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)0.1110100−60−40−20020ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 100/((s + 5)(s + 9)) in decibels, |G(0)| in dB.

G(s) = 100/((s + 5)(s + 9))
|G(0)| = dB
2.Easy
|H| (dB)0.1110100100002040ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 1500(s + 4)/((s + 40)(s + 8)) in decibels, |G(0)| in dB.

G(s) = 1500(s + 4)/((s + 40)(s + 8))
|G(0)| = dB
3.Medium
vin​C = 22 nFR = 1 kΩvout​

The RC high-pass filter shown has R = 1 kΩ, C = 22 nF. A sinusoidal input of 1.4 kHz is applied. Find the gain |H| = |vout/vin| in dB.

R = 1 kΩC = 22 nFf = 1.4 kHz
|H| = dB
4.Medium
|H| (dB)0.10.1111010100100−40−2002040ω (rad/s)φ (°)ω (rad/s)−135−90−450ω = 5

Find the phase ∠G(jω) of G(s) = 3(s + 9)/(s(s + 4)) at ω = 5 rad/s, in degrees.

G(s) = 3(s + 9)/(s(s + 4))ω = 5 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 + 1)(s + 3)). Find the gain K that gives a gain margin of 4 dB.

L(s) = K/(s(s + 1)(s + 3))GM = 4 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) = K/(s(s + 6)(s + 8)). Find the gain K that gives a gain margin of 5 dB.

L(s) = K/(s(s + 6)(s + 8))GM = 5 dB
K =

Answer key

  1. 1. |G(0)| = 6.936 dB
  2. 2. |G(0)| = 25.46 dB
  3. 3. |H| = −14.43 dB
  4. 4. ∠G(jω) = −112.3 °
  5. 5. K = 7.571
  6. 6. K = 377.9

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