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)0.11101000204060ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 220(s + 10)/((s + 1)(s + 9)) in decibels, |G(0)| in dB.

G(s) = 220(s + 10)/((s + 1)(s + 9))
|G(0)| = dB
2.Easy
|H| (dB)0.11101001000−60−40−200ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 3(s + 2)/((s + 50)(s + 6)) in decibels, |G(0)| in dB.

G(s) = 3(s + 2)/((s + 50)(s + 6))
|G(0)| = dB
3.Medium
vin​C = 22 nFR = 1 kΩvout​

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

R = 1 kΩC = 22 nFf = 22 kHz
|H| = dB
4.Medium
vin​C = 2.2 nFR = 1 kΩvout​

The RC high-pass filter shown has R = 1 kΩ, C = 2.2 nF. A sinusoidal input of 360 kHz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 1 kΩC = 2.2 nFf = 360 kHz
φ = °
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) = 144/(s(s + 6)(s + 9)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 144/(s(s + 6)(s + 9))
ω180 = rad/s
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) = K/(s(s + 3)(s + 7)). Find the gain K that gives a gain margin of 10 dB.

L(s) = K/(s(s + 3)(s + 7))GM = 10 dB
K =

Answer key

  1. 1. |G(0)| = 47.76 dB
  2. 2. |G(0)| = −33.98 dB
  3. 3. |H| = −0.4459 dB
  4. 4. φ = 11.36 °
  5. 5. ω180 = 7.348 rad/s
  6. 6. K = 66.41

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