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)0.1110100−2002040ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 2500/((s + 4)(s + 7)) in decibels, |G(0)| in dB.

G(s) = 2500/((s + 4)(s + 7))
|G(0)| = dB
2.Easy
vin​R = 220 ΩL = 4.7 mHvout​

Find the corner (−3 dB) frequency ωc of the RL high-pass filter shown, with R = 220 Ω, L = 4.7 mH. Give it in rad/s.

R = 220 ΩL = 4.7 mH
ωc = rad/s
3.Medium
|H| (dB)0.010.010.10.111101010010010001000−40−20020406080ω (rad/s)φ (°)ω (rad/s)−135−90−450ω = 0.5

Find the phase ∠G(jω) of G(s) = 11(s + 18)/(s(s + 17)) at ω = 0.5 rad/s, in degrees.

G(s) = 11(s + 18)/(s(s + 17))ω = 0.5 rad/s
∠G(jω) = °
4.Medium
vin​L = 2 mHC = 2.2 µFR = 2 Ωvout​

In the series RLC band-pass filter shown the output is taken across R = 2 Ω, with L = 2 mH and C = 2.2 µF. Find the quality factor Q.

R = 2 ΩL = 2 mHC = 2.2 µF
Q =
5.Hard
|H| (dB)11101010010010001000−60−40−200204060ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​ = ?

A unity-feedback loop has the open-loop transfer function L(s) = 3500/(s(s + 20)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 3500/(s(s + 20))
ωc = rad/s
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) = 354/(s(s + 5)(s + 9)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 354/(s(s + 5)(s + 9))
ω180 = rad/s

Answer key

  1. 1. |G(0)| = 39.02 dB
  2. 2. ωc = 46809 rad/s
  3. 3. ∠G(jω) = −90.09 °
  4. 4. Q = 15.08
  5. 5. ωc = 57.5 rad/s
  6. 6. ω180 = 6.708 rad/s

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