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)0.11101001000−120−100−80−60−40−200ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 4/((s + 6)(s + 80)) in decibels, |G(0)| in dB.

G(s) = 4/((s + 6)(s + 80))
|G(0)| = dB
2.Easy
vin​L = 10 mHR = 47 Ωvout​

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

R = 47 ΩL = 10 mH
fc = Hz
3.Medium
|H| (dB)1101001000−60−40−20020ω (rad/s)ω = 10

Find the exact magnitude |G(jω)| of G(s) = 2340/((s + 13)(s + 20)) at ω = 10 rad/s, in dB.

G(s) = 2340/((s + 13)(s + 20))ω = 10 rad/s
|G(jω)| = dB
4.Medium
vin​C = 2.2 nFR = 1 kΩvout​

The RC high-pass filter shown has R = 1 kΩ, C = 2.2 nF. A sinusoidal input of 18 kHz is applied. Find the gain |H| = |vout/vin| in dB.

R = 1 kΩC = 2.2 nFf = 18 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 + 5)(s + 8)). Find the gain K that gives a gain margin of 5 dB.

L(s) = K/(s(s + 5)(s + 8))GM = 5 dB
K =
6.Hard
|H| (dB)0.10.1111010100100−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​

A unity-feedback loop has the open-loop transfer function L(s) = 19.5/(s(s + 5)). Find the phase margin PM in degrees.

L(s) = 19.5/(s(s + 5))
PM = °

Answer key

  1. 1. |G(0)| = −41.58 dB
  2. 2. fc = 748 Hz
  3. 3. |G(jω)| = 16.1 dB
  4. 4. |H| = −12.34 dB
  5. 5. K = 292.4
  6. 6. PM = 56.85 °

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