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)0.11101001000−100−80−60−40−20020?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 250/(s(s + 50)(s + 5)). What is the slope n of the straight-line asymptote between 5 and 50 rad/s, in dB/decade?

G(s) = 250/(s(s + 50)(s + 5))
n = dB/dec
2.Easy
vin​C = 47 nFR = 1 kΩvout​

Find the corner (−3 dB) frequency ωc of the RC high-pass filter shown, with R = 1 kΩ, C = 47 nF. Give it in rad/s.

R = 1 kΩC = 47 nF
ωc = rad/s
3.Medium
vin​C = 10 nFR = 4.7 kΩvout​

The RC high-pass filter shown has R = 4.7 kΩ, C = 10 nF. A sinusoidal input of 850 Hz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 4.7 kΩC = 10 nFf = 850 Hz
φ = °
4.Medium
vin​L = 10 mHC = 0.22 µFR = 50 Ωvout​

In the series RLC band-pass filter shown the output is taken across R = 50 Ω, with L = 10 mH and C = 0.22 µF. Find the −3 dB bandwidth BW in Hz.

R = 50 ΩL = 10 mHC = 0.22 µF
BW = Hz
5.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) = 58/(s(s + 5)(s + 6)). Find the gain margin GM in dB.

L(s) = 58/(s(s + 5)(s + 6))
GM = dB
6.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) = 240/(s(s + 10)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 240/(s(s + 10))
ωc = rad/s

Answer key

  1. 1. n = −40 dB/dec
  2. 2. ωc = 21277 rad/s
  3. 3. φ = 75.91 °
  4. 4. BW = 795.8 Hz
  5. 5. GM = 15.1 dB
  6. 6. ωc = 13.97 rad/s

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