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)0.11101001000−40−200ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 19(s + 16)/((s + 6)(s + 90)) in decibels, |G(0)| in dB.

G(s) = 19(s + 16)/((s + 6)(s + 90))
|G(0)| = dB
2.Easy
|H| (dB)0.1110100100010000020406080?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 20000(s + 1)/(s(s + 200)). What is the slope n of the straight-line asymptote above 200 rad/s, in dB/decade?

G(s) = 20000(s + 1)/(s(s + 200))
n = dB/dec
3.Medium
|H| (dB)0.10.1111010100100−200204060ω (rad/s)φ (°)ω (rad/s)−135−90−450ω = 8

Find the phase ∠G(jω) of G(s) = 37(s + 8)/(s(s + 7)) at ω = 8 rad/s, in degrees.

G(s) = 37(s + 8)/(s(s + 7))ω = 8 rad/s
∠G(jω) = °
4.Medium
vin​R = 100 ΩL = 4.7 mHvout​

The RL high-pass filter shown has R = 100 Ω, L = 4.7 mH. A sinusoidal input of 680 Hz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 100 ΩL = 4.7 mHf = 680 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) = 272/(s(s + 4)(s + 8)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 272/(s(s + 4)(s + 8))
ω180 = rad/s
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) = 54/(s(s + 6)(s + 7)). Find the gain margin GM in dB.

L(s) = 54/(s(s + 6)(s + 7))
GM = dB

Answer key

  1. 1. |G(0)| = −4.99 dB
  2. 2. n = −20 dB/dec
  3. 3. ∠G(jω) = −93.81 °
  4. 4. φ = 78.65 °
  5. 5. ω180 = 5.657 rad/s
  6. 6. GM = 20.1 dB

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