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)0.1110100100010000−100−80−60−40−20020?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 0.1(s + 1000)/((s + 1)(s + 10)). What is the slope n of the straight-line asymptote between 1 and 10 rad/s, in dB/decade?

G(s) = 0.1(s + 1000)/((s + 1)(s + 10))
n = dB/dec
2.Easy
vin​R = 47 kΩC = 2.2 nFvout​

Find the corner (−3 dB) frequency ωc of the RC low-pass filter shown, with R = 47 kΩ, C = 2.2 nF. Give it in rad/s.

R = 47 kΩC = 2.2 nF
ωc = rad/s
3.Medium
vin​R = 1000 ΩL = 2.2 mHvout​

The RL high-pass filter shown has R = 1000 Ω, L = 2.2 mH. A sinusoidal input of 18 kHz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 1000 ΩL = 2.2 mHf = 18 kHz
φ = °
4.Medium
vin​R = 10 kΩC = 10 nFvout​

The RC low-pass filter shown has R = 10 kΩ, C = 10 nF. A sinusoidal input of 4.8 kHz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 10 kΩC = 10 nFf = 4.8 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) = 84/(s(s + 3)(s + 8)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 84/(s(s + 3)(s + 8))
ω180 = rad/s
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) = 4/(s(s + 2)). Find the phase margin PM in degrees.

L(s) = 4/(s(s + 2))
PM = °

Answer key

  1. 1. n = −20 dB/dec
  2. 2. ωc = 9671 rad/s
  3. 3. φ = 76.03 °
  4. 4. φ = −71.66 °
  5. 5. ω180 = 4.899 rad/s
  6. 6. PM = 51.83 °

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