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 = 4.7 kΩC = 10 nFvout​

Find the corner (−3 dB) frequency fc of the RC low-pass filter shown, with R = 4.7 kΩ, C = 10 nF. Give it in Hz.

R = 4.7 kΩC = 10 nF
fc = Hz
2.Easy
|H| (dB)0.1110100−80−60−40−2002040?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 4/(s(s + 2)). What is the slope n of the straight-line asymptote below 2 rad/s, in dB/decade?

G(s) = 4/(s(s + 2))
n = dB/dec
3.Medium
|H| (dB)0.10.111101010010010001000−40−200204060ω (rad/s)φ (°)ω (rad/s)−135−90−450ω = 2

Find the phase ∠G(jω) of G(s) = 45(s + 16)/(s(s + 11)) at ω = 2 rad/s, in degrees.

G(s) = 45(s + 16)/(s(s + 11))ω = 2 rad/s
∠G(jω) = °
4.Medium
vin​R = 47 kΩC = 47 nFvout​

The RC low-pass filter shown has R = 47 kΩ, C = 47 nF. A sinusoidal input of 220 Hz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 47 kΩC = 47 nFf = 220 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 + 6)(s + 9)). Find the gain K that gives a gain margin of 6 dB.

L(s) = K/(s(s + 6)(s + 9))GM = 6 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) = 700/(s(s + 20)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 700/(s(s + 20))
ωc = rad/s

Answer key

  1. 1. fc = 3386 Hz
  2. 2. n = −20 dB/dec
  3. 3. ∠G(jω) = −93.18 °
  4. 4. φ = −71.87 °
  5. 5. K = 406
  6. 6. ωc = 22.98 rad/s

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