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PART TWO: AC Circuits
Chapter 6Magnetically coupled circuits
phasors
THIS COURSE CAN BE FOUND AT:
http://users.utcluj.ro/~denisad
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When two coils with or without contacts between them affect each other
through the magnetic field generated by one of them, they are said to be
magnetically coupled.
Inductive coupling is widely used throughout
electrical technology; examples include:
✓ Electric motors and generators
✓ Inductive charging products
✓ Induction cookers and induction heating
systems
✓ Induction loop communication systems
✓ Metal detectors
✓ Radio-frequency identification
✓ Transformers
✓ Wireless power transfer
NFC (Near Field Communication) works based on the principle
of inductive coupling, where loosely coupled inductive circuits share
power and data over a distance of a few centimeters. All NFC devices
operate at 13.56MHz. NFC devices share the basic technology with
proximity (13.56MHz) RFID (Radio-Frequency Identification) tags and
contactless smartcards, but have a number of key additional features.
Working principle of inductive coupling in NFC devices
Source: [www.wireless.intgckts.com]
6.1. INTRODUCTION
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When two coils are in a close proximity to each other, the magnetic flux caused by current in
one coil links with the other coil, and inducing voltage in the latter. This phenomenon is known
as mutual inductance.
- Consider a coil with N turns, when current i flows through the coil, a magnetic flux φ is produced around it.
According to Faraday’s law, the voltage v induced in the coil is proportional to the number of turns N and the time
rate of change of the magnetic flux φ; that is,
6.2. MUTUAL INDUCTANCE
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6.2. MUTUAL INDUCTANCE
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6.2. MUTUAL INDUCTANCE
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6.2. MUTUAL INDUCTANCE
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6.2. MUTUAL INDUCTANCE
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Examples illustrating how to apply the dot convention:
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6.2. MUTUAL INDUCTANCE
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6.2. MUTUAL INDUCTANCE
6.2.1. Series-Aiding Connection
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6.2. MUTUAL INDUCTANCE
6.2.2. Series-Opposing Connection
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6.2.3. Circuit Model for Coupled Inductors
6.2. MUTUAL INDUCTANCE
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Example 1:
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6.2. MUTUAL INDUCTANCE
Example 2:
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6.2. MUTUAL INDUCTANCE
6.2.4. Energy in a Coupled Circuit
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6.2. MUTUAL INDUCTANCE
6.2.4. Energy in a Coupled Circuit
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6.2. MUTUAL INDUCTANCE
6.2.4. Energy in a Coupled Circuit
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6.2. MUTUAL INDUCTANCE
6.2.4. Energy in a Coupled Circuit
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6.2. MUTUAL INDUCTANCE
6.2.5. Coupling Coefficient
The coupling coefficient k is a measure of magnetic coupling between two coils;
0 ≤ k ≤ 1.
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Figure 1- Loose coupling Figure 2 – Tight coupling
Figure 1
Figure 2
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6.2. MUTUAL INDUCTANCE
Example 3:
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6.3. LINEAR TRANSFORMER
A transformer is a magnetic device that takes advantage of the phenomenon of mutual inductance.
✓ The coil that is directly connected to the voltage source is called the primary winding.
✓ The coil connected to the load is called the secondary winding.
✓ The resistances R1 and R2 are included to account for the losses (power dissipation) in the coils.
✓ The transformer is said to be linear if the coils are wound on a magnetically linear material.
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6.3. LINEAR TRANSFORMER
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6.3. LINEAR TRANSFORMER
6.3.1. T (or Y) Equivalent Circuits
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6.3. LINEAR TRANSFORMER
6.3.2. Π (or Δ) Equivalent Circuits
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6.4. IDEAL TRANSFORMER
➢ An ideal transformer is one with perfect coupling (k = 1). It consists of two (or more)
coils with a large number of turns wound on a common core of high permeability.
Because of this high permeability of the core, the flux links all the turns of both coils,
thereby resulting in a perfect coupling.
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When a sinusoidal voltage is applied to the primary winding,
the same magnetic flux φ goes through both windings.
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6.4. IDEAL TRANSFORMER
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6.4. IDEAL TRANSFORMER
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6.4. IDEAL TRANSFORMER
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6.4. IDEAL TRANSFORMER
6.4.1. Impedance Transformation
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References
[1] Charlews K. Alexander, Matthew N.O.Sadiku, Fundamentals of Electric
Circuits (Fifth Edition), published by McGraw-Hill, 2013
[2] Radu V. Ciupa, Vasile Topa, The Theory of Electric Circuits, published
by Casa Cartii de Stiinta, 1998
[3] Dan. D Micu, Laura Darabant, Denisa Stet et al., Teoria circuitelor
electrice. Probleme, published by UTPress, 2016