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
vin​L = 100 mHR = 220 Ωvout​

Find the corner (−3 dB) frequency ωc of the RL low-pass filter shown, with R = 220 Ω, L = 100 mH. Give it in rad/s.

R = 220 ΩL = 100 mH
ωc = rad/s
2.Easy
|H| (dB)0.11101001000−200204060ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 400(s + 18)/((s + 6)(s + 7)) in decibels, |G(0)| in dB.

G(s) = 400(s + 18)/((s + 6)(s + 7))
|G(0)| = dB
3.Medium
|H| (dB)0.11101001000−60−40−2002040ω (rad/s)ω = 3

Find the exact magnitude |G(jω)| of G(s) = 2550/((s + 10)(s + 15)) at ω = 3 rad/s, in dB.

G(s) = 2550/((s + 10)(s + 15))ω = 3 rad/s
|G(jω)| = dB
4.Medium
vin​L = 1 mHC = 0.47 µFR = 2 Ωvout​

In the series RLC band-pass filter shown the output is taken across R = 2 Ω, with L = 1 mH and C = 0.47 µF. Find the quality factor Q.

R = 2 ΩL = 1 mHC = 0.47 µF
Q =
5.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) = 340/(s(s + 20)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 340/(s(s + 20))
ωc = 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) = 12/(s(s + 5)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 12/(s(s + 5))
ωc = rad/s

Answer key

  1. 1. ωc = 2200 rad/s
  2. 2. |G(0)| = 44.68 dB
  3. 3. |G(jω)| = 24.06 dB
  4. 4. Q = 23.06
  5. 5. ωc = 13.94 rad/s
  6. 6. ωc = 2.197 rad/s

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