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)0.11101001000−100−80−60−40−200ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 21/((s + 40)(s + 5)) in decibels, |G(0)| in dB.

G(s) = 21/((s + 40)(s + 5))
|G(0)| = dB
2.Easy
|H| (dB)0.1110100−200204060ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 4500/((s + 3)(s + 4)) in decibels, |G(0)| in dB.

G(s) = 4500/((s + 3)(s + 4))
|G(0)| = dB
3.Medium
vin​C = 1 nFR = 47 kΩvout​

The RC high-pass filter shown has R = 47 kΩ, C = 1 nF. A sinusoidal input of 10 kHz is applied. Find the gain |H| = |vout/vin| in dB.

R = 47 kΩC = 1 nFf = 10 kHz
|H| = dB
4.Medium
|H| (dB)0.10.1111010100100−200204060ω (rad/s)φ (°)ω (rad/s)−135−90−450ω = 5

Find the phase ∠G(jω) of G(s) = 17(s + 9)/(s(s + 2)) at ω = 5 rad/s, in degrees.

G(s) = 17(s + 9)/(s(s + 2))ω = 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) = 18/(s(s + 2)(s + 5)). Find the gain margin GM in dB.

L(s) = 18/(s(s + 2)(s + 5))
GM = dB
6.Hard
|H| (dB)0.10.1111010100100−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​ = ?

A unity-feedback loop has the open-loop transfer function L(s) = 24/(s(s + 4)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 24/(s(s + 4))
ωc = rad/s

Answer key

  1. 1. |G(0)| = −19.58 dB
  2. 2. |G(0)| = 51.48 dB
  3. 3. |H| = −0.4715 dB
  4. 4. ∠G(jω) = −129.1 °
  5. 5. GM = 11.8 dB
  6. 6. ωc = 4.159 rad/s

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