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TRƯỜNG ĐẠI HỌC SƯ PHẠM KỸ THUẬT

TP. HỒ CHÍ MINH

ELECTRICAL AND ELECTRONIC
PRINCIPLES
WEEK 7, 8

Cuong Q. Ngo


Last classes
• Trigonometric Fourier series
• Plot function - MATLAB

• Circuit Application (Applying Fourier series)

2


Contents (Today class)
• Laplace transform
• Circuit element models

• Circuit analysis
• Transient analysis

3


1. Laplace Transform

• The Laplace transform is an integral transformation of a
function f (t) from the time domain into the complex frequency
domain, giving F (s).

• Where s is a complex variable: 𝑠 = 𝜎 + 𝑗𝜔

4


1. Laplace Transform
• Determine the Laplace transform of

5


1. Laplace Transform
• Laplace transform
pairs (f(t) = 0, for t < 0)

6


1. Laplace Transform
• Laplace transform
pairs (f(t) = 0, for t < 0)

7


1. Laplace Transform

• Inverse Laplace transform
1. Decompose F(s) into simple terms using partial fraction
expansion.

2. Find the inverse of each term by matching entries in the
previous table.

8


1. Laplace Transform
• Find the inverse Laplace transform of

9


1. Laplace Transform
• Answer:
𝑓 𝑡 = 3𝑢 𝑡 − 5𝑒 −𝑡 𝑢 𝑡 + 3 sin 2𝑡 𝑢(𝑡)

10