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) = 10000/((s + 200)(s + 5)). What is the slope n of the straight-line asymptote above 200 rad/s, in dB/decade?

G(s) = 10000/((s + 200)(s + 5))
n = dB/dec
2.Easy
vin​R = 2.2 kΩC = 4.7 nFvout​

Find the corner (−3 dB) frequency fc of the RC low-pass filter shown, with R = 2.2 kΩ, C = 4.7 nF. Give it in Hz.

R = 2.2 kΩC = 4.7 nF
fc = Hz
3.Medium
|H| (dB)1101001000−80−60−40−20020ω (rad/s)ω = 20

Find the exact magnitude |G(jω)| of G(s) = 720/((s + 10)(s + 18)) at ω = 20 rad/s, in dB.

G(s) = 720/((s + 10)(s + 18))ω = 20 rad/s
|G(jω)| = dB
4.Medium
vin​L = 2 mHC = 1 µFR = 10 Ωvout​

In the series RLC band-pass filter shown the output is taken across R = 10 Ω, with L = 2 mH and C = 1 µF. Find the centre (resonant) frequency f0 in Hz.

R = 10 ΩL = 2 mHC = 1 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) = 50/(s(s + 2)(s + 9)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 50/(s(s + 2)(s + 9))
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) = 444/(s(s + 4)(s + 10)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 444/(s(s + 4)(s + 10))
ω180 = rad/s

Answer key

  1. 1. n = −40 dB/dec
  2. 2. fc = 15392 Hz
  3. 3. |G(jω)| = 1.56 dB
  4. 4. f0 = 3559 Hz
  5. 5. ω180 = 4.243 rad/s
  6. 6. ω180 = 6.325 rad/s

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