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)0.11101001000−100−80−60−40−200?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 100/((s + 5)(s + 20)). What is the slope n of the straight-line asymptote between 5 and 20 rad/s, in dB/decade?

G(s) = 100/((s + 5)(s + 20))
n = dB/dec
2.Easy
|H| (dB)1101001000−100−80−60−40−200ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 80/((s + 10)(s + 20)) in decibels, |G(0)| in dB.

G(s) = 80/((s + 10)(s + 20))
|G(0)| = dB
3.Medium
vin​R = 47 kΩC = 2.2 nFvout​

The RC low-pass filter shown has R = 47 kΩ, C = 2.2 nF. A sinusoidal input of 6.2 kHz is applied. Find the gain |H| = |vout/vin| in dB.

R = 47 kΩC = 2.2 nFf = 6.2 kHz
|H| = dB
4.Medium
|H| (dB)1101001000−60−40−20020ω (rad/s)ω = 10

Find the exact magnitude |G(jω)| of G(s) = 1904/((s + 14)(s + 17)) at ω = 10 rad/s, in dB.

G(s) = 1904/((s + 14)(s + 17))ω = 10 rad/s
|G(jω)| = dB
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) = 96/(s(s + 4)). Find the phase margin PM in degrees.

L(s) = 96/(s(s + 4))
PM = °
6.Hard
|H| (dB)0.10.1111010100100−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​ = ?

A unity-feedback loop has the open-loop transfer function L(s) = 28/(s(s + 4)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 28/(s(s + 4))
ωc = rad/s

Answer key

  1. 1. n = −20 dB/dec
  2. 2. |G(0)| = −7.959 dB
  3. 3. |H| = −12.36 dB
  4. 4. |G(jω)| = 14.98 dB
  5. 5. PM = 23.05 °
  6. 6. ωc = 4.596 rad/s

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