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)0.1110100−60−40−20020?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 100/((s + 10)(s + 1)). What is the slope n of the straight-line asymptote above 10 rad/s, in dB/decade?

G(s) = 100/((s + 10)(s + 1))
n = dB/dec
2.Easy
|H| (dB)0.1110100−40−2002040ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 460/((s + 1)(s + 9)) in decibels, |G(0)| in dB.

G(s) = 460/((s + 1)(s + 9))
|G(0)| = dB
3.Medium
vin​R = 22 kΩC = 22 nFvout​

The RC low-pass filter shown has R = 22 kΩ, C = 22 nF. A sinusoidal input of 1.3 kHz is applied. Find the gain |H| = |vout/vin| in dB.

R = 22 kΩC = 22 nFf = 1.3 kHz
|H| = dB
4.Medium
|H| (dB)0.11101001000−80−60−40−2002040ω (rad/s)ω = 10

Find the exact magnitude |G(jω)| of G(s) = 660/((s + 4)(s + 11)) at ω = 10 rad/s, in dB.

G(s) = 660/((s + 4)(s + 11))ω = 10 rad/s
|G(jω)| = dB
5.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 + 4)(s + 9)). Find the gain K that gives a gain margin of 8 dB.

L(s) = K/(s(s + 4)(s + 9))GM = 8 dB
K =
6.Hard
|H| (dB)0.10.1111010100100−80−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​ = ?

A unity-feedback loop has the open-loop transfer function L(s) = 8/(s(s + 2)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 8/(s(s + 2))
ωc = rad/s

Answer key

  1. 1. n = −40 dB/dec
  2. 2. |G(0)| = 34.17 dB
  3. 3. |H| = −12.21 dB
  4. 4. |G(jω)| = 12.3 dB
  5. 5. K = 186.3
  6. 6. ωc = 2.499 rad/s

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