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)0.11101001000−20020ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 120(s + 11)/((s + 60)(s + 8)) in decibels, |G(0)| in dB.

G(s) = 120(s + 11)/((s + 60)(s + 8))
|G(0)| = dB
2.Easy
vin​L = 1 mHR = 470 Ωvout​

Find the corner (−3 dB) frequency fc of the RL low-pass filter shown, with R = 470 Ω, L = 1 mH. Give it in Hz.

R = 470 ΩL = 1 mH
fc = Hz
3.Medium
|H| (dB)1101001000−60−40−20020ω (rad/s)ω = 20

Find the exact magnitude |G(jω)| of G(s) = 2448/((s + 16)(s + 17)) at ω = 20 rad/s, in dB.

G(s) = 2448/((s + 16)(s + 17))ω = 20 rad/s
|G(jω)| = dB
4.Medium
vin​L = 1 mHC = 1 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 = 1 µF. Find the centre (resonant) frequency f0 in Hz.

R = 20 ΩL = 1 mHC = 1 µF
f0 = Hz
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) = 600/(s(s + 10)). Find the phase margin PM in degrees.

L(s) = 600/(s(s + 10))
PM = °
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) = K/(s(s + 3)(s + 7)). Find the gain K that gives a gain margin of 12 dB.

L(s) = K/(s(s + 3)(s + 7))GM = 12 dB
K =

Answer key

  1. 1. |G(0)| = 8.787 dB
  2. 2. fc = 74803 Hz
  3. 3. |G(jω)| = 11.22 dB
  4. 4. f0 = 5033 Hz
  5. 5. PM = 23.05 °
  6. 6. K = 52.75

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