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 = 47 nFR = 22 kΩvout​

Find the corner (−3 dB) frequency ωc of the RC high-pass filter shown, with R = 22 kΩ, C = 47 nF. Give it in rad/s.

R = 22 kΩC = 47 nF
ωc = rad/s
2.Easy
vin​R = 1000 ΩL = 1 mHvout​

Find the corner (−3 dB) frequency fc of the RL high-pass filter shown, with R = 1000 Ω, L = 1 mH. Give it in Hz.

R = 1000 ΩL = 1 mH
fc = Hz
3.Medium
|H| (dB)0.10.1111010100100−2002040ω (rad/s)φ (°)ω (rad/s)−90−450ω = 3

Find the phase ∠G(jω) of G(s) = 34(s + 2)/(s(s + 9)) at ω = 3 rad/s, in degrees.

G(s) = 34(s + 2)/(s(s + 9))ω = 3 rad/s
∠G(jω) = °
4.Medium
vin​R = 1 kΩC = 100 nFvout​

The RC low-pass filter shown has R = 1 kΩ, C = 100 nF. A sinusoidal input of 8 kHz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 1 kΩC = 100 nFf = 8 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) = 74/(s(s + 5)(s + 7)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 74/(s(s + 5)(s + 7))
ω180 = rad/s
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 + 6)(s + 7)). Find the gain K that gives a gain margin of 4 dB.

L(s) = K/(s(s + 6)(s + 7))GM = 4 dB
K =

Answer key

  1. 1. ωc = 967.1 rad/s
  2. 2. fc = 159155 Hz
  3. 3. ∠G(jω) = −52.13 °
  4. 4. φ = −78.75 °
  5. 5. ω180 = 5.916 rad/s
  6. 6. K = 344.5

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