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 = 100 nFR = 22 kΩvout​

Find the corner (−3 dB) frequency ωc of the RC high-pass filter shown, with R = 22 kΩ, C = 100 nF. Give it in rad/s.

R = 22 kΩC = 100 nF
ωc = rad/s
2.Easy
|H| (dB)10100100010000−2002040?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 2 × 10⁷/((s + 1000)(s + 200)). What is the slope n of the straight-line asymptote above 1000 rad/s, in dB/decade?

G(s) = 2 × 10⁷/((s + 1000)(s + 200))
n = dB/dec
3.Medium
|H| (dB)0.10.111101010010010001000−40−20020406080ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ω = 4

Find the phase ∠G(jω) of G(s) = 24(s + 12)/(s(s + 2)) at ω = 4 rad/s, in degrees.

G(s) = 24(s + 12)/(s(s + 2))ω = 4 rad/s
∠G(jω) = °
4.Medium
vin​L = 100 mHC = 0.1 µFR = 20 Ωvout​

In the series RLC band-pass filter shown the output is taken across R = 20 Ω, with L = 100 mH and C = 0.1 µF. Find the quality factor Q.

R = 20 ΩL = 100 mHC = 0.1 µF
Q =
5.Hard
|H| (dB)11101010010010001000−80−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​

A unity-feedback loop has the open-loop transfer function L(s) = 300/(s(s + 20)). Find the phase margin PM in degrees.

L(s) = 300/(s(s + 20))
PM = °
6.Hard
|H| (dB)0.10.1111010100100−60−40−200204060ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​

A unity-feedback loop has the open-loop transfer function L(s) = 96/(s(s + 8)). Find the phase margin PM in degrees.

L(s) = 96/(s(s + 8))
PM = °

Answer key

  1. 1. ωc = 454.5 rad/s
  2. 2. n = −40 dB/dec
  3. 3. ∠G(jω) = −135 °
  4. 4. Q = 50
  5. 5. PM = 57.64 °
  6. 6. PM = 43.88 °

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