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)0.010.1110100−100−80−60−40−200?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 1/((s + 2)(s + 0.5)). What is the slope n of the straight-line asymptote above 2 rad/s, in dB/decade?

G(s) = 1/((s + 2)(s + 0.5))
n = dB/dec
2.Easy
|H| (dB)0.11101001000−60−40−2002040ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 2500/((s + 30)(s + 5)) in decibels, |G(0)| in dB.

G(s) = 2500/((s + 30)(s + 5))
|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 phase shift φ of vout relative to vin, in degrees.

R = 10 kΩC = 1 nFf = 8 kHz
φ = °
4.Medium
|H| (dB)0.11101001000−80−60−40−20020ω (rad/s)ω = 15

Find the exact magnitude |G(jω)| of G(s) = 720/((s + 9)(s + 10)) at ω = 15 rad/s, in dB.

G(s) = 720/((s + 9)(s + 10))ω = 15 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) = 56/(s(s + 4)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 56/(s(s + 4))
ωc = rad/s
6.Hard
|H| (dB)0.10.111101010010010001000−60−40−200204060ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​

A unity-feedback loop has the open-loop transfer function L(s) = 230/(s(s + 5)). Find the phase margin PM in degrees.

L(s) = 230/(s(s + 5))
PM = °

Answer key

  1. 1. n = −40 dB/dec
  2. 2. |G(0)| = 24.44 dB
  3. 3. φ = −26.69 °
  4. 4. |G(jω)| = 7.171 dB
  5. 5. ωc = 6.969 rad/s
  6. 6. PM = 18.71 °

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