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 = 47 nFR = 22 kΩvout​

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

R = 22 kΩC = 47 nF
ωc = rad/s
2.Easy
|H| (dB)0.010.11101001000−2002040?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 250(s + 10)/((s + 0.5)(s + 100)). What is the slope n of the straight-line asymptote between 0.5 and 10 rad/s, in dB/decade?

G(s) = 250(s + 10)/((s + 0.5)(s + 100))
n = dB/dec
3.Medium
|H| (dB)0.11101001000−60−40−2002040ω (rad/s)ω = 5

Find the exact magnitude |G(jω)| of G(s) = 4320/((s + 18)(s + 20)) at ω = 5 rad/s, in dB.

G(s) = 4320/((s + 18)(s + 20))ω = 5 rad/s
|G(jω)| = dB
4.Medium
vin​L = 100 mHC = 4.7 µFR = 5 Ωvout​

In the series RLC band-pass filter shown the output is taken across R = 5 Ω, with L = 100 mH and C = 4.7 µF. Find the centre (resonant) frequency f0 in Hz.

R = 5 ΩL = 100 mHC = 4.7 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) = 946/(s(s + 7)(s + 10)). Find the gain margin GM in dB.

L(s) = 946/(s(s + 7)(s + 10))
GM = dB
6.Hard
|H| (dB)0.10.1111010100100−80−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​

A unity-feedback loop has the open-loop transfer function L(s) = 2/(s(s + 1)). Find the phase margin PM in degrees.

L(s) = 2/(s(s + 1))
PM = °

Answer key

  1. 1. ωc = 967.1 rad/s
  2. 2. n = −20 dB/dec
  3. 3. |G(jω)| = 21 dB
  4. 4. f0 = 232.2 Hz
  5. 5. GM = 1.993 dB
  6. 6. PM = 38.67 °

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