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)0.11101001000−80−60−40−200ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 250/((s + 6)(s + 80)) in decibels, |G(0)| in dB.

G(s) = 250/((s + 6)(s + 80))
|G(0)| = dB
2.Easy
vin​L = 10 mHR = 1000 Ωvout​

Find the corner (−3 dB) frequency fc of the RL low-pass filter shown, with R = 1000 Ω, L = 10 mH. Give it in Hz.

R = 1000 ΩL = 10 mH
fc = Hz
3.Medium
vin​L = 100 mHC = 0.47 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 = 0.47 µF. Find the quality factor Q.

R = 10 ΩL = 100 mHC = 0.47 µF
Q =
4.Medium
|H| (dB)1101001000−80−60−40−20020ω (rad/s)ω = 20

Find the exact magnitude |G(jω)| of G(s) = 400/((s + 10)(s + 20)) at ω = 20 rad/s, in dB.

G(s) = 400/((s + 10)(s + 20))ω = 20 rad/s
|G(jω)| = dB
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) = 76/(s(s + 4)(s + 6)). Find the gain margin GM in dB.

L(s) = 76/(s(s + 4)(s + 6))
GM = dB
6.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) = 78/(s(s + 2)(s + 9)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 78/(s(s + 2)(s + 9))
ω180 = rad/s

Answer key

  1. 1. |G(0)| = −5.666 dB
  2. 2. fc = 15915 Hz
  3. 3. Q = 46.13
  4. 4. |G(jω)| = −3.979 dB
  5. 5. GM = 9.988 dB
  6. 6. ω180 = 4.243 rad/s

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