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 = 22 kΩC = 10 nFvout​

Find the corner (−3 dB) frequency ωc of the RC low-pass filter shown, with R = 22 kΩ, C = 10 nF. Give it in rad/s.

R = 22 kΩC = 10 nF
ωc = rad/s
2.Easy
|H| (dB)0.1110100100010000−100−80−60−40−20020?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 0.5(s + 200)/(s(s + 2)(s + 50)). What is the slope n of the straight-line asymptote between 50 and 200 rad/s, in dB/decade?

G(s) = 0.5(s + 200)/(s(s + 2)(s + 50))
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
vin​R = 1 kΩC = 100 nFvout​

The RC low-pass filter shown has R = 1 kΩ, C = 100 nF. A sinusoidal input of 6.4 kHz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 1 kΩC = 100 nFf = 6.4 kHz
φ = °
5.Hard
|H| (dB)0.10.1111010100100−100−80−60−40−20020ω (rad/s)φ (°)ω (rad/s)−270−180−900ω180​

A unity-feedback loop has the open-loop transfer function L(s) = K/(s(s + 1)(s + 2)). Find the gain K that gives a gain margin of 15 dB.

L(s) = K/(s(s + 1)(s + 2))GM = 15 dB
K =
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) = 224/(s(s + 4)). Find the phase margin PM in degrees.

L(s) = 224/(s(s + 4))
PM = °

Answer key

  1. 1. ωc = 4545 rad/s
  2. 2. n = −60 dB/dec
  3. 3. f0 = 4799 Hz
  4. 4. φ = −76.03 °
  5. 5. K = 1.067
  6. 6. PM = 15.22 °

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