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 = 22 ΩL = 10 mHvout​

Find the corner (−3 dB) frequency fc of the RL high-pass filter shown, with R = 22 Ω, L = 10 mH. Give it in Hz.

R = 22 ΩL = 10 mH
fc = Hz
2.Easy
vin​C = 4.7 nFR = 47 kΩvout​

Find the corner (−3 dB) frequency fc of the RC high-pass filter shown, with R = 47 kΩ, C = 4.7 nF. Give it in Hz.

R = 47 kΩC = 4.7 nF
fc = Hz
3.Medium
|H| (dB)0.11101001000−80−60−40−2002040ω (rad/s)ω = 10

Find the exact magnitude |G(jω)| of G(s) = 578/((s + 2)(s + 17)) at ω = 10 rad/s, in dB.

G(s) = 578/((s + 2)(s + 17))ω = 10 rad/s
|G(jω)| = dB
4.Medium
vin​L = 10 mHC = 10 µFR = 5 Ωvout​

In the series RLC band-pass filter shown the output is taken across R = 5 Ω, with L = 10 mH and C = 10 µF. Find the centre (resonant) frequency f0 in Hz.

R = 5 ΩL = 10 mHC = 10 µF
f0 = Hz
5.Hard
|H| (dB)0.10.1111010100100−60−40−200204060ω (rad/s)φ (°)ω (rad/s)−270−180−900ω180​ = ?

A unity-feedback loop has the open-loop transfer function L(s) = 1078/(s(s + 9)(s + 10)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 1078/(s(s + 9)(s + 10))
ω180 = rad/s
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 + 5)(s + 8)). Find the gain K that gives a gain margin of 15 dB.

L(s) = K/(s(s + 5)(s + 8))GM = 15 dB
K =

Answer key

  1. 1. fc = 350.1 Hz
  2. 2. fc = 720.5 Hz
  3. 3. |G(jω)| = 9.169 dB
  4. 4. f0 = 503.3 Hz
  5. 5. ω180 = 9.487 rad/s
  6. 6. K = 92.47

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