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)0.1110100−200204060ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 3600/((s + 4)(s + 6)) in decibels, |G(0)| in dB.

G(s) = 3600/((s + 4)(s + 6))
|G(0)| = dB
2.Easy
vin​R = 47 ΩL = 22 mHvout​

Find the corner (−3 dB) frequency ωc of the RL high-pass filter shown, with R = 47 Ω, L = 22 mH. Give it in rad/s.

R = 47 ΩL = 22 mH
ωc = rad/s
3.Medium
vin​L = 22 mHR = 100 Ωvout​

The RL low-pass filter shown has R = 100 Ω, L = 22 mH. A sinusoidal input of 140 Hz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 100 ΩL = 22 mHf = 140 Hz
φ = °
4.Medium
vin​C = 10 nFR = 1 kΩvout​

The RC high-pass filter shown has R = 1 kΩ, C = 10 nF. A sinusoidal input of 3.2 kHz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 1 kΩC = 10 nFf = 3.2 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) = K/(s(s + 1)(s + 7)). Find the gain K that gives a gain margin of 3 dB.

L(s) = K/(s(s + 1)(s + 7))GM = 3 dB
K =
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) = 2/(s(s + 1)(s + 4)). Find the gain margin GM in dB.

L(s) = 2/(s(s + 1)(s + 4))
GM = dB

Answer key

  1. 1. |G(0)| = 43.52 dB
  2. 2. ωc = 2136 rad/s
  3. 3. φ = −10.95 °
  4. 4. φ = 78.63 °
  5. 5. K = 39.64
  6. 6. GM = 20 dB

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