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
vin​R = 470 ΩL = 100 mHvout​

Find the corner (−3 dB) frequency ωc of the RL high-pass filter shown, with R = 470 Ω, L = 100 mH. Give it in rad/s.

R = 470 ΩL = 100 mH
ωc = rad/s
2.Easy
|H| (dB)100100010000−100−80−60−40−200?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 5000/(s(s + 1000)). What is the slope n of the straight-line asymptote above 1000 rad/s, in dB/decade?

G(s) = 5000/(s(s + 1000))
n = dB/dec
3.Medium
vin​L = 20 mHC = 0.47 µFR = 100 Ωvout​

In the series RLC band-pass filter shown the output is taken across R = 100 Ω, with L = 20 mH and C = 0.47 µF. Find the quality factor Q.

R = 100 ΩL = 20 mHC = 0.47 µF
Q =
4.Medium
|H| (dB)0.10.111101010010010001000−40−200204060ω (rad/s)φ (°)ω (rad/s)−135−90−450ω = 8

Find the phase ∠G(jω) of G(s) = 47(s + 11)/(s(s + 9)) at ω = 8 rad/s, in degrees.

G(s) = 47(s + 11)/(s(s + 9))ω = 8 rad/s
∠G(jω) = °
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) = 128/(s(s + 4)(s + 5)). Find the gain margin GM in dB.

L(s) = 128/(s(s + 4)(s + 5))
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) = 13.2/(s(s + 4)). Find the phase margin PM in degrees.

L(s) = 13.2/(s(s + 4))
PM = °

Answer key

  1. 1. ωc = 4700 rad/s
  2. 2. n = −40 dB/dec
  3. 3. Q = 2.063
  4. 4. ∠G(jω) = −95.61 °
  5. 5. GM = 2.961 dB
  6. 6. PM = 55.72 °

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