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) = 125000(s + 2)/(s(s + 1000)(s + 50)). What is the slope n of the straight-line asymptote between 50 and 1000 rad/s, in dB/decade?

G(s) = 125000(s + 2)/(s(s + 1000)(s + 50))

n = dB/dec

2.Easy

Find the corner (−3 dB) frequency f_c of the RC low-pass filter shown, with R = 22 kΩ, C = 4.7 nF. Give it in Hz.

R = 22 kΩC = 4.7 nF

f_c = Hz

3.Medium

The RC low-pass filter shown has R = 2.2 kΩ, C = 4.7 nF. A sinusoidal input of 77 kHz is applied. Find the gain |H| = |v_out/v_in| in dB.

R = 2.2 kΩC = 4.7 nFf = 77 kHz

|H| = dB

4.Medium

The RL low-pass filter shown has R = 100 Ω, L = 22 mH. A sinusoidal input of 1.4 kHz is applied. Find the gain |H| = |v_out/v_in| in dB.

R = 100 ΩL = 22 mHf = 1.4 kHz

|H| = dB

5.Hard

A unity-feedback loop has the open-loop transfer function L(s) = 98/(s(s + 4)(s + 7)). Find the gain margin GM in dB.

L(s) = 98/(s(s + 4)(s + 7))

GM = dB

6.Hard

A unity-feedback loop has the open-loop transfer function L(s) = 47.5/(s(s + 5)). Find the gain crossover frequency ω_c, where |L(jω)| = 1.

L(s) = 47.5/(s(s + 5))

ω_c = rad/s

Answer key

1. n = −20 dB/dec
2. f_c = 1539 Hz
3. |H| = −14.15 dB
4. |H| = −6.762 dB
5. GM = 9.946 dB
6. ω_c = 6.051 rad/s

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