Bài giảng Electrical and electronic principles - Week 5

TRƯỜNG ĐẠI HỌC SƯ PHẠM KỸ THUẬT 
TP. HỒ CHÍ MINH 
ELECTRICAL AND ELECTRONIC 
PRINCIPLES 
WEEK 5 
Cuong Q. Ngo 
Last classes 
• Maximum power transfer 
• MATLAB fundamentals 
• Single frequency AC analysis (MultiSim) 
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CONTENTS (Today) 
• Magnetically coupled circuits 
• Transformer 
• Resonance 
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1.Magnetically coupled circuits 
• Mutual inductance 
– Mutual inductance is the ability of one inductor to induce a 
voltage across a neighboring inductor, measured in henrys 
(H). 
– If a current enters the dotted terminal of one coil, the 
reference polarity of the mutual voltage in the second coil 
is positive at the dotted terminal of the second coil 
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1.Magnetically coupled circuits 
• If a current leaves the dotted terminal of one coil, the 
reference polarity of the mutual voltage in the second coil is 
negative at the dotted terminal of the second coil 
• 
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1.Magnetically coupled circuits 
• Model 
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1.Magnetically coupled circuits 
• Example 1 
• Calculate the phasor currents I1 and I2 
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1.Magnetically coupled circuits 
• Answer 
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AI 04.1491.22 
AI 39.4901.131 
2. Transformer 
Courtesy: Jensen Transformers 
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2. Transformer 
• Ideal transformer 
– Coils have very large reactances 
– Coupling coefficient is equal to unity 
– Primary and secondary coils are lossless 
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2. Transformer 
• Typical circuits illustrating proper voltage polarities and 
current directions in an ideal transformer. 
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2. Transformer 
• Input impedance 
• Complex power supplied by the source 
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2. Transformer 
• Example 
 Find Vo and complex power supplied by the source 
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2. Transformer 
• Answer 
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3. Resonant circuits 
Series resonance 
• Resonance is a condition in an RLC circuit in which the 
capacitive and inductive reactances are equal in magnitude, 
thereby resulting in a purely resistive impedance. 
• The value of 𝜔 that satisfies this condition is call resonant 
frequency 𝜔𝑜 
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3. Resonant circuits 
• Half-power frequencies 
• Relate the half-power frequencies with the resonant 
frequency 
• Bandwidth 
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3. Resonant circuits 
• Amplitude of current 
– At 𝜔 = 𝜔𝑜 
– At 𝜔 = 𝜔1 
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3. Resonant circuits 
• The quality factor of a resonant circuit is the ratio of its 
resonant frequency to its bandwidth. 
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3. Resonant circuits 
• Example 
• With R = 2 Ω, L = 1 mH, C = 0.4 µF 
• Find the resonant frequency and half-power frequencies 
• Calculate the quality factor and bandwidth 
• Determine the amplitude of current at 𝜔𝑜, 𝜔1 
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3. Resonant circuits 
• Answer 
• 50 krad/s; 25; 2 krad/s; 10 A; 7.071 A 
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3. Resonant circuits 
Parallel resonance 
• Resonant frequency 
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3. Resonant circuits 
Parallel resonance 
• Half-power frequencies, bandwidth, and quality factor 
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