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​C = 22 nFR = 47 kΩvout​

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

R = 47 kΩC = 22 nF
fc = Hz
2.Easy
vin​R = 10 kΩC = 10 nFvout​

Find the corner (−3 dB) frequency ωc of the RC low-pass filter shown, with R = 10 kΩ, C = 10 nF. Give it in rad/s.

R = 10 kΩC = 10 nF
ωc = rad/s
3.Medium
|H| (dB)1101001000−80−60−40−20020ω (rad/s)ω = 30

Find the exact magnitude |G(jω)| of G(s) = 260/((s + 10)(s + 13)) at ω = 30 rad/s, in dB.

G(s) = 260/((s + 10)(s + 13))ω = 30 rad/s
|G(jω)| = dB
4.Medium
vin​L = 10 mHC = 1 µFR = 2 Ωvout​

In the series RLC band-pass filter shown the output is taken across R = 2 Ω, with L = 10 mH and C = 1 µF. Find the quality factor Q.

R = 2 ΩL = 10 mHC = 1 µF
Q =
5.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) = 28/(s(s + 10)). Find the phase margin PM in degrees.

L(s) = 28/(s(s + 10))
PM = °
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) = 120/(s(s + 6)(s + 8)). Find the gain margin GM in dB.

L(s) = 120/(s(s + 6)(s + 8))
GM = dB

Answer key

  1. 1. fc = 153.9 Hz
  2. 2. ωc = 10000 rad/s
  3. 3. |G(jω)| = −11.99 dB
  4. 4. Q = 50
  5. 5. PM = 74.87 °
  6. 6. GM = 14.96 dB

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