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​L = 47 mHR = 22 Ωvout​

Find the corner (−3 dB) frequency ωc of the RL low-pass filter shown, with R = 22 Ω, L = 47 mH. Give it in rad/s.

R = 22 ΩL = 47 mH
ωc = rad/s
2.Easy
vin​C = 47 nFR = 22 kΩvout​

Find the corner (−3 dB) frequency fc of the RC high-pass filter shown, with R = 22 kΩ, C = 47 nF. Give it in Hz.

R = 22 kΩC = 47 nF
fc = Hz
3.Medium
vin​L = 10 mHC = 1 µFR = 10 Ωvout​

In the series RLC band-pass filter shown the output is taken across R = 10 Ω, with L = 10 mH and C = 1 µF. Find the −3 dB bandwidth BW in Hz.

R = 10 ΩL = 10 mHC = 1 µF
BW = Hz
4.Medium
|H| (dB)0.10.111101010010010001000−40−20020406080ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ω = 10

Find the phase ∠G(jω) of G(s) = 35(s + 14)/(s(s + 1)) at ω = 10 rad/s, in degrees.

G(s) = 35(s + 14)/(s(s + 1))ω = 10 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) = 96/(s(s + 6)(s + 10)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 96/(s(s + 6)(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 + 2)(s + 8)). Find the gain K that gives a gain margin of 15 dB.

L(s) = K/(s(s + 2)(s + 8))GM = 15 dB
K =

Answer key

  1. 1. ωc = 468.1 rad/s
  2. 2. fc = 153.9 Hz
  3. 3. BW = 159.2 Hz
  4. 4. ∠G(jω) = −138.8 °
  5. 5. ω180 = 7.746 rad/s
  6. 6. K = 28.45

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