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)0.010.11101001000−60−40−200204060?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 0.1(s + 100)/(s(s + 0.5)(s + 10)). What is the slope n of the straight-line asymptote above 100 rad/s, in dB/decade?

G(s) = 0.1(s + 100)/(s(s + 0.5)(s + 10))
n = dB/dec
2.Easy
|H| (dB)0.010.1110100100010000−100−80−60−40−20020?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 0.04(s + 500)/((s + 20)(s + 0.5)). What is the slope n of the straight-line asymptote between 20 and 500 rad/s, in dB/decade?

G(s) = 0.04(s + 500)/((s + 20)(s + 0.5))
n = dB/dec
3.Medium
vin​L = 5 mHC = 1 µFR = 2 Ωvout​

In the series RLC band-pass filter shown the output is taken across R = 2 Ω, with L = 5 mH and C = 1 µF. Find the −3 dB bandwidth BW in Hz.

R = 2 ΩL = 5 mHC = 1 µF
BW = Hz
4.Medium
|H| (dB)0.10.1111010100100−200204060ω (rad/s)φ (°)ω (rad/s)−90−450ω = 4

Find the phase ∠G(jω) of G(s) = 38(s + 3)/(s(s + 7)) at ω = 4 rad/s, in degrees.

G(s) = 38(s + 3)/(s(s + 7))ω = 4 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) = 54/(s(s + 3)(s + 4)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 54/(s(s + 3)(s + 4))
ω180 = rad/s
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) = 40/(s(s + 5)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 40/(s(s + 5))
ωc = rad/s

Answer key

  1. 1. n = −40 dB/dec
  2. 2. n = −40 dB/dec
  3. 3. BW = 63.66 Hz
  4. 4. ∠G(jω) = −66.61 °
  5. 5. ω180 = 3.464 rad/s
  6. 6. ωc = 5.423 rad/s

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