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)110100100010000−80−60−40−2002040?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 500000/(s(s + 20)(s + 500)). What is the slope n of the straight-line asymptote between 20 and 500 rad/s, in dB/decade?

G(s) = 500000/(s(s + 20)(s + 500))
n = dB/dec
2.Easy
|H| (dB)110100100002040ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 2200(s + 10)/((s + 80)(s + 90)) in decibels, |G(0)| in dB.

G(s) = 2200(s + 10)/((s + 80)(s + 90))
|G(0)| = dB
3.Medium
vin​R = 3.3 kΩC = 1 nFvout​

The RC low-pass filter shown has R = 3.3 kΩ, C = 1 nF. A sinusoidal input of 140 kHz is applied. Find the gain |H| = |vout/vin| in dB.

R = 3.3 kΩC = 1 nFf = 140 kHz
|H| = dB
4.Medium
vin​L = 20 mHC = 0.1 µFR = 10 Ωvout​

In the series RLC band-pass filter shown the output is taken across R = 10 Ω, with L = 20 mH and C = 0.1 µF. Find the quality factor Q.

R = 10 ΩL = 20 mHC = 0.1 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 + 3)(s + 8)). Find the gain K that gives a gain margin of 20 dB.

L(s) = K/(s(s + 3)(s + 8))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 + 7)). Find the gain K that gives a gain margin of 4 dB.

L(s) = K/(s(s + 1)(s + 7))GM = 4 dB
K =

Answer key

  1. 1. n = −40 dB/dec
  2. 2. |G(0)| = 9.702 dB
  3. 3. |H| = −9.743 dB
  4. 4. Q = 44.72
  5. 5. K = 26.4
  6. 6. K = 35.33

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