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)0.11101001000−40−200ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 13(s + 2)/((s + 50)(s + 6)) in decibels, |G(0)| in dB.

G(s) = 13(s + 2)/((s + 50)(s + 6))
|G(0)| = dB
2.Easy
|H| (dB)0.11101001000−60−40−2002040?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 10000/((s + 1)(s + 100)). What is the slope n of the straight-line asymptote between 1 and 100 rad/s, in dB/decade?

G(s) = 10000/((s + 1)(s + 100))
n = dB/dec
3.Medium
|H| (dB)0.10.111101010010010001000−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−90−450ω = 15

Find the phase ∠G(jω) of G(s) = 9(s + 3)/(s(s + 5)) at ω = 15 rad/s, in degrees.

G(s) = 9(s + 3)/(s(s + 5))ω = 15 rad/s
∠G(jω) = °
4.Medium
vin​C = 4.7 nFR = 10 kΩvout​

The RC high-pass filter shown has R = 10 kΩ, C = 4.7 nF. A sinusoidal input of 1.7 kHz is applied. Find the gain |H| = |vout/vin| in dB.

R = 10 kΩC = 4.7 nFf = 1.7 kHz
|H| = dB
5.Hard
|H| (dB)0.10.1111010100100−100−80−60−40−20020ω (rad/s)φ (°)ω (rad/s)−270−180−900ω180​

A unity-feedback loop has the open-loop transfer function L(s) = K/(s(s + 3)(s + 5)). Find the gain K that gives a gain margin of 20 dB.

L(s) = K/(s(s + 3)(s + 5))GM = 20 dB
K =
6.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) = 52/(s(s + 4)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 52/(s(s + 4))
ωc = rad/s

Answer key

  1. 1. |G(0)| = −21.24 dB
  2. 2. n = −20 dB/dec
  3. 3. ∠G(jω) = −82.87 °
  4. 4. |H| = −6.962 dB
  5. 5. K = 12
  6. 6. ωc = 6.679 rad/s

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