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)0.11101001000−20020?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 500(s + 1)/((s + 50)(s + 10)). What is the slope n of the straight-line asymptote above 50 rad/s, in dB/decade?

G(s) = 500(s + 1)/((s + 50)(s + 10))
n = dB/dec
2.Easy
|H| (dB)110100100010000−100−80−60−40−20020?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 200000/(s(s + 20)(s + 1000)). What is the slope n of the straight-line asymptote between 20 and 1000 rad/s, in dB/decade?

G(s) = 200000/(s(s + 20)(s + 1000))
n = dB/dec
3.Medium
|H| (dB)0.10.111101010010010001000−40−2002040ω (rad/s)φ (°)ω (rad/s)−90−450ω = 15

Find the phase ∠G(jω) of G(s) = 13(s + 2)/(s(s + 15)) at ω = 15 rad/s, in degrees.

G(s) = 13(s + 2)/(s(s + 15))ω = 15 rad/s
∠G(jω) = °
4.Medium
vin​L = 1 mHC = 0.47 µFR = 20 Ωvout​

In the series RLC band-pass filter shown the output is taken across R = 20 Ω, with L = 1 mH and C = 0.47 µF. Find the centre (resonant) frequency f0 in Hz.

R = 20 ΩL = 1 mHC = 0.47 µF
f0 = Hz
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) = 80/(s(s + 2)(s + 7)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 80/(s(s + 2)(s + 7))
ω180 = rad/s
6.Hard
|H| (dB)0.10.1111010100100−60−40−200204060ω (rad/s)φ (°)ω (rad/s)−270−180−900ω180​

A unity-feedback loop has the open-loop transfer function L(s) = 1078/(s(s + 9)(s + 10)). Find the gain margin GM in dB.

L(s) = 1078/(s(s + 9)(s + 10))
GM = dB

Answer key

  1. 1. n = −20 dB/dec
  2. 2. n = −40 dB/dec
  3. 3. ∠G(jω) = −52.59 °
  4. 4. f0 = 7341 Hz
  5. 5. ω180 = 3.742 rad/s
  6. 6. GM = 4.008 dB

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