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)0.11101001000−2002040ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 400(s + 2)/((s + 20)(s + 5)) in decibels, |G(0)| in dB.

G(s) = 400(s + 2)/((s + 20)(s + 5))
|G(0)| = dB
2.Easy
|H| (dB)110100100010000−100−80−60−40−200?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 0.5(s + 1000)/((s + 10)(s + 50)). What is the slope n of the straight-line asymptote above 1000 rad/s, in dB/decade?

G(s) = 0.5(s + 1000)/((s + 10)(s + 50))
n = dB/dec
3.Medium
|H| (dB)0.11101001000−80−60−40−2002040ω (rad/s)ω = 2

Find the exact magnitude |G(jω)| of G(s) = 308/((s + 2)(s + 14)) at ω = 2 rad/s, in dB.

G(s) = 308/((s + 2)(s + 14))ω = 2 rad/s
|G(jω)| = dB
4.Medium
vin​R = 10 kΩC = 4.7 nFvout​

The RC low-pass filter shown has R = 10 kΩ, C = 4.7 nF. A sinusoidal input of 17 kHz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 10 kΩC = 4.7 nFf = 17 kHz
φ = °
5.Hard
|H| (dB)0.10.1111010100100−40−200204060ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​ = ?

A unity-feedback loop has the open-loop transfer function L(s) = 110/(s(s + 5)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 110/(s(s + 5))
ωc = rad/s
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) = K/(s(s + 1)(s + 8)). Find the gain K that gives a gain margin of 12 dB.

L(s) = K/(s(s + 1)(s + 8))GM = 12 dB
K =

Answer key

  1. 1. |G(0)| = 18.06 dB
  2. 2. n = −20 dB/dec
  3. 3. |G(jω)| = 17.73 dB
  4. 4. φ = −78.73 °
  5. 5. ωc = 9.91 rad/s
  6. 6. K = 18.09

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