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 = 4.7 nFR = 2.2 kΩvout​

Find the corner (−3 dB) frequency fc of the RC high-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)0.1110100100010000−60−40−200204060?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 800000(s + 5)/(s(s + 1000)(s + 200)). What is the slope n of the straight-line asymptote between 200 and 1000 rad/s, in dB/decade?

G(s) = 800000(s + 5)/(s(s + 1000)(s + 200))
n = dB/dec
3.Medium
|H| (dB)0.10.1111010100100−200204060ω (rad/s)φ (°)ω (rad/s)−90−450ω = 10

Find the phase ∠G(jω) of G(s) = 16(s + 7)/(s(s + 8)) at ω = 10 rad/s, in degrees.

G(s) = 16(s + 7)/(s(s + 8))ω = 10 rad/s
∠G(jω) = °
4.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 380 Hz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 2.2 kΩC = 47 nFf = 380 Hz
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 + 5)). Find the gain K that gives a gain margin of 5 dB.

L(s) = K/(s(s + 4)(s + 5))GM = 5 dB
K =
6.Hard
|H| (dB)0.10.1111010100100−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​

A unity-feedback loop has the open-loop transfer function L(s) = 15/(s(s + 5)). Find the phase margin PM in degrees.

L(s) = 15/(s(s + 5))
PM = °

Answer key

  1. 1. fc = 15392 Hz
  2. 2. n = −20 dB/dec
  3. 3. ∠G(jω) = −86.33 °
  4. 4. φ = −13.87 °
  5. 5. K = 101.2
  6. 6. PM = 62.07 °

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