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 = 2.2 kΩC = 47 nFvout​

Find the corner (−3 dB) frequency ωc of the RC low-pass filter shown, with R = 2.2 kΩ, C = 47 nF. Give it in rad/s.

R = 2.2 kΩC = 47 nF
ωc = rad/s
2.Easy
|H| (dB)0.111010010000204060ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 3800(s + 8)/((s + 5)(s + 60)) in decibels, |G(0)| in dB.

G(s) = 3800(s + 8)/((s + 5)(s + 60))
|G(0)| = dB
3.Medium
vin​L = 4.7 mHR = 1000 Ωvout​

The RL low-pass filter shown has R = 1000 Ω, L = 4.7 mH. A sinusoidal input of 340 kHz is applied. Find the gain |H| = |vout/vin| in dB.

R = 1000 ΩL = 4.7 mHf = 340 kHz
|H| = dB
4.Medium
|H| (dB)0.11101001000−60−40−2002040ω (rad/s)ω = 8

Find the exact magnitude |G(jω)| of G(s) = 5415/((s + 15)(s + 19)) at ω = 8 rad/s, in dB.

G(s) = 5415/((s + 15)(s + 19))ω = 8 rad/s
|G(jω)| = dB
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 + 4)(s + 10)). Find the gain K that gives a gain margin of 20 dB.

L(s) = K/(s(s + 4)(s + 10))GM = 20 dB
K =
6.Hard
|H| (dB)0.10.1111010100100−60−40−200204060ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​

A unity-feedback loop has the open-loop transfer function L(s) = 56/(s(s + 4)). Find the phase margin PM in degrees.

L(s) = 56/(s(s + 4))
PM = °

Answer key

  1. 1. ωc = 9671 rad/s
  2. 2. |G(0)| = 40.12 dB
  3. 3. |H| = −20.08 dB
  4. 4. |G(jω)| = 23.78 dB
  5. 5. K = 56
  6. 6. PM = 29.85 °

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