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
|H| (dB)0.11101001000−60−40−2002040?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 2500/((s + 50)(s + 1)). What is the slope n of the straight-line asymptote above 50 rad/s, in dB/decade?

G(s) = 2500/((s + 50)(s + 1))
n = dB/dec
2.Easy
vin​C = 2.2 nFR = 2.2 kΩvout​

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

R = 2.2 kΩC = 2.2 nF
fc = Hz
3.Medium
vin​C = 22 nFR = 47 kΩvout​

The RC high-pass filter shown has R = 47 kΩ, C = 22 nF. A sinusoidal input of 77 Hz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 47 kΩC = 22 nFf = 77 Hz
φ = °
4.Medium
|H| (dB)0.10.1111010100100−200204060ω (rad/s)φ (°)ω (rad/s)−90−450ω = 4

Find the phase ∠G(jω) of G(s) = 40(s + 2)/(s(s + 7)) at ω = 4 rad/s, in degrees.

G(s) = 40(s + 2)/(s(s + 7))ω = 4 rad/s
∠G(jω) = °
5.Hard
|H| (dB)0.10.1111010100100−80−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​

A unity-feedback loop has the open-loop transfer function L(s) = 8.4/(s(s + 4)). Find the phase margin PM in degrees.

L(s) = 8.4/(s(s + 4))
PM = °
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) = 376/(s(s + 5)(s + 10)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 376/(s(s + 5)(s + 10))
ω180 = rad/s

Answer key

  1. 1. n = −40 dB/dec
  2. 2. fc = 32883 Hz
  3. 3. φ = 63.42 °
  4. 4. ∠G(jω) = −56.31 °
  5. 5. PM = 64.62 °
  6. 6. ω180 = 7.071 rad/s

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