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 f_c of the RL low-pass filter shown, with R = 22 Ω, L = 47 mH. Give it in Hz.

R = 22 ΩL = 47 mH

f_c = Hz

2.Easy

Sketch the asymptotic Bode magnitude plot of G(s) = 50(s + 1000)/((s + 5)(s + 200)). What is the slope n of the straight-line asymptote above 1000 rad/s, in dB/decade?

G(s) = 50(s + 1000)/((s + 5)(s + 200))

n = dB/dec

3.Medium

The RC low-pass filter shown has R = 1 kΩ, C = 4.7 nF. A sinusoidal input of 100 kHz is applied. Find the phase shift φ of v_out relative to v_in, in degrees.

R = 1 kΩC = 4.7 nFf = 100 kHz

φ = °

4.Medium

The RC low-pass filter shown has R = 3.3 kΩ, C = 22 nF. A sinusoidal input of 4.4 kHz is applied. Find the gain |H| = |v_out/v_in| in dB.

R = 3.3 kΩC = 22 nFf = 4.4 kHz

|H| = dB

5.Hard

A unity-feedback loop has the open-loop transfer function L(s) = 106/(s(s + 5)(s + 7)). Find the gain margin GM in dB.

L(s) = 106/(s(s + 5)(s + 7))

GM = dB

6.Hard

A unity-feedback loop has the open-loop transfer function L(s) = 17/(s(s + 2)). Find the gain crossover frequency ω_c, where |L(jω)| = 1.

L(s) = 17/(s(s + 2))

ω_c = rad/s

Answer key

1. f_c = 74.5 Hz
2. n = −20 dB/dec
3. φ = −71.29 °
4. |H| = −7.014 dB
5. GM = 11.96 dB
6. ω_c = 3.888 rad/s

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