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)0.1110100100002040?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 1250(s + 1)/((s + 5)(s + 50)). What is the slope n of the straight-line asymptote above 50 rad/s, in dB/decade?

G(s) = 1250(s + 1)/((s + 5)(s + 50))
n = dB/dec
2.Easy
|H| (dB)1101001000−100−80−60−40−200ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 41/((s + 20)(s + 30)) in decibels, |G(0)| in dB.

G(s) = 41/((s + 20)(s + 30))
|G(0)| = dB
3.Medium
|H| (dB)0.10.111101010010010001000−40−200204060ω (rad/s)φ (°)ω (rad/s)−135−90−450ω = 15

Find the phase ∠G(jω) of G(s) = 25(s + 11)/(s(s + 8)) at ω = 15 rad/s, in degrees.

G(s) = 25(s + 11)/(s(s + 8))ω = 15 rad/s
∠G(jω) = °
4.Medium
vin​L = 10 mHC = 1 µFR = 5 Ωvout​

In the series RLC band-pass filter shown the output is taken across R = 5 Ω, with L = 10 mH and C = 1 µF. Find the quality factor Q.

R = 5 ΩL = 10 mHC = 1 µF
Q =
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) = 272/(s(s + 4)(s + 8)). Find the gain margin GM in dB.

L(s) = 272/(s(s + 4)(s + 8))
GM = dB
6.Hard
|H| (dB)0.10.111101010010010001000−60−40−200204060ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​

A unity-feedback loop has the open-loop transfer function L(s) = 156/(s(s + 4)). Find the phase margin PM in degrees.

L(s) = 156/(s(s + 4))
PM = °

Answer key

  1. 1. n = −20 dB/dec
  2. 2. |G(0)| = −23.31 dB
  3. 3. ∠G(jω) = −98.18 °
  4. 4. Q = 20
  5. 5. GM = 2.995 dB
  6. 6. PM = 18.19 °

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