Bài giảng Electrical and electronic principles - Week 6

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 
𝑎𝑜 =
1
2
𝑎𝑛 = 0 
𝑏𝑛 = 
2
𝑛𝜋
; 𝑛 = 𝑜𝑑𝑑
0; 𝑛 = 𝑒𝑣𝑒𝑛
𝑓 𝑡 =
1
2
+
2
𝜋
𝑠𝑖𝑛𝜋𝑡 +
2
3𝜋
𝑠𝑖𝑛3𝜋𝑡 +
2
5𝜋
𝑠𝑖𝑛5𝜋𝑡 + ⋯ 
8 
Exercise 
• Find the Fourier series of the square wave 
9 
• Answer 
10 
2. Applying Fourier series 
• Steps for applying Fourier series 
1. Express the excitation as a Fourier series. 
2. Transform the circuit from the time domain to the frequency 
domain. 
3. Find the response of the dc and ac components in the 
Fourier series. 
4. Add the individual dc and ac responses using the 
superposition principle. 
11 
2. Applying Fourier series 
12 
2. Applying Fourier series 
13 
2. Applying Fourier series 
• Find the response 𝑣𝑜(𝑡) in the circuit 
• Where 
14 
2. Applying Fourier series 
• Answer 
15 
2. Applying Fourier series 
Average power 
• Let 
• The average power 
16 
2. Applying Fourier series 
• Apparent power (review) 
• RMS value (with a given function f(t)) 
• Or 
17 
2. Applying Fourier series 
• The voltage and current at the terminals of a circuit are 
• Find the average power absorbed by the circuit. 
18 
2. Applying Fourier series 
• Answer: 444.7 W 
19 
2. Applying Fourier series 
• Find an estimate for the RMS value of the voltage 
20 
2. Applying Fourier series 
• Answer: 1.649 V 
21 
2. Applying Fourier series 
• Find the rms value of the periodic current 
22 
2. Applying Fourier series 
• Answer: 29.61 A 
23