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.

New worksheet Practise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________ Date: ____________

1.Easy

Find the low-frequency (DC) gain of G(s) = 900/((s + 1)(s + 40)) in decibels, |G(0)| in dB.

G(s) = 900/((s + 1)(s + 40))

|G(0)| = dB

2.Easy

Sketch the asymptotic Bode magnitude plot of G(s) = 50000/((s + 50)(s + 200)). What is the slope n of the straight-line asymptote above 200 rad/s, in dB/decade?

G(s) = 50000/((s + 50)(s + 200))

n = dB/dec

3.Medium

In the series RLC band-pass filter shown the output is taken across R = 10 Ω, with L = 2 mH and C = 4.7 µF. Find the −3 dB bandwidth BW in Hz.

R = 10 ΩL = 2 mHC = 4.7 µF

BW = Hz

4.Medium

Find the exact magnitude |G(jω)| of G(s) = 360/((s + 3)(s + 20)) at ω = 2 rad/s, in dB.

G(s) = 360/((s + 3)(s + 20))ω = 2 rad/s

|G(jω)| = dB

5.Hard

A unity-feedback loop has the open-loop transfer function L(s) = 2.3/(s(s + 1)). Find the gain crossover frequency ω_c, where |L(jω)| = 1.

L(s) = 2.3/(s(s + 1))

ω_c = rad/s

6.Hard

A unity-feedback loop has the open-loop transfer function L(s) = 31/(s(s + 2)). Find the phase margin PM in degrees.

L(s) = 31/(s(s + 2))

PM = °

Answer key

1. |G(0)| = 27.04 dB
2. n = −40 dB/dec
3. BW = 795.8 Hz
4. |G(jω)| = 13.92 dB
5. ω_c = 1.362 rad/s
6. PM = 20.35 °

Full step-by-step solutions: practise this topic on examproblems.com.