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​R = 47 ΩL = 1 mHvout​

Find the corner (−3 dB) frequency ωc of the RL high-pass filter shown, with R = 47 Ω, L = 1 mH. Give it in rad/s.

R = 47 ΩL = 1 mH
ωc = rad/s
2.Easy
vin​C = 2.2 nFR = 22 kΩvout​

Find the corner (−3 dB) frequency fc of the RC high-pass filter shown, with R = 22 kΩ, C = 2.2 nF. Give it in Hz.

R = 22 kΩC = 2.2 nF
fc = Hz
3.Medium
|H| (dB)0.10.111101010010010001000−40−20020406080ω (rad/s)φ (°)ω (rad/s)−135−90−450ω = 2

Find the phase ∠G(jω) of G(s) = 37(s + 17)/(s(s + 5)) at ω = 2 rad/s, in degrees.

G(s) = 37(s + 17)/(s(s + 5))ω = 2 rad/s
∠G(jω) = °
4.Medium
vin​C = 1 nFR = 10 kΩvout​

The RC high-pass filter shown has R = 10 kΩ, C = 1 nF. A sinusoidal input of 64 kHz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 10 kΩC = 1 nFf = 64 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) = 28/(s(s + 2)(s + 8)). Find the gain margin GM in dB.

L(s) = 28/(s(s + 2)(s + 8))
GM = dB
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) = K/(s(s + 3)(s + 5)). Find the gain K that gives a gain margin of 10 dB.

L(s) = K/(s(s + 3)(s + 5))GM = 10 dB
K =

Answer key

  1. 1. ωc = 47000 rad/s
  2. 2. fc = 3288 Hz
  3. 3. ∠G(jω) = −105.1 °
  4. 4. φ = 13.97 °
  5. 5. GM = 15.14 dB
  6. 6. K = 37.95

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