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) = 20/((s + 1)(s + 10)). What is the slope n of the straight-line asymptote above 10 rad/s, in dB/decade?

G(s) = 20/((s + 1)(s + 10))
n = dB/dec
2.Easy
|H| (dB)1101001000−80−60−40−2002040?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 1000/(s(s + 20)). What is the slope n of the straight-line asymptote above 20 rad/s, in dB/decade?

G(s) = 1000/(s(s + 20))
n = dB/dec
3.Medium
vin​C = 47 nFR = 2.2 kΩvout​

The RC high-pass filter shown has R = 2.2 kΩ, C = 47 nF. A sinusoidal input of 380 Hz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 2.2 kΩC = 47 nFf = 380 Hz
φ = °
4.Medium
vin​R = 4.7 kΩC = 2.2 nFvout​

The RC low-pass filter shown has R = 4.7 kΩ, C = 2.2 nF. A sinusoidal input of 7.7 kHz is applied. Find the gain |H| = |vout/vin| in dB.

R = 4.7 kΩC = 2.2 nFf = 7.7 kHz
|H| = 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 + 3)(s + 4)). Find the gain K that gives a gain margin of 15 dB.

L(s) = K/(s(s + 3)(s + 4))GM = 15 dB
K =
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) = 36/(s(s + 1)(s + 7)). Find the gain margin GM in dB.

L(s) = 36/(s(s + 1)(s + 7))
GM = dB

Answer key

  1. 1. n = −40 dB/dec
  2. 2. n = −40 dB/dec
  3. 3. φ = 76.13 °
  4. 4. |H| = −0.97 dB
  5. 5. K = 14.94
  6. 6. GM = 3.838 dB

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