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
|H| (dB)110100100010000−80−60−40−200?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 25000/((s + 50)(s + 500)). What is the slope n of the straight-line asymptote between 50 and 500 rad/s, in dB/decade?

G(s) = 25000/((s + 50)(s + 500))
n = dB/dec
2.Easy
vin​C = 47 nFR = 10 kΩvout​

Find the corner (−3 dB) frequency fc of the RC high-pass filter shown, with R = 10 kΩ, C = 47 nF. Give it in Hz.

R = 10 kΩC = 47 nF
fc = Hz
3.Medium
vin​R = 2.2 kΩC = 47 nFvout​

The RC low-pass filter shown has R = 2.2 kΩ, C = 47 nF. A sinusoidal input of 7.7 kHz is applied. Find the gain |H| = |vout/vin| in dB.

R = 2.2 kΩC = 47 nFf = 7.7 kHz
|H| = dB
4.Medium
vin​L = 5 mHC = 10 µFR = 1 Ωvout​

In the series RLC band-pass filter shown the output is taken across R = 1 Ω, with L = 5 mH and C = 10 µF. Find the quality factor Q.

R = 1 ΩL = 5 mHC = 10 µF
Q =
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 + 8)). Find the gain K that gives a gain margin of 3 dB.

L(s) = K/(s(s + 4)(s + 8))GM = 3 dB
K =
6.Hard
|H| (dB)11101010010010001000−80−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​ = ?

A unity-feedback loop has the open-loop transfer function L(s) = 760/(s(s + 20)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 760/(s(s + 20))
ωc = rad/s

Answer key

  1. 1. n = −20 dB/dec
  2. 2. fc = 338.6 Hz
  3. 3. |H| = −14.15 dB
  4. 4. Q = 22.36
  5. 5. K = 271.9
  6. 6. ωc = 24.2 rad/s

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