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 RC low-pass filter shown, with R = 10 kΩ, C = 100 nF. Give it in Hz.

R = 10 kΩC = 100 nF

f_c = Hz

2.Easy

Sketch the asymptotic Bode magnitude plot of G(s) = 500000/((s + 1000)(s + 10)). What is the slope n of the straight-line asymptote above 1000 rad/s, in dB/decade?

G(s) = 500000/((s + 1000)(s + 10))

n = dB/dec

3.Medium

In the series RLC band-pass filter shown the output is taken across R = 10 Ω, with L = 1 mH and C = 0.1 µF. Find the −3 dB bandwidth BW in Hz.

R = 10 ΩL = 1 mHC = 0.1 µF

BW = Hz

4.Medium

The RC high-pass filter shown has R = 1 kΩ, C = 10 nF. A sinusoidal input of 3.2 kHz is applied. Find the gain |H| = |v_out/v_in| in dB.

R = 1 kΩC = 10 nFf = 3.2 kHz

|H| = dB

5.Hard

A unity-feedback loop has the open-loop transfer function L(s) = 8/(s(s + 2)(s + 3)). Find the phase crossover frequency ω₁₈₀, where ∠L(jω) = −180°.

L(s) = 8/(s(s + 2)(s + 3))

ω₁₈₀ = rad/s

6.Hard

A unity-feedback loop has the open-loop transfer function L(s) = 614/(s(s + 8)(s + 9)). Find the gain margin GM in dB.

L(s) = 614/(s(s + 8)(s + 9))

GM = dB

Answer key

1. f_c = 159.2 Hz
2. n = −40 dB/dec
3. BW = 1592 Hz
4. |H| = −14.11 dB
5. ω₁₈₀ = 2.449 rad/s
6. GM = 5.992 dB

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