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)1101001000−80−60−40−200ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 700/((s + 30)(s + 40)) in decibels, |G(0)| in dB.

G(s) = 700/((s + 30)(s + 40))
|G(0)| = dB
2.Easy
|H| (dB)0.1110100−60−40−20020ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 90/((s + 7)(s + 8)) in decibels, |G(0)| in dB.

G(s) = 90/((s + 7)(s + 8))
|G(0)| = dB
3.Medium
vin​L = 1 mHC = 4.7 µFR = 2 Ωvout​

In the series RLC band-pass filter shown the output is taken across R = 2 Ω, with L = 1 mH and C = 4.7 µF. Find the centre (resonant) frequency f0 in Hz.

R = 2 ΩL = 1 mHC = 4.7 µF
f0 = Hz
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) = 14(s + 17)/(s(s + 12)) at ω = 8 rad/s, in degrees.

G(s) = 14(s + 17)/(s(s + 12))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) = 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)0.10.1111010100100−80−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−270−180−900ω180​ = ?

A unity-feedback loop has the open-loop transfer function L(s) = 46/(s(s + 4)(s + 9)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 46/(s(s + 4)(s + 9))
ω180 = rad/s

Answer key

  1. 1. |G(0)| = −4.682 dB
  2. 2. |G(0)| = 4.121 dB
  3. 3. f0 = 2322 Hz
  4. 4. ∠G(jω) = −98.49 °
  5. 5. GM = 2.995 dB
  6. 6. ω180 = 6 rad/s

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