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​L = 22 mHR = 220 Ωvout​

Find the corner (−3 dB) frequency ωc of the RL low-pass filter shown, with R = 220 Ω, L = 22 mH. Give it in rad/s.

R = 220 ΩL = 22 mH
ωc = rad/s
2.Easy
vin​R = 47 kΩC = 4.7 nFvout​

Find the corner (−3 dB) frequency ωc of the RC low-pass filter shown, with R = 47 kΩ, C = 4.7 nF. Give it in rad/s.

R = 47 kΩC = 4.7 nF
ωc = rad/s
3.Medium
|H| (dB)0.11101001000−80−60−40−20020ω (rad/s)ω = 2

Find the exact magnitude |G(jω)| of G(s) = 165/((s + 5)(s + 11)) at ω = 2 rad/s, in dB.

G(s) = 165/((s + 5)(s + 11))ω = 2 rad/s
|G(jω)| = dB
4.Medium
vin​L = 2 mHC = 2.2 µFR = 10 Ωvout​

In the series RLC band-pass filter shown the output is taken across R = 10 Ω, with L = 2 mH and C = 2.2 µF. Find the −3 dB bandwidth BW in Hz.

R = 10 ΩL = 2 mHC = 2.2 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) = 78/(s(s + 1)(s + 10)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 78/(s(s + 1)(s + 10))
ω180 = rad/s
6.Hard
|H| (dB)0.10.1111010100100−60−40−200204060ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​ = ?

A unity-feedback loop has the open-loop transfer function L(s) = 26/(s(s + 2)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 26/(s(s + 2))
ωc = rad/s

Answer key

  1. 1. ωc = 10000 rad/s
  2. 2. ωc = 4527 rad/s
  3. 3. |G(jω)| = 8.757 dB
  4. 4. BW = 795.8 Hz
  5. 5. ω180 = 3.162 rad/s
  6. 6. ωc = 4.907 rad/s

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