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)0.010.11101001000−40−20020406080?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 100000(s + 0.5)/(s(s + 100)(s + 10)). What is the slope n of the straight-line asymptote between 10 and 100 rad/s, in dB/decade?

G(s) = 100000(s + 0.5)/(s(s + 100)(s + 10))
n = dB/dec
2.Easy
|H| (dB)0.010.1110100100010000−120−100−80−60−40−200?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 100/((s + 200)(s + 0.5)). What is the slope n of the straight-line asymptote between 0.5 and 200 rad/s, in dB/decade?

G(s) = 100/((s + 200)(s + 0.5))
n = dB/dec
3.Medium
vin​C = 22 nFR = 2.2 kΩvout​

The RC high-pass filter shown has R = 2.2 kΩ, C = 22 nF. A sinusoidal input of 1.6 kHz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 2.2 kΩC = 22 nFf = 1.6 kHz
φ = °
4.Medium
|H| (dB)0.10.111101010010010001000−40−20020406080ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ω = 30

Find the phase ∠G(jω) of G(s) = 38(s + 20)/(s(s + 1)) at ω = 30 rad/s, in degrees.

G(s) = 38(s + 20)/(s(s + 1))ω = 30 rad/s
∠G(jω) = °
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 + 7)(s + 9)). Find the gain K that gives a gain margin of 5 dB.

L(s) = K/(s(s + 7)(s + 9))GM = 5 dB
K =
6.Hard
|H| (dB)0.10.1111010100100−80−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​ = ?

A unity-feedback loop has the open-loop transfer function L(s) = 4/(s(s + 1)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 4/(s(s + 1))
ωc = rad/s

Answer key

  1. 1. n = −20 dB/dec
  2. 2. n = −20 dB/dec
  3. 3. φ = 64.05 °
  4. 4. ∠G(jω) = −121.8 °
  5. 5. K = 566.8
  6. 6. ωc = 1.879 rad/s

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