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 = 2.2 mHR = 100 Ωvout​

Find the corner (−3 dB) frequency ωc of the RL low-pass filter shown, with R = 100 Ω, L = 2.2 mH. Give it in rad/s.

R = 100 ΩL = 2.2 mH
ωc = rad/s
2.Easy
vin​C = 4.7 nFR = 3.3 kΩvout​

Find the corner (−3 dB) frequency fc of the RC high-pass filter shown, with R = 3.3 kΩ, C = 4.7 nF. Give it in Hz.

R = 3.3 kΩC = 4.7 nF
fc = Hz
3.Medium
|H| (dB)0.11101001000−80−60−40−20020ω (rad/s)ω = 1

Find the exact magnitude |G(jω)| of G(s) = 280/((s + 7)(s + 20)) at ω = 1 rad/s, in dB.

G(s) = 280/((s + 7)(s + 20))ω = 1 rad/s
|G(jω)| = dB
4.Medium
vin​C = 2.2 nFR = 47 kΩvout​

The RC high-pass filter shown has R = 47 kΩ, C = 2.2 nF. A sinusoidal input of 770 Hz is applied. Find the gain |H| = |vout/vin| in dB.

R = 47 kΩC = 2.2 nFf = 770 Hz
|H| = dB
5.Hard
|H| (dB)0.10.1111010100100−80−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​ = ?

A unity-feedback loop has the open-loop transfer function L(s) = 7.5/(s(s + 1)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 7.5/(s(s + 1))
ωc = rad/s
6.Hard
|H| (dB)0.10.1111010100100−80−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​

A unity-feedback loop has the open-loop transfer function L(s) = 3.6/(s(s + 1)). Find the phase margin PM in degrees.

L(s) = 3.6/(s(s + 1))
PM = °

Answer key

  1. 1. ωc = 45455 rad/s
  2. 2. fc = 10261 Hz
  3. 3. |G(jω)| = 5.922 dB
  4. 4. |H| = −6.986 dB
  5. 5. ωc = 2.649 rad/s
  6. 6. PM = 29.46 °

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