 nF. A sinusoidal input of 1.8 kHz is applied. Find the gain |H| = |vout/vin| in dB.

R = 22 kΩC = 1 nFf = 1.8 kHz
|H| = dB
4.Medium
|H| (dB)0.010.010.10.111101010010010001000−60−40−200204060ω (rad/s)φ (°)ω (rad/s)−135−90−450ω = 0.5

Find the phase ∠G(jω) of G(s) = 4(s + 13)/(s(s + 9)) at ω = 0.5 rad/s, in degrees.

G(s) = 4(s + 13)/(s(s + 9))ω = 0.5 rad/s
∠G(jω) = °
5.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) = 488/(s(s + 8)(s + 9)). Find the gain margin GM in dB.

L(s) = 488/(s(s + 8)(s + 9))
GM = dB
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) = 472/(s(s + 7)(s + 8)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 472/(s(s + 7)(s + 8))
ω180 = rad/s

Answer key

  1. 1. |G(0)| = −10.14 dB
  2. 2. |G(0)| = 22.3 dB
  3. 3. |H| = −12.34 dB
  4. 4. ∠G(jω) = −90.98 °
  5. 5. GM = 7.987 dB
  6. 6. ω180 = 7.483 rad/s

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