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)110100100010000−80−60−40−20020?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 20000/((s + 20)(s + 500)). What is the slope n of the straight-line asymptote between 20 and 500 rad/s, in dB/decade?

G(s) = 20000/((s + 20)(s + 500))
n = dB/dec
2.Easy
vin​R = 220 ΩL = 10 mHvout​

Find the corner (−3 dB) frequency fc of the RL high-pass filter shown, with R = 220 Ω, L = 10 mH. Give it in Hz.

R = 220 ΩL = 10 mH
fc = Hz
3.Medium
vin​L = 2 mHC = 2.2 µFR = 5 Ωvout​

In the series RLC band-pass filter shown the output is taken across R = 5 Ω, with L = 2 mH and C = 2.2 µF. Find the centre (resonant) frequency f0 in Hz.

R = 5 ΩL = 2 mHC = 2.2 µF
f0 = Hz
4.Medium
vin​L = 50 mHC = 2.2 µFR = 10 Ωvout​

In the series RLC band-pass filter shown the output is taken across R = 10 Ω, with L = 50 mH and C = 2.2 µF. Find the centre (resonant) frequency f0 in Hz.

R = 10 ΩL = 50 mHC = 2.2 µF
f0 = Hz
5.Hard
|H| (dB)0.10.1111010100100−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​

A unity-feedback loop has the open-loop transfer function L(s) = 20/(s(s + 2)). Find the phase margin PM in degrees.

L(s) = 20/(s(s + 2))
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) = 42/(s(s + 4)(s + 6)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 42/(s(s + 4)(s + 6))
ω180 = rad/s

Answer key

  1. 1. n = −20 dB/dec
  2. 2. fc = 3501 Hz
  3. 3. f0 = 2399 Hz
  4. 4. f0 = 479.9 Hz
  5. 5. PM = 25.18 °
  6. 6. ω180 = 4.899 rad/s

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