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)0.1110100100002040ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 2600(s + 8)/((s + 60)(s + 80)) in decibels, |G(0)| in dB.

G(s) = 2600(s + 8)/((s + 60)(s + 80))
|G(0)| = dB
2.Easy
vin​C = 1 nFR = 22 kΩvout​

Find the corner (−3 dB) frequency fc of the RC high-pass filter shown, with R = 22 kΩ, C = 1 nF. Give it in Hz.

R = 22 kΩC = 1 nF
fc = Hz
3.Medium
|H| (dB)0.1110100−60−40−20020ω (rad/s)ω = 5

Find the exact magnitude |G(jω)| of G(s) = 20/((s + 1)(s + 5)) at ω = 5 rad/s, in dB.

G(s) = 20/((s + 1)(s + 5))ω = 5 rad/s
|G(jω)| = dB
4.Medium
vin​L = 100 mHC = 4.7 µFR = 10 Ωvout​

In the series RLC band-pass filter shown the output is taken across R = 10 Ω, with L = 100 mH and C = 4.7 µF. Find the quality factor Q.

R = 10 ΩL = 100 mHC = 4.7 µF
Q =
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) = 42/(s(s + 5)(s + 7)). Find the gain margin GM in dB.

L(s) = 42/(s(s + 5)(s + 7))
GM = dB
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) = 130/(s(s + 5)(s + 8)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 130/(s(s + 5)(s + 8))
ω180 = rad/s

Answer key

  1. 1. |G(0)| = 12.74 dB
  2. 2. fc = 7234 Hz
  3. 3. |G(jω)| = −5.119 dB
  4. 4. Q = 14.59
  5. 5. GM = 20 dB
  6. 6. ω180 = 6.325 rad/s

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