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)1101001000−100−80−60−40−20020?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 1000/(s(s + 50)(s + 10)). What is the slope n of the straight-line asymptote between 10 and 50 rad/s, in dB/decade?

G(s) = 1000/(s(s + 50)(s + 10))
n = dB/dec
2.Easy
vin​L = 4.7 mHR = 470 Ωvout​

Find the corner (−3 dB) frequency fc of the RL low-pass filter shown, with R = 470 Ω, L = 4.7 mH. Give it in Hz.

R = 470 ΩL = 4.7 mH
fc = Hz
3.Medium
|H| (dB)0.11101001000−80−60−40−20020ω (rad/s)ω = 20

Find the exact magnitude |G(jω)| of G(s) = 560/((s + 5)(s + 16)) at ω = 20 rad/s, in dB.

G(s) = 560/((s + 5)(s + 16))ω = 20 rad/s
|G(jω)| = dB
4.Medium
vin​L = 100 mHC = 4.7 µFR = 10 Ωvout​

In the series RLC band-pass filter shown the output is taken across R = 10 Ω, with L = 100 mH and C = 4.7 µF. Find the quality factor Q.

R = 10 ΩL = 100 mHC = 4.7 µF
Q =
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) = 46/(s(s + 4)(s + 5)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 46/(s(s + 4)(s + 5))
ω180 = rad/s
6.Hard
|H| (dB)11101010010010001000−80−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​ = ?

A unity-feedback loop has the open-loop transfer function L(s) = 480/(s(s + 10)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 480/(s(s + 10))
ωc = rad/s

Answer key

  1. 1. n = −40 dB/dec
  2. 2. fc = 15915 Hz
  3. 3. |G(jω)| = 0.5108 dB
  4. 4. Q = 14.59
  5. 5. ω180 = 4.472 rad/s
  6. 6. ωc = 20.8 rad/s

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