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 low-frequency (DC) gain of G(s) = 3100(s + 15)/((s + 1)(s + 80)) in decibels, |G(0)| in dB.

G(s) = 3100(s + 15)/((s + 1)(s + 80))

|G(0)| = dB

2.Easy

Find the corner (−3 dB) frequency ω_c of the RC low-pass filter shown, with R = 4.7 kΩ, C = 47 nF. Give it in rad/s.

R = 4.7 kΩC = 47 nF

ω_c = rad/s

3.Medium

The RC high-pass filter shown has R = 10 kΩ, C = 22 nF. A sinusoidal input of 2.9 kHz is applied. Find the phase shift φ of v_out relative to v_in, in degrees.

R = 10 kΩC = 22 nFf = 2.9 kHz

φ = °

4.Medium

The RC low-pass filter shown has R = 10 kΩ, C = 100 nF. A sinusoidal input of 80 Hz is applied. Find the phase shift φ of v_out relative to v_in, in degrees.

R = 10 kΩC = 100 nFf = 80 Hz

φ = °

5.Hard

A unity-feedback loop has the open-loop transfer function L(s) = 35/(s(s + 2)). Find the gain crossover frequency ω_c, where |L(jω)| = 1.

L(s) = 35/(s(s + 2))

ω_c = rad/s

6.Hard

A unity-feedback loop has the open-loop transfer function L(s) = 10/(s(s + 1)(s + 3)). Find the phase crossover frequency ω₁₈₀, where ∠L(jω) = −180°.

L(s) = 10/(s(s + 1)(s + 3))

ω₁₈₀ = rad/s

Answer key

1. |G(0)| = 55.29 dB
2. ω_c = 4527 rad/s
3. φ = 14.01 °
4. φ = −26.69 °
5. ω_c = 5.75 rad/s
6. ω₁₈₀ = 1.732 rad/s

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