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)1101001000−80−60−40−200ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 480/((s + 50)(s + 90)) in decibels, |G(0)| in dB.

G(s) = 480/((s + 50)(s + 90))
|G(0)| = dB
2.Easy
vin​L = 10 mHR = 47 Ωvout​

Find the corner (−3 dB) frequency ωc of the RL low-pass filter shown, with R = 47 Ω, L = 10 mH. Give it in rad/s.

R = 47 ΩL = 10 mH
ωc = rad/s
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 22 kHz is applied. Find the gain |H| = |vout/vin| in dB.

R = 4.7 kΩC = 4.7 nFf = 22 kHz
|H| = dB
4.Medium
vin​R = 10 ΩL = 2.2 mHvout​

The RL high-pass filter shown has R = 10 Ω, L = 2.2 mH. A sinusoidal input of 2.9 kHz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 10 ΩL = 2.2 mHf = 2.9 kHz
φ = °
5.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) = 220/(s(s + 20)). Find the phase margin PM in degrees.

L(s) = 220/(s(s + 20))
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) = 314/(s(s + 4)(s + 10)). Find the gain margin GM in dB.

L(s) = 314/(s(s + 4)(s + 10))
GM = dB

Answer key

  1. 1. |G(0)| = −19.44 dB
  2. 2. ωc = 4700 rad/s
  3. 3. |H| = −10.14 dB
  4. 4. φ = 14.01 °
  5. 5. PM = 63.74 °
  6. 6. GM = 5.025 dB

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