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)0.1110100−40−2002040?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 1000/((s + 2)(s + 10)). What is the slope n of the straight-line asymptote above 10 rad/s, in dB/decade?

G(s) = 1000/((s + 2)(s + 10))
n = dB/dec
2.Easy
vin​L = 22 mHR = 10 Ωvout​

Find the corner (−3 dB) frequency fc of the RL low-pass filter shown, with R = 10 Ω, L = 22 mH. Give it in Hz.

R = 10 ΩL = 22 mH
fc = Hz
3.Medium
|H| (dB)0.10.111101010010010001000−40−20020406080ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ω = 10

Find the phase ∠G(jω) of G(s) = 25(s + 12)/(s(s + 2)) at ω = 10 rad/s, in degrees.

G(s) = 25(s + 12)/(s(s + 2))ω = 10 rad/s
∠G(jω) = °
4.Medium
vin​L = 5 mHC = 10 µFR = 2 Ωvout​

In the series RLC band-pass filter shown the output is taken across R = 2 Ω, with L = 5 mH and C = 10 µF. Find the −3 dB bandwidth BW in Hz.

R = 2 ΩL = 5 mHC = 10 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) = 168/(s(s + 5)(s + 7)). Find the gain margin GM in dB.

L(s) = 168/(s(s + 5)(s + 7))
GM = dB
6.Hard
|H| (dB)0.10.1111010100100−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​

A unity-feedback loop has the open-loop transfer function L(s) = 25/(s(s + 10)). Find the phase margin PM in degrees.

L(s) = 25/(s(s + 10))
PM = °

Answer key

  1. 1. n = −40 dB/dec
  2. 2. fc = 72.34 Hz
  3. 3. ∠G(jω) = −128.9 °
  4. 4. BW = 63.66 Hz
  5. 5. GM = 7.959 dB
  6. 6. PM = 76.35 °

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