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 RC high-pass filter shown, with R = 3.3 kΩ, C = 47 nF. Give it in rad/s.

R = 3.3 kΩC = 47 nF

ω_c = rad/s

2.Easy

Find the low-frequency (DC) gain of G(s) = 2300/((s + 40)(s + 7)) in decibels, |G(0)| in dB.

G(s) = 2300/((s + 40)(s + 7))

|G(0)| = dB

3.Medium

The RC low-pass filter shown has R = 22 kΩ, C = 100 nF. A sinusoidal input of 140 Hz is applied. Find the gain |H| = |v_out/v_in| in dB.

R = 22 kΩC = 100 nFf = 140 Hz

|H| = dB

4.Medium

The RC low-pass filter shown has R = 4.7 kΩ, C = 4.7 nF. A sinusoidal input of 1.8 kHz is applied. Find the phase shift φ of v_out relative to v_in, in degrees.

R = 4.7 kΩC = 4.7 nFf = 1.8 kHz

φ = °

5.Hard

A unity-feedback loop has the open-loop transfer function L(s) = 304/(s(s + 6)(s + 10)). Find the phase crossover frequency ω₁₈₀, where ∠L(jω) = −180°.

L(s) = 304/(s(s + 6)(s + 10))

ω₁₈₀ = rad/s

6.Hard

A unity-feedback loop has the open-loop transfer function L(s) = 68/(s(s + 2)(s + 6)). Find the phase crossover frequency ω₁₈₀, where ∠L(jω) = −180°.

L(s) = 68/(s(s + 2)(s + 6))

ω₁₈₀ = rad/s

Answer key

1. ω_c = 6447 rad/s
2. |G(0)| = 18.29 dB
3. |H| = −6.762 dB
4. φ = −14.03 °
5. ω₁₈₀ = 7.746 rad/s
6. ω₁₈₀ = 3.464 rad/s

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