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)0.11101001000−40−200ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 14(s + 3)/((s + 50)(s + 6)) in decibels, |G(0)| in dB.

G(s) = 14(s + 3)/((s + 50)(s + 6))
|G(0)| = dB
2.Easy
vin​R = 1 kΩC = 2.2 nFvout​

Find the corner (−3 dB) frequency ωc of the RC low-pass filter shown, with R = 1 kΩ, C = 2.2 nF. Give it in rad/s.

R = 1 kΩC = 2.2 nF
ωc = rad/s
3.Medium
|H| (dB)0.10.1111010100100−200204060ω (rad/s)φ (°)ω (rad/s)−90−450ω = 3

Find the phase ∠G(jω) of G(s) = 28(s + 6)/(s(s + 10)) at ω = 3 rad/s, in degrees.

G(s) = 28(s + 6)/(s(s + 10))ω = 3 rad/s
∠G(jω) = °
4.Medium
vin​R = 47 ΩL = 10 mHvout​

The RL high-pass filter shown has R = 47 Ω, L = 10 mH. A sinusoidal input of 150 Hz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 47 ΩL = 10 mHf = 150 Hz
φ = °
5.Hard
|H| (dB)0.10.111101010010010001000−60−40−200204060ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​

A unity-feedback loop has the open-loop transfer function L(s) = 350/(s(s + 5)). Find the phase margin PM in degrees.

L(s) = 350/(s(s + 5))
PM = °
6.Hard
|H| (dB)0.10.1111010100100−80−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​

A unity-feedback loop has the open-loop transfer function L(s) = 3.7/(s(s + 1)). Find the phase margin PM in degrees.

L(s) = 3.7/(s(s + 1))
PM = °

Answer key

  1. 1. |G(0)| = −17.08 dB
  2. 2. ωc = 454545 rad/s
  3. 3. ∠G(jω) = −80.13 °
  4. 4. φ = 78.66 °
  5. 5. PM = 15.22 °
  6. 6. PM = 29.08 °

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