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 = 2.2 mHR = 100 Ωvout​

Find the corner (−3 dB) frequency ωc of the RL low-pass filter shown, with R = 100 Ω, L = 2.2 mH. Give it in rad/s.

R = 100 ΩL = 2.2 mH
ωc = rad/s
2.Easy
|H| (dB)0.1110100100010000−60−40−200204060?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 25000/(s(s + 500)(s + 1)). What is the slope n of the straight-line asymptote between 1 and 500 rad/s, in dB/decade?

G(s) = 25000/(s(s + 500)(s + 1))
n = dB/dec
3.Medium
|H| (dB)1101001000−60−40−20020ω (rad/s)ω = 20

Find the exact magnitude |G(jω)| of G(s) = 1530/((s + 15)(s + 17)) at ω = 20 rad/s, in dB.

G(s) = 1530/((s + 15)(s + 17))ω = 20 rad/s
|G(jω)| = dB
4.Medium
vin​C = 100 nFR = 2.2 kΩvout​

The RC high-pass filter shown has R = 2.2 kΩ, C = 100 nF. A sinusoidal input of 140 Hz is applied. Find the gain |H| = |vout/vin| in dB.

R = 2.2 kΩC = 100 nFf = 140 Hz
|H| = dB
5.Hard
|H| (dB)11101010010010001000−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​

A unity-feedback loop has the open-loop transfer function L(s) = 1360/(s(s + 20)). Find the phase margin PM in degrees.

L(s) = 1360/(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) = 396/(s(s + 4)(s + 10)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 396/(s(s + 4)(s + 10))
ω180 = rad/s

Answer key

  1. 1. ωc = 45455 rad/s
  2. 2. n = −40 dB/dec
  3. 3. |G(jω)| = 7.353 dB
  4. 4. |H| = −14.43 dB
  5. 5. PM = 30.27 °
  6. 6. ω180 = 6.325 rad/s

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