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 = 2.2 nFR = 2.2 kΩvout​

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

R = 2.2 kΩC = 2.2 nF
ωc = rad/s
2.Easy
|H| (dB)0.1110100100010000−80−60−40−2002040?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 0.16(s + 500)/(s(s + 2)(s + 20)). What is the slope n of the straight-line asymptote above 500 rad/s, in dB/decade?

G(s) = 0.16(s + 500)/(s(s + 2)(s + 20))
n = dB/dec
3.Medium
|H| (dB)0.010.11101001000−60−40−2002040ω (rad/s)ω = 0.5

Find the exact magnitude |G(jω)| of G(s) = 1890/((s + 9)(s + 15)) at ω = 0.5 rad/s, in dB.

G(s) = 1890/((s + 9)(s + 15))ω = 0.5 rad/s
|G(jω)| = dB
4.Medium
vin​C = 10 nFR = 3.3 kΩvout​

The RC high-pass filter shown has R = 3.3 kΩ, C = 10 nF. A sinusoidal input of 19 kHz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 3.3 kΩC = 10 nFf = 19 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) = 6/(s(s + 1)(s + 3)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 6/(s(s + 1)(s + 3))
ω180 = rad/s
6.Hard
|H| (dB)0.10.111101010010010001000−60−40−200204060ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​ = ?

A unity-feedback loop has the open-loop transfer function L(s) = 160/(s(s + 5)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 160/(s(s + 5))
ωc = rad/s

Answer key

  1. 1. ωc = 206612 rad/s
  2. 2. n = −40 dB/dec
  3. 3. |G(jω)| = 22.9 dB
  4. 4. φ = 14.24 °
  5. 5. ω180 = 1.732 rad/s
  6. 6. ωc = 12.17 rad/s

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