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 = 1 kΩC = 4.7 nFvout​

Find the corner (−3 dB) frequency fc of the RC low-pass filter shown, with R = 1 kΩ, C = 4.7 nF. Give it in Hz.

R = 1 kΩC = 4.7 nF
fc = Hz
2.Easy
vin​R = 10 kΩC = 47 nFvout​

Find the corner (−3 dB) frequency ωc of the RC low-pass filter shown, with R = 10 kΩ, C = 47 nF. Give it in rad/s.

R = 10 kΩC = 47 nF
ωc = rad/s
3.Medium
vin​R = 47 kΩC = 22 nFvout​

The RC low-pass filter shown has R = 47 kΩ, C = 22 nF. A sinusoidal input of 460 Hz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 47 kΩC = 22 nFf = 460 Hz
φ = °
4.Medium
vin​R = 47 kΩC = 4.7 nFvout​

The RC low-pass filter shown has R = 47 kΩ, C = 4.7 nF. A sinusoidal input of 140 Hz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 47 kΩC = 4.7 nFf = 140 Hz
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 + 3)(s + 6)). Find the gain K that gives a gain margin of 2 dB.

L(s) = K/(s(s + 3)(s + 6))GM = 2 dB
K =
6.Hard
|H| (dB)0.10.111101010010010001000−80−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​

A unity-feedback loop has the open-loop transfer function L(s) = 110/(s(s + 20)). Find the phase margin PM in degrees.

L(s) = 110/(s(s + 20))
PM = °

Answer key

  1. 1. fc = 33863 Hz
  2. 2. ωc = 2128 rad/s
  3. 3. φ = −71.5 °
  4. 4. φ = −11 °
  5. 5. K = 128.7
  6. 6. PM = 75.12 °

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