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

Sketch the asymptotic Bode magnitude plot of G(s) = 10000/((s + 20)(s + 100)). What is the slope n of the straight-line asymptote between 20 and 100 rad/s, in dB/decade?

G(s) = 10000/((s + 20)(s + 100))

n = dB/dec

2.Easy

Find the low-frequency (DC) gain of G(s) = 28/((s + 8)(s + 9)) in decibels, |G(0)| in dB.

G(s) = 28/((s + 8)(s + 9))

|G(0)| = dB

3.Medium

Find the phase ∠G(jω) of G(s) = 20(s + 11)/(s(s + 12)) at ω = 20 rad/s, in degrees.

G(s) = 20(s + 11)/(s(s + 12))ω = 20 rad/s

∠G(jω) = °

4.Medium

The RC low-pass filter shown has R = 1 kΩ, C = 1 nF. A sinusoidal input of 32 kHz is applied. Find the phase shift φ of v_out relative to v_in, in degrees.

R = 1 kΩC = 1 nFf = 32 kHz

φ = °

5.Hard

A unity-feedback loop has the open-loop transfer function L(s) = 100/(s(s + 2)(s + 8)). Find the gain margin GM in dB.

L(s) = 100/(s(s + 2)(s + 8))

GM = dB

6.Hard

A unity-feedback loop has the open-loop transfer function L(s) = 0.7/(s(s + 1)). Find the gain crossover frequency ω_c, where |L(jω)| = 1.

L(s) = 0.7/(s(s + 1))

ω_c = rad/s

Answer key

1. n = −20 dB/dec
2. |G(0)| = −8.203 dB
3. ∠G(jω) = −87.85 °
4. φ = −11.37 °
5. GM = 4.082 dB
6. ω_c = 0.6002 rad/s

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