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

Find the corner (−3 dB) frequency ω_c of the RL high-pass filter shown, with R = 10 Ω, L = 100 mH. Give it in rad/s.

R = 10 ΩL = 100 mH

ω_c = rad/s

2.Easy

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

G(s) = 0.5(s + 100)/(s(s + 0.5))

n = dB/dec

3.Medium

The RC high-pass filter shown has R = 3.3 kΩ, C = 2.2 nF. A sinusoidal input of 44 kHz is applied. Find the gain |H| = |v_out/v_in| in dB.

R = 3.3 kΩC = 2.2 nFf = 44 kHz

|H| = dB

4.Medium

The RC high-pass filter shown has R = 10 kΩ, C = 100 nF. A sinusoidal input of 480 Hz is applied. Find the gain |H| = |v_out/v_in| in dB.

R = 10 kΩC = 100 nFf = 480 Hz

|H| = dB

5.Hard

A unity-feedback loop has the open-loop transfer function L(s) = 76/(s(s + 8)). Find the phase margin PM in degrees.

L(s) = 76/(s(s + 8))

PM = °

6.Hard

A unity-feedback loop has the open-loop transfer function L(s) = 482/(s(s + 6)(s + 10)). Find the phase crossover frequency ω₁₈₀, where ∠L(jω) = −180°.

L(s) = 482/(s(s + 6)(s + 10))

ω₁₈₀ = rad/s

Answer key

1. ω_c = 100 rad/s
2. n = −20 dB/dec
3. |H| = −0.963 dB
4. |H| = −0.453 dB
5. PM = 48.4 °
6. ω₁₈₀ = 7.746 rad/s

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