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)0.1110100−200204060ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 4700/((s + 2)(s + 7)) in decibels, |G(0)| in dB.

G(s) = 4700/((s + 2)(s + 7))
|G(0)| = dB
2.Easy
vin​C = 47 nFR = 10 kΩvout​

Find the corner (−3 dB) frequency ωc of the RC high-pass filter shown, with R = 10 kΩ, C = 47 nF. Give it in rad/s.

R = 10 kΩC = 47 nF
ωc = rad/s
3.Medium
|H| (dB)1101001000−60−40−2002040ω (rad/s)ω = 20

Find the exact magnitude |G(jω)| of G(s) = 4256/((s + 14)(s + 16)) at ω = 20 rad/s, in dB.

G(s) = 4256/((s + 14)(s + 16))ω = 20 rad/s
|G(jω)| = dB
4.Medium
|H| (dB)0.10.1111010100100−2002040ω (rad/s)φ (°)ω (rad/s)−90−450ω = 4

Find the phase ∠G(jω) of G(s) = 43(s + 1)/(s(s + 5)) at ω = 4 rad/s, in degrees.

G(s) = 43(s + 1)/(s(s + 5))ω = 4 rad/s
∠G(jω) = °
5.Hard
|H| (dB)0.10.1111010100100−100−80−60−40−20020ω (rad/s)φ (°)ω (rad/s)−270−180−900ω180​ = ?

A unity-feedback loop has the open-loop transfer function L(s) = 8/(s(s + 2)(s + 5)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 8/(s(s + 2)(s + 5))
ω180 = rad/s
6.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) = 460/(s(s + 20)). Find the phase margin PM in degrees.

L(s) = 460/(s(s + 20))
PM = °

Answer key

  1. 1. |G(0)| = 50.52 dB
  2. 2. ωc = 2128 rad/s
  3. 3. |G(jω)| = 16.66 dB
  4. 4. ∠G(jω) = −52.7 °
  5. 5. ω180 = 3.162 rad/s
  6. 6. PM = 49.03 °

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