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) = 350(s + 4)/((s + 2)(s + 90)) in decibels, |G(0)| in dB.

G(s) = 350(s + 4)/((s + 2)(s + 90))
|G(0)| = dB
2.Easy
vin​L = 2.2 mHR = 47 Ωvout​

Find the corner (−3 dB) frequency fc of the RL low-pass filter shown, with R = 47 Ω, L = 2.2 mH. Give it in Hz.

R = 47 ΩL = 2.2 mH
fc = Hz
3.Medium
|H| (dB)0.10.111101010010010001000−40−200204060ω (rad/s)φ (°)ω (rad/s)−135−90−450ω = 2

Find the phase ∠G(jω) of G(s) = 21(s + 18)/(s(s + 13)) at ω = 2 rad/s, in degrees.

G(s) = 21(s + 18)/(s(s + 13))ω = 2 rad/s
∠G(jω) = °
4.Medium
|H| (dB)0.10.1111010100100−200204060ω (rad/s)φ (°)ω (rad/s)−135−90−450ω = 3

Find the phase ∠G(jω) of G(s) = 17(s + 10)/(s(s + 4)) at ω = 3 rad/s, in degrees.

G(s) = 17(s + 10)/(s(s + 4))ω = 3 rad/s
∠G(jω) = °
5.Hard
|H| (dB)0.10.1111010100100−60−40−200204060ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​

A unity-feedback loop has the open-loop transfer function L(s) = 42/(s(s + 4)). Find the phase margin PM in degrees.

L(s) = 42/(s(s + 4))
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) = 382/(s(s + 6)(s + 10)). Find the gain margin GM in dB.

L(s) = 382/(s(s + 6)(s + 10))
GM = dB

Answer key

  1. 1. |G(0)| = 17.82 dB
  2. 2. fc = 3400 Hz
  3. 3. ∠G(jω) = −92.41 °
  4. 4. ∠G(jω) = −110.2 °
  5. 5. PM = 34.16 °
  6. 6. GM = 8.004 dB

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