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) = 250000/(s(s + 1000)(s + 5)). What is the slope n of the straight-line asymptote above 1000 rad/s, in dB/decade?

G(s) = 250000/(s(s + 1000)(s + 5))
n = dB/dec
2.Easy
vin​L = 10 mHR = 470 Ωvout​

Find the corner (−3 dB) frequency fc of the RL low-pass filter shown, with R = 470 Ω, L = 10 mH. Give it in Hz.

R = 470 ΩL = 10 mH
fc = Hz
3.Medium
vin​R = 100 ΩL = 2.2 mHvout​

The RL high-pass filter shown has R = 100 Ω, L = 2.2 mH. A sinusoidal input of 36 kHz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 100 ΩL = 2.2 mHf = 36 kHz
φ = °
4.Medium
vin​L = 10 mHC = 1 µFR = 50 Ωvout​

In the series RLC band-pass filter shown the output is taken across R = 50 Ω, with L = 10 mH and C = 1 µF. Find the −3 dB bandwidth BW in Hz.

R = 50 ΩL = 10 mHC = 1 µF
BW = Hz
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) = 82/(s(s + 3)(s + 6)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 82/(s(s + 3)(s + 6))
ω180 = 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) = 85/(s(s + 5)). Find the phase margin PM in degrees.

L(s) = 85/(s(s + 5))
PM = °

Answer key

  1. 1. n = −60 dB/dec
  2. 2. fc = 7480 Hz
  3. 3. φ = 11.36 °
  4. 4. BW = 795.8 Hz
  5. 5. ω180 = 4.243 rad/s
  6. 6. PM = 30.27 °

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