Engineering Circuit Analysis

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Engineering Circuit Analysis
CH7 Magnetically Coupled Circuits
7.1 Self-inductance and mutual inductance 7.2 Dot
convention 7.3 Transformer
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Ch7 Magnetically Coupled Circuits

• Physical phenomenon
• By having two closely located coils, the
  magnetic flux created by one coil will affect the
  other leading to the mutual inductance.
• Voltage across a coil is introduced by the self
  inductance and mutual inductance.
• Application The transformer coverts the ac
  voltage to a higher or lower value required by
  the load.

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Ch7 Magnetically Coupled Circuits
7.1 Self-inductance and mutual inductance
Coupled Circuits and v i relationship
Magnetic flux ?1 f(i1) (?1 N1?1)

The flux is proportional to the current in linear
inductor ?1 (t) L1i1(t)
L is a lumped element abstraction for the coil.
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Ch7 Magnetically Coupled Circuits
7.1 Self-inductance and mutual inductance
Coupled Circuits and v i relationship
Ideal Coupled Circuits v i relationship

• L1?L2?M represent Ideal Coupled Inductor,

Self inductance vol.
Mutual inductance vol.
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Ch7 Magnetically Coupled Circuits
7.1 Self-inductance and mutual inductance
Coupled Circuits and v i relationship
v2
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Ch7 Magnetically Coupled Circuits
7.2 Dot Convention
A current entering the dotted terminal of one
coil produces an open circuit voltage with a
positive voltage reference at the dotted terminal
of the second coil.
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Ch7 Magnetically Coupled Circuits
7.2 Dot Convention

• Example

Apply dot convention , M creates a negative
potential at the dot position of the primary mesh
Apply dot convention , M creates a negative
potential at the dot position of the secondary
mesh
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Ch7 Magnetically Coupled Circuits
7.2 Dot Convention
QuestionThe terminal is dotted,how can we get v
i equations to coupled inductor?
Steps to determine the coupled circuit voltage
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Ch7 Magnetically Coupled Circuits
7.2 Dot Convention
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Ch7 Magnetically Coupled Circuits
7.2 Dot Convention
Coupled Circuits and v i relationship
Ideal Coupled Circuitss v i relationship
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Ch7 Magnetically Coupled Circuits
7.2 Dot Convention

• Example (Practice 10.2, p267)

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Ch7 Magnetically Coupled Circuits
7.2 Dot Convention

• Example10.2 (KVLS for the three meshes)

Mesh 1
Mesh 2
Mesh 3
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Ch7 Magnetically Coupled Circuits
7.3 Transformer
Equivalent networks---- equivalent network
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Ch7 Magnetically Coupled Circuits
7.3 Transformer

• Example10.4 (P274)

One the equivalence
Let
Let
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Ch7 Magnetically Coupled Circuits
7.3 Transformer
---- equivalent network (?)
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Ch7 Magnetically Coupled Circuits
7.3 Transformer
-- ideal transformer
Turn ratio
Number of turns of wire forming the coil
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Ch7 Magnetically Coupled Circuits
7.3 Transformer
KVL for both primary and secondary meshes
V1 jwL1I1 jwMI2 0 -jwMI1 (ZL jwL2)I2
With
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Ch7 Magnetically Coupled Circuits
7.3 Transformer
Impedance Matching Condition of maximizing the
power that is being transferred One can apply
the ideal transformer to have the above matching
to be achieved.
if
if
Current and voltage adjustment
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Ch7 Magnetically Coupled Circuits
7.3 Transformer
Thevenin equivalent for mesh 1
Example 10.6 (P281)
Thevenin equivalent for mesh 2