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) = 380/((s + 1)(s + 90)) in decibels, |G(0)| in dB.

G(s) = 380/((s + 1)(s + 90))

|G(0)| = dB

2.Easy

Sketch the asymptotic Bode magnitude plot of G(s) = 200000/(s(s + 500)(s + 20)). What is the slope n of the straight-line asymptote below 20 rad/s, in dB/decade?

G(s) = 200000/(s(s + 500)(s + 20))

n = dB/dec

3.Medium

Find the exact magnitude |G(jω)| of G(s) = 2100/((s + 15)(s + 20)) at ω = 0.5 rad/s, in dB.

G(s) = 2100/((s + 15)(s + 20))ω = 0.5 rad/s

|G(jω)| = dB

4.Medium

The RC low-pass filter shown has R = 22 kΩ, C = 4.7 nF. A sinusoidal input of 15 kHz is applied. Find the gain |H| = |v_out/v_in| in dB.

R = 22 kΩC = 4.7 nFf = 15 kHz

|H| = dB

5.Hard

A unity-feedback loop has the open-loop transfer function L(s) = 1600/(s(s + 20)). Find the phase margin PM in degrees.

L(s) = 1600/(s(s + 20))

PM = °

6.Hard

A unity-feedback loop has the open-loop transfer function L(s) = 80/(s(s + 20)). Find the gain crossover frequency ω_c, where |L(jω)| = 1.

L(s) = 80/(s(s + 20))

ω_c = rad/s

Answer key

1. |G(0)| = 12.51 dB
2. n = −20 dB/dec
3. |G(jω)| = 16.89 dB
4. |H| = −19.82 dB
5. PM = 28.02 °
6. ω_c = 3.925 rad/s

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