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 = 4.7 nFvout​

Find the corner (−3 dB) frequency fc of the RC low-pass filter shown, with R = 2.2 kΩ, C = 4.7 nF. Give it in Hz.

R = 2.2 kΩC = 4.7 nF
fc = Hz
2.Easy
|H| (dB)110100−40−2002040?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 500/(s(s + 10)). What is the slope n of the straight-line asymptote above 10 rad/s, in dB/decade?

G(s) = 500/(s(s + 10))
n = dB/dec
3.Medium
vin​L = 1 mHC = 0.22 µFR = 2 Ωvout​

In the series RLC band-pass filter shown the output is taken across R = 2 Ω, with L = 1 mH and C = 0.22 µF. Find the quality factor Q.

R = 2 ΩL = 1 mHC = 0.22 µF
Q =
4.Medium
vin​C = 1 nFR = 2.2 kΩvout​

The RC high-pass filter shown has R = 2.2 kΩ, C = 1 nF. A sinusoidal input of 220 kHz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 2.2 kΩC = 1 nFf = 220 kHz
φ = °
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 + 7)). Find the gain K that gives a gain margin of 6 dB.

L(s) = K/(s(s + 4)(s + 7))GM = 6 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) = 48/(s(s + 3)(s + 4)). Find the gain margin GM in dB.

L(s) = 48/(s(s + 3)(s + 4))
GM = dB

Answer key

  1. 1. fc = 15392 Hz
  2. 2. n = −40 dB/dec
  3. 3. Q = 33.71
  4. 4. φ = 18.2 °
  5. 5. K = 154.4
  6. 6. GM = 4.861 dB

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