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 = 10 ΩL = 22 mHvout​

Find the corner (−3 dB) frequency fc of the RL high-pass filter shown, with R = 10 Ω, L = 22 mH. Give it in Hz.

R = 10 ΩL = 22 mH
fc = Hz
2.Easy
|H| (dB)0.1110100−40−20020ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 10(s + 2)/((s + 3)(s + 5)) in decibels, |G(0)| in dB.

G(s) = 10(s + 2)/((s + 3)(s + 5))
|G(0)| = dB
3.Medium
vin​C = 4.7 nFR = 2.2 kΩvout​

The RC high-pass filter shown has R = 2.2 kΩ, C = 4.7 nF. A sinusoidal input of 3.8 kHz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 2.2 kΩC = 4.7 nFf = 3.8 kHz
φ = °
4.Medium
vin​L = 100 mHC = 0.47 µFR = 100 Ωvout​

In the series RLC band-pass filter shown the output is taken across R = 100 Ω, with L = 100 mH and C = 0.47 µF. Find the quality factor Q.

R = 100 ΩL = 100 mHC = 0.47 µF
Q =
5.Hard
|H| (dB)0.10.1111010100100−40−200204060ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​

A unity-feedback loop has the open-loop transfer function L(s) = 140/(s(s + 10)). Find the phase margin PM in degrees.

L(s) = 140/(s(s + 10))
PM = °
6.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) = 1900/(s(s + 20)). Find the phase margin PM in degrees.

L(s) = 1900/(s(s + 20))
PM = °

Answer key

  1. 1. fc = 72.34 Hz
  2. 2. |G(0)| = 2.499 dB
  3. 3. φ = 76.13 °
  4. 4. Q = 4.613
  5. 5. PM = 45.19 °
  6. 6. PM = 25.81 °

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