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​L = 10 mHR = 1000 Ωvout​

Find the corner (−3 dB) frequency ωc of the RL low-pass filter shown, with R = 1000 Ω, L = 10 mH. Give it in rad/s.

R = 1000 ΩL = 10 mH
ωc = rad/s
2.Easy
|H| (dB)101001000−60−40−20020?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 2000/(s(s + 100)). What is the slope n of the straight-line asymptote above 100 rad/s, in dB/decade?

G(s) = 2000/(s(s + 100))
n = dB/dec
3.Medium
vin​R = 4.7 kΩC = 4.7 nFvout​

The RC low-pass filter shown has R = 4.7 kΩ, C = 4.7 nF. A sinusoidal input of 14 kHz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 4.7 kΩC = 4.7 nFf = 14 kHz
φ = °
4.Medium
|H| (dB)0.010.11101001000−60−40−2002040ω (rad/s)ω = 0.5

Find the exact magnitude |G(jω)| of G(s) = 1470/((s + 7)(s + 14)) at ω = 0.5 rad/s, in dB.

G(s) = 1470/((s + 7)(s + 14))ω = 0.5 rad/s
|G(jω)| = dB
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) = 16/(s(s + 4)). Find the phase margin PM in degrees.

L(s) = 16/(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) = K/(s(s + 6)(s + 8)). Find the gain K that gives a gain margin of 6 dB.

L(s) = K/(s(s + 6)(s + 8))GM = 6 dB
K =

Answer key

  1. 1. ωc = 100000 rad/s
  2. 2. n = −40 dB/dec
  3. 3. φ = −62.77 °
  4. 4. |G(jω)| = 23.49 dB
  5. 5. PM = 51.83 °
  6. 6. K = 336.8

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