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) = 300(s + 9)/((s + 3)(s + 5)) in decibels, |G(0)| in dB.

G(s) = 300(s + 9)/((s + 3)(s + 5))

|G(0)| = dB

2.Easy

Sketch the asymptotic Bode magnitude plot of G(s) = 4(s + 5)/(s(s + 1)). What is the slope n of the straight-line asymptote between 1 and 5 rad/s, in dB/decade?

G(s) = 4(s + 5)/(s(s + 1))

n = dB/dec

3.Medium

In the series RLC band-pass filter shown the output is taken across R = 2 Ω, with L = 50 mH and C = 4.7 µF. Find the centre (resonant) frequency f₀ in Hz.

R = 2 ΩL = 50 mHC = 4.7 µF

f₀ = Hz

4.Medium

The RC low-pass filter shown has R = 3.3 kΩ, C = 2.2 nF. A sinusoidal input of 11 kHz is applied. Find the phase shift φ of v_out relative to v_in, in degrees.

R = 3.3 kΩC = 2.2 nFf = 11 kHz

φ = °

5.Hard

A unity-feedback loop has the open-loop transfer function L(s) = 688/(s(s + 8)(s + 9)). Find the gain margin GM in dB.

L(s) = 688/(s(s + 8)(s + 9))

GM = dB

6.Hard

A unity-feedback loop has the open-loop transfer function L(s) = 304/(s(s + 9)(s + 10)). Find the gain margin GM in dB.

L(s) = 304/(s(s + 9)(s + 10))

GM = dB

Answer key

1. |G(0)| = 45.11 dB
2. n = −40 dB/dec
3. f₀ = 328.3 Hz
4. φ = −26.65 °
5. GM = 5.004 dB
6. GM = 15 dB

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