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)0.1110100100010000−40−2002040?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 1000(s + 20)/((s + 1)(s + 1000)). What is the slope n of the straight-line asymptote above 1000 rad/s, in dB/decade?

G(s) = 1000(s + 20)/((s + 1)(s + 1000))
n = dB/dec
2.Easy
|H| (dB)0.1110100100010000−100−80−60−40−20020?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 0.04(s + 1000)/((s + 1)(s + 20)). What is the slope n of the straight-line asymptote between 20 and 1000 rad/s, in dB/decade?

G(s) = 0.04(s + 1000)/((s + 1)(s + 20))
n = dB/dec
3.Medium
|H| (dB)0.10.111101010010010001000−60−40−200204060ω (rad/s)φ (°)ω (rad/s)−135−90−450ω = 4

Find the phase ∠G(jω) of G(s) = 8(s + 16)/(s(s + 11)) at ω = 4 rad/s, in degrees.

G(s) = 8(s + 16)/(s(s + 11))ω = 4 rad/s
∠G(jω) = °
4.Medium
vin​C = 4.7 nFR = 3.3 kΩvout​

The RC high-pass filter shown has R = 3.3 kΩ, C = 4.7 nF. A sinusoidal input of 2.1 kHz is applied. Find the gain |H| = |vout/vin| in dB.

R = 3.3 kΩC = 4.7 nFf = 2.1 kHz
|H| = dB
5.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) = 7.2/(s(s + 2)). Find the phase margin PM in degrees.

L(s) = 7.2/(s(s + 2))
PM = °
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) = 190/(s(s + 4)(s + 6)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 190/(s(s + 4)(s + 6))
ω180 = rad/s

Answer key

  1. 1. n = −20 dB/dec
  2. 2. n = −40 dB/dec
  3. 3. ∠G(jω) = −95.95 °
  4. 4. |H| = −13.96 dB
  5. 5. PM = 40.53 °
  6. 6. ω180 = 4.899 rad/s

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