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
vin​R = 100 ΩL = 1 mHvout​

Find the corner (−3 dB) frequency fc of the RL high-pass filter shown, with R = 100 Ω, L = 1 mH. Give it in Hz.

R = 100 ΩL = 1 mH
fc = Hz
2.Easy
|H| (dB)0.1110100−60−40−20020ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 37/((s + 2)(s + 5)) in decibels, |G(0)| in dB.

G(s) = 37/((s + 2)(s + 5))
|G(0)| = dB
3.Medium
vin​C = 100 nFR = 1 kΩvout​

The RC high-pass filter shown has R = 1 kΩ, C = 100 nF. A sinusoidal input of 800 Hz is applied. Find the gain |H| = |vout/vin| in dB.

R = 1 kΩC = 100 nFf = 800 Hz
|H| = dB
4.Medium
vin​L = 100 mHC = 10 µFR = 2 Ωvout​

In the series RLC band-pass filter shown the output is taken across R = 2 Ω, with L = 100 mH and C = 10 µF. Find the centre (resonant) frequency f0 in Hz.

R = 2 ΩL = 100 mHC = 10 µF
f0 = Hz
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 + 8)). Find the gain K that gives a gain margin of 15 dB.

L(s) = K/(s(s + 4)(s + 8))GM = 15 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) = 28/(s(s + 1)(s + 10)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 28/(s(s + 1)(s + 10))
ω180 = rad/s

Answer key

  1. 1. fc = 15915 Hz
  2. 2. |G(0)| = 11.36 dB
  3. 3. |H| = −6.953 dB
  4. 4. f0 = 159.2 Hz
  5. 5. K = 68.29
  6. 6. ω180 = 3.162 rad/s

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