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)0.010.1110100100010000−40−2002040?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 500(s + 20)/((s + 0.5)(s + 1000)). What is the slope n of the straight-line asymptote above 1000 rad/s, in dB/decade?

G(s) = 500(s + 20)/((s + 0.5)(s + 1000))
n = dB/dec
2.Easy
|H| (dB)0.1110100100010000−60−40−200?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 50(s + 50)/((s + 5)(s + 500)). What is the slope n of the straight-line asymptote above 500 rad/s, in dB/decade?

G(s) = 50(s + 50)/((s + 5)(s + 500))
n = dB/dec
3.Medium
|H| (dB)0.10.1111010100100−20020406080ω (rad/s)φ (°)ω (rad/s)−135−90−450ω = 4

Find the phase ∠G(jω) of G(s) = 35(s + 6)/(s(s + 2)) at ω = 4 rad/s, in degrees.

G(s) = 35(s + 6)/(s(s + 2))ω = 4 rad/s
∠G(jω) = °
4.Medium
vin​R = 1 kΩC = 100 nFvout​

The RC low-pass filter shown has R = 1 kΩ, C = 100 nF. A sinusoidal input of 400 Hz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 1 kΩC = 100 nFf = 400 Hz
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 + 2)). Find the gain K that gives a gain margin of 4 dB.

L(s) = K/(s(s + 1)(s + 2))GM = 4 dB
K =
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) = 106/(s(s + 3)(s + 7)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 106/(s(s + 3)(s + 7))
ω180 = rad/s

Answer key

  1. 1. n = −20 dB/dec
  2. 2. n = −20 dB/dec
  3. 3. ∠G(jω) = −119.7 °
  4. 4. φ = −14.11 °
  5. 5. K = 3.786
  6. 6. ω180 = 4.583 rad/s

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