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 = 47 ΩL = 22 mHvout​

Find the corner (−3 dB) frequency fc of the RL high-pass filter shown, with R = 47 Ω, L = 22 mH. Give it in Hz.

R = 47 ΩL = 22 mH
fc = Hz
2.Easy
vin​R = 47 kΩC = 4.7 nFvout​

Find the corner (−3 dB) frequency ωc of the RC low-pass filter shown, with R = 47 kΩ, C = 4.7 nF. Give it in rad/s.

R = 47 kΩC = 4.7 nF
ωc = rad/s
3.Medium
|H| (dB)0.010.11101001000−60−40−2002040ω (rad/s)ω = 0.5

Find the exact magnitude |G(jω)| of G(s) = 1596/((s + 7)(s + 12)) at ω = 0.5 rad/s, in dB.

G(s) = 1596/((s + 7)(s + 12))ω = 0.5 rad/s
|G(jω)| = dB
4.Medium
|H| (dB)0.10.111101010010010001000−40−20020406080ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ω = 30

Find the phase ∠G(jω) of G(s) = 34(s + 14)/(s(s + 1)) at ω = 30 rad/s, in degrees.

G(s) = 34(s + 14)/(s(s + 1))ω = 30 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 + 6)(s + 7)). Find the gain K that gives a gain margin of 20 dB.

L(s) = K/(s(s + 6)(s + 7))GM = 20 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 + 1)(s + 6)). Find the gain K that gives a gain margin of 10 dB.

L(s) = K/(s(s + 1)(s + 6))GM = 10 dB
K =

Answer key

  1. 1. fc = 340 Hz
  2. 2. ωc = 4527 rad/s
  3. 3. |G(jω)| = 25.55 dB
  4. 4. ∠G(jω) = −113.1 °
  5. 5. K = 54.6
  6. 6. K = 13.28

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