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 = 47 mHR = 1000 Ωvout​

Find the corner (−3 dB) frequency ωc of the RL low-pass filter shown, with R = 1000 Ω, L = 47 mH. Give it in rad/s.

R = 1000 ΩL = 47 mH
ωc = rad/s
2.Easy
|H| (dB)0.11101001000−100−80−60−40−200ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 38/((s + 60)(s + 8)) in decibels, |G(0)| in dB.

G(s) = 38/((s + 60)(s + 8))
|G(0)| = dB
3.Medium
vin​R = 10 kΩC = 1 nFvout​

The RC low-pass filter shown has R = 10 kΩ, C = 1 nF. A sinusoidal input of 8 kHz is applied. Find the gain |H| = |vout/vin| in dB.

R = 10 kΩC = 1 nFf = 8 kHz
|H| = dB
4.Medium
|H| (dB)0.10.111101010010010001000−40−200204060ω (rad/s)φ (°)ω (rad/s)−135−90−450ω = 1

Find the phase ∠G(jω) of G(s) = 18(s + 16)/(s(s + 4)) at ω = 1 rad/s, in degrees.

G(s) = 18(s + 16)/(s(s + 4))ω = 1 rad/s
∠G(jω) = °
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) = 320/(s(s + 20)). Find the phase margin PM in degrees.

L(s) = 320/(s(s + 20))
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 + 2)(s + 10)). Find the gain K that gives a gain margin of 12 dB.

L(s) = K/(s(s + 2)(s + 10))GM = 12 dB
K =

Answer key

  1. 1. ωc = 21277 rad/s
  2. 2. |G(0)| = −22.03 dB
  3. 3. |H| = −0.9783 dB
  4. 4. ∠G(jω) = −100.5 °
  5. 5. PM = 56.34 °
  6. 6. K = 60.29

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