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 = 10 Ωvout​

Find the corner (−3 dB) frequency fc of the RL low-pass filter shown, with R = 10 Ω, L = 2.2 mH. Give it in Hz.

R = 10 ΩL = 2.2 mH
fc = Hz
2.Easy
vin​R = 22 ΩL = 1 mHvout​

Find the corner (−3 dB) frequency fc of the RL high-pass filter shown, with R = 22 Ω, L = 1 mH. Give it in Hz.

R = 22 ΩL = 1 mH
fc = Hz
3.Medium
|H| (dB)0.11101001000−80−60−40−20020ω (rad/s)ω = 4

Find the exact magnitude |G(jω)| of G(s) = 945/((s + 7)(s + 15)) at ω = 4 rad/s, in dB.

G(s) = 945/((s + 7)(s + 15))ω = 4 rad/s
|G(jω)| = dB
4.Medium
vin​R = 1 kΩC = 22 nFvout​

The RC low-pass filter shown has R = 1 kΩ, C = 22 nF. A sinusoidal input of 3.6 kHz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 1 kΩC = 22 nFf = 3.6 kHz
φ = °
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) = K/(s(s + 2)(s + 7)). Find the gain K that gives a gain margin of 4 dB.

L(s) = K/(s(s + 2)(s + 7))GM = 4 dB
K =
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) = 40/(s(s + 2)). Find the phase margin PM in degrees.

L(s) = 40/(s(s + 2))
PM = °

Answer key

  1. 1. fc = 723.4 Hz
  2. 2. fc = 3501 Hz
  3. 3. |G(jω)| = 17.56 dB
  4. 4. φ = −26.46 °
  5. 5. K = 79.5
  6. 6. PM = 17.96 °

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