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​R = 100 ΩL = 10 mHvout​

Find the corner (−3 dB) frequency fc of the RL high-pass filter shown, with R = 100 Ω, L = 10 mH. Give it in Hz.

R = 100 ΩL = 10 mH
fc = Hz
2.Easy
|H| (dB)0.1110100−60−40−200204060?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 200/(s(s + 1)(s + 10)). What is the slope n of the straight-line asymptote below 1 rad/s, in dB/decade?

G(s) = 200/(s(s + 1)(s + 10))
n = dB/dec
3.Medium
vin​L = 5 mHC = 0.22 µFR = 100 Ωvout​

In the series RLC band-pass filter shown the output is taken across R = 100 Ω, with L = 5 mH and C = 0.22 µF. Find the centre (resonant) frequency f0 in Hz.

R = 100 ΩL = 5 mHC = 0.22 µF
f0 = Hz
4.Medium
|H| (dB)0.1110100−60−40−20020ω (rad/s)ω = 2

Find the exact magnitude |G(jω)| of G(s) = 72/((s + 3)(s + 8)) at ω = 2 rad/s, in dB.

G(s) = 72/((s + 3)(s + 8))ω = 2 rad/s
|G(jω)| = dB
5.Hard
|H| (dB)11101010010010001000−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​ = ?

A unity-feedback loop has the open-loop transfer function L(s) = 1240/(s(s + 20)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 1240/(s(s + 20))
ωc = 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) = 144/(s(s + 4)). Find the phase margin PM in degrees.

L(s) = 144/(s(s + 4))
PM = °

Answer key

  1. 1. fc = 1592 Hz
  2. 2. n = −20 dB/dec
  3. 3. f0 = 4799 Hz
  4. 4. |G(jω)| = 7.682 dB
  5. 5. ωc = 32.5 rad/s
  6. 6. PM = 18.92 °

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