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 ω_c of the RC high-pass filter shown, with R = 3.3 kΩ, C = 1 nF. Give it in rad/s.

R = 3.3 kΩC = 1 nF

ω_c = rad/s

2.Easy

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

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

n = dB/dec

3.Medium

The RC low-pass filter shown has R = 1 kΩ, C = 2.2 nF. A sinusoidal input of 360 kHz is applied. Find the gain |H| = |v_out/v_in| in dB.

R = 1 kΩC = 2.2 nFf = 360 kHz

|H| = dB

4.Medium

In the series RLC band-pass filter shown the output is taken across R = 50 Ω, with L = 5 mH and C = 0.22 µF. Find the centre (resonant) frequency f₀ in Hz.

R = 50 ΩL = 5 mHC = 0.22 µF

f₀ = Hz

5.Hard

A unity-feedback loop has the open-loop transfer function L(s) = 24/(s(s + 1)(s + 5)). Find the gain margin GM in dB.

L(s) = 24/(s(s + 1)(s + 5))

GM = dB

6.Hard

A unity-feedback loop has the open-loop transfer function L(s) = 56/(s(s + 4)(s + 5)). Find the phase crossover frequency ω₁₈₀, where ∠L(jω) = −180°.

L(s) = 56/(s(s + 4)(s + 5))

ω₁₈₀ = rad/s

Answer key

1. ω_c = 303030 rad/s
2. n = −20 dB/dec
3. |H| = −14.11 dB
4. f₀ = 4799 Hz
5. GM = 1.938 dB
6. ω₁₈₀ = 4.472 rad/s

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