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​C = 22 nFR = 22 kΩvout​

Find the corner (−3 dB) frequency ωc of the RC high-pass filter shown, with R = 22 kΩ, C = 22 nF. Give it in rad/s.

R = 22 kΩC = 22 nF
ωc = rad/s
2.Easy
vin​R = 4.7 kΩC = 4.7 nFvout​

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

R = 4.7 kΩC = 4.7 nF
fc = Hz
3.Medium
vin​L = 1 mHC = 0.22 µFR = 10 Ωvout​

In the series RLC band-pass filter shown the output is taken across R = 10 Ω, with L = 1 mH and C = 0.22 µF. Find the centre (resonant) frequency f0 in Hz.

R = 10 ΩL = 1 mHC = 0.22 µF
f0 = Hz
4.Medium
|H| (dB)0.010.11101001000−60−40−2002040ω (rad/s)ω = 0.5

Find the exact magnitude |G(jω)| of G(s) = 1836/((s + 6)(s + 17)) at ω = 0.5 rad/s, in dB.

G(s) = 1836/((s + 6)(s + 17))ω = 0.5 rad/s
|G(jω)| = dB
5.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) = 17.5/(s(s + 5)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 17.5/(s(s + 5))
ωc = rad/s
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) = 30/(s(s + 10)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 30/(s(s + 10))
ωc = rad/s

Answer key

  1. 1. ωc = 2066 rad/s
  2. 2. fc = 7205 Hz
  3. 3. f0 = 10730 Hz
  4. 4. |G(jω)| = 25.07 dB
  5. 5. ωc = 3.001 rad/s
  6. 6. ωc = 2.883 rad/s

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