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) = 20/((s + 10)(s + 4)) in decibels, |G(0)| in dB.

G(s) = 20/((s + 10)(s + 4))

|G(0)| = dB

2.Easy

Find the low-frequency (DC) gain of G(s) = 30/((s + 40)(s + 9)) in decibels, |G(0)| in dB.

G(s) = 30/((s + 40)(s + 9))

|G(0)| = dB

3.Medium

The RL low-pass filter shown has R = 22 Ω, L = 10 mH. A sinusoidal input of 3.5 kHz is applied. Find the phase shift φ of v_out relative to v_in, in degrees.

R = 22 ΩL = 10 mHf = 3.5 kHz

φ = °

4.Medium

The RL low-pass filter shown has R = 47 Ω, L = 47 mH. A sinusoidal input of 640 Hz is applied. Find the phase shift φ of v_out relative to v_in, in degrees.

R = 47 ΩL = 47 mHf = 640 Hz

φ = °

5.Hard

A unity-feedback loop has the open-loop transfer function L(s) = 60/(s(s + 2)(s + 6)). Find the phase crossover frequency ω₁₈₀, where ∠L(jω) = −180°.

L(s) = 60/(s(s + 2)(s + 6))

ω₁₈₀ = rad/s

6.Hard

A unity-feedback loop has the open-loop transfer function L(s) = 148/(s(s + 3)(s + 7)). Find the phase crossover frequency ω₁₈₀, where ∠L(jω) = −180°.

L(s) = 148/(s(s + 3)(s + 7))

ω₁₈₀ = rad/s

Answer key

1. |G(0)| = −6.021 dB
2. |G(0)| = −21.58 dB
3. φ = −84.29 °
4. φ = −76.03 °
5. ω₁₈₀ = 3.464 rad/s
6. ω₁₈₀ = 4.583 rad/s

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