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 = 4.7 nFR = 2.2 kΩvout​

Find the corner (−3 dB) frequency fc of the RC high-pass filter shown, with R = 2.2 kΩ, C = 4.7 nF. Give it in Hz.

R = 2.2 kΩC = 4.7 nF
fc = Hz
2.Easy
vin​R = 22 kΩC = 1 nFvout​

Find the corner (−3 dB) frequency ωc of the RC low-pass filter shown, with R = 22 kΩ, C = 1 nF. Give it in rad/s.

R = 22 kΩC = 1 nF
ωc = rad/s
3.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 3.1 kHz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 47 kΩC = 2.2 nFf = 3.1 kHz
φ = °
4.Medium
|H| (dB)11101010010010001000−40−2002040ω (rad/s)φ (°)ω (rad/s)−135−90−450ω = 20

Find the phase ∠G(jω) of G(s) = 43(s + 17)/(s(s + 16)) at ω = 20 rad/s, in degrees.

G(s) = 43(s + 17)/(s(s + 16))ω = 20 rad/s
∠G(jω) = °
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 + 8)). Find the gain K that gives a gain margin of 15 dB.

L(s) = K/(s(s + 2)(s + 8))GM = 15 dB
K =
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 + 5)(s + 8)). Find the gain K that gives a gain margin of 5 dB.

L(s) = K/(s(s + 5)(s + 8))GM = 5 dB
K =

Answer key

  1. 1. fc = 15392 Hz
  2. 2. ωc = 45455 rad/s
  3. 3. φ = 26.41 °
  4. 4. ∠G(jω) = −91.7 °
  5. 5. K = 28.45
  6. 6. K = 292.4

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