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)0.010.1110100100010000−60−40−200204060?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 100(s + 2)/(s(s + 200)(s + 0.5)). What is the slope n of the straight-line asymptote between 0.5 and 2 rad/s, in dB/decade?

G(s) = 100(s + 2)/(s(s + 200)(s + 0.5))
n = dB/dec
2.Easy
|H| (dB)0.11101001000−60−40−200204060?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 0.2(s + 100)/(s(s + 1)). What is the slope n of the straight-line asymptote above 100 rad/s, in dB/decade?

G(s) = 0.2(s + 100)/(s(s + 1))
n = dB/dec
3.Medium
vin​R = 4.7 kΩC = 4.7 nFvout​

The RC low-pass filter shown has R = 4.7 kΩ, C = 4.7 nF. A sinusoidal input of 14 kHz is applied. Find the gain |H| = |vout/vin| in dB.

R = 4.7 kΩC = 4.7 nFf = 14 kHz
|H| = dB
4.Medium
|H| (dB)0.11101001000−80−60−40−2002040ω (rad/s)ω = 8

Find the exact magnitude |G(jω)| of G(s) = 176/((s + 1)(s + 16)) at ω = 8 rad/s, in dB.

G(s) = 176/((s + 1)(s + 16))ω = 8 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 + 8)). Find the phase margin PM in degrees.

L(s) = 96/(s(s + 8))
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) = 234/(s(s + 4)(s + 9)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 234/(s(s + 4)(s + 9))
ω180 = rad/s

Answer key

  1. 1. n = −40 dB/dec
  2. 2. n = −20 dB/dec
  3. 3. |H| = −6.79 dB
  4. 4. |G(jω)| = 1.73 dB
  5. 5. PM = 43.88 °
  6. 6. ω180 = 6 rad/s

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