TRƯỜNG ĐẠI HỌC SƯ PHẠM KỸ THUẬT

TP. HỒ CHÍ MINH

ELECTRICAL AND ELECTRONIC PRINCIPLES WEEK 5

Cuong Q. Ngo

Last classes

• MATLAB fundamentals • Single frequency AC analysis (MultiSim)

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• Maximum power transfer

CONTENTS (Today)

• Magnetically coupled circuits

• Transformer

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• Resonance

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

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reference polarity of the mutual voltage in the second coil is positive at the dotted terminal of the second coil

1.Magnetically coupled circuits

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•

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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

1.Magnetically coupled circuits

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• Model

1.Magnetically coupled circuits

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• Example 1 • Calculate the phasor currents I1 and I2

1.Magnetically coupled circuits

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• Answer

2. Transformer

Courtesy: Jensen Transformers

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2. Transformer

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Ideal transformer – Coils have very large reactances – Coupling coefficient is equal to unity – Primary and secondary coils are lossless

2. Transformer

• Typical circuits illustrating proper voltage polarities and

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current directions in an ideal transformer.

2. Transformer

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Input impedance

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• Complex power supplied by the source

2. Transformer

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• Example Find Vo and complex power supplied by the source

2. Transformer

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• Answer

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

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frequency 𝜔𝑜

3. Resonant circuits

• Half-power frequencies

• Relate the half-power frequencies with the resonant

frequency

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• Bandwidth

3. Resonant circuits

• Amplitude of current

– At 𝜔 = 𝜔𝑜

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– At 𝜔 = 𝜔1

3. Resonant circuits

• The quality factor of a resonant circuit is the ratio of its

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resonant frequency to its bandwidth.

3. Resonant circuits

• Example • With R = 2 Ω, L = 1 mH, C = 0.4 µF

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• Find the resonant frequency and half-power frequencies • Calculate the quality factor and bandwidth • Determine the amplitude of current at 𝜔𝑜, 𝜔1

3. Resonant circuits

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• Answer • 50 krad/s; 25; 2 krad/s; 10 A; 7.071 A

3. Resonant circuits Parallel resonance

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• Resonant frequency

3. Resonant circuits Parallel resonance

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• Half-power frequencies, bandwidth, and quality factor