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)0.11101001000−80−60−40−20020ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 460/((s + 20)(s + 9)) in decibels, |G(0)| in dB.

G(s) = 460/((s + 20)(s + 9))
|G(0)| = dB
2.Easy
vin​C = 4.7 nFR = 4.7 kΩvout​

Find the corner (−3 dB) frequency fc of the RC high-pass filter shown, with R = 4.7 kΩ, C = 4.7 nF. Give it in Hz.

R = 4.7 kΩC = 4.7 nF
fc = Hz
3.Medium
|H| (dB)0.11101001000−60−40−2002040ω (rad/s)ω = 8

Find the exact magnitude |G(jω)| of G(s) = 2717/((s + 13)(s + 19)) at ω = 8 rad/s, in dB.

G(s) = 2717/((s + 13)(s + 19))ω = 8 rad/s
|G(jω)| = dB
4.Medium
|H| (dB)0.10.1111010100100−200204060ω (rad/s)φ (°)ω (rad/s)−135−90−450ω = 1

Find the phase ∠G(jω) of G(s) = 42(s + 3)/(s(s + 2)) at ω = 1 rad/s, in degrees.

G(s) = 42(s + 3)/(s(s + 2))ω = 1 rad/s
∠G(jω) = °
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 + 4)(s + 9)). Find the gain K that gives a gain margin of 10 dB.

L(s) = K/(s(s + 4)(s + 9))GM = 10 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) = 268/(s(s + 6)(s + 8)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 268/(s(s + 6)(s + 8))
ω180 = rad/s

Answer key

  1. 1. |G(0)| = 8.15 dB
  2. 2. fc = 7205 Hz
  3. 3. |G(jω)| = 18.72 dB
  4. 4. ∠G(jω) = −98.13 °
  5. 5. K = 148
  6. 6. ω180 = 6.928 rad/s

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