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TRƯỜNG ĐẠI HỌC SƯ PHẠM KỸ THUẬT

TP. HỒ CHÍ MINH

ELECTRICAL AND ELECTRONIC
PRINCIPLES
WEEK 6

Cuong Q. Ngo


Last classes
• Magnetically coupled circuits

• Transformer
• Resonance

2


Contents (Today class)
• Trigonometric Fourier series

• Plot function - MATLAB
• Circuit Application (Applying Fourier series)

3


1. Trigonometric Fourier series
• Fourier theorem: any practical periodic function of frequency

𝜔𝑜 can be expressed as an infinite sum of sine or cosine
functions that are integral multiples of 𝜔𝑜

• Or

• In amplitude – phase form:
where:
4


1. Trigonometric Fourier series
• Fourier analysis

5


1. Trigonometric Fourier series
• Some common integrals:

6


1. Trigonometric Fourier series
• Determine the Fourier series of the waveform

7


1. Trigonometric Fourier series
• Answer

1
𝑎𝑜 =
2
𝑎𝑛 = 0
2
𝑏𝑛 = 𝑛𝜋 ; 𝑛 = 𝑜𝑑𝑑
0; 𝑛 = 𝑒𝑣𝑒𝑛
1 2
2
2
𝑓 𝑡 = + 𝑠𝑖𝑛𝜋𝑡 +
𝑠𝑖𝑛3𝜋𝑡 +
𝑠𝑖𝑛5𝜋𝑡 + ⋯
2 𝜋
3𝜋
5𝜋

8


Exercise
• Find the Fourier series of the square wave

9


• Answer

10