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)1101001000−40−20020ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 80(s + 18)/((s + 40)(s + 60)) in decibels, |G(0)| in dB.

G(s) = 80(s + 18)/((s + 40)(s + 60))
|G(0)| = dB
2.Easy
vin​C = 47 nFR = 47 kΩvout​

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

R = 47 kΩC = 47 nF
fc = Hz
3.Medium
vin​L = 100 mHC = 2.2 µFR = 5 Ωvout​

In the series RLC band-pass filter shown the output is taken across R = 5 Ω, with L = 100 mH and C = 2.2 µF. Find the quality factor Q.

R = 5 ΩL = 100 mHC = 2.2 µF
Q =
4.Medium
vin​R = 3.3 kΩC = 22 nFvout​

The RC low-pass filter shown has R = 3.3 kΩ, C = 22 nF. A sinusoidal input of 4.4 kHz is applied. Find the gain |H| = |vout/vin| in dB.

R = 3.3 kΩC = 22 nFf = 4.4 kHz
|H| = dB
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) = K/(s(s + 1)(s + 2)). Find the gain K that gives a gain margin of 3 dB.

L(s) = K/(s(s + 1)(s + 2))GM = 3 dB
K =
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) = 50/(s(s + 2)(s + 8)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 50/(s(s + 2)(s + 8))
ω180 = rad/s

Answer key

  1. 1. |G(0)| = −4.437 dB
  2. 2. fc = 72.05 Hz
  3. 3. Q = 42.64
  4. 4. |H| = −7.014 dB
  5. 5. K = 4.248
  6. 6. ω180 = 4 rad/s

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