Bài giảng Electrical and electronic principles: Chương 5 - ThS. Ngô Quốc Cường

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

I1  13.01  49.39 A

I 2  2.9114.04 A

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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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