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)0.1110100100010000−60−40−200204060?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 1000(s + 10)/(s(s + 1)(s + 200)). What is the slope n of the straight-line asymptote above 200 rad/s, in dB/decade?

G(s) = 1000(s + 10)/(s(s + 1)(s + 200))
n = dB/dec
2.Easy
|H| (dB)0.010.11101001000−2002040?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 1000(s + 0.5)/((s + 20)(s + 5)). What is the slope n of the straight-line asymptote above 20 rad/s, in dB/decade?

G(s) = 1000(s + 0.5)/((s + 20)(s + 5))
n = dB/dec
3.Medium
vin​L = 50 mHC = 0.47 µFR = 10 Ωvout​

In the series RLC band-pass filter shown the output is taken across R = 10 Ω, with L = 50 mH and C = 0.47 µF. Find the centre (resonant) frequency f0 in Hz.

R = 10 ΩL = 50 mHC = 0.47 µF
f0 = Hz
4.Medium
vin​C = 22 nFR = 10 kΩvout​

The RC high-pass filter shown has R = 10 kΩ, C = 22 nF. A sinusoidal input of 3.6 kHz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 10 kΩC = 22 nFf = 3.6 kHz
φ = °
5.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) = 2/(s(s + 1)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 2/(s(s + 1))
ωc = rad/s
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) = 82.5/(s(s + 5)). Find the phase margin PM in degrees.

L(s) = 82.5/(s(s + 5))
PM = °

Answer key

  1. 1. n = −40 dB/dec
  2. 2. n = −20 dB/dec
  3. 3. f0 = 1038 Hz
  4. 4. φ = 11.36 °
  5. 5. ωc = 1.25 rad/s
  6. 6. PM = 30.69 °

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