Transcript Figure 1.1 A telephone system.

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EE 1270: Introduction to Electric Circuits
Lecture 16:
Mutual Inductance
Chapter 6
Inductance, Capacitance, and
Mutual Inductance
Sections 6.4, 6.5
EE 1270 Introduction to Electric Circuits
Suketu Naik
Transformers and Their Applications
Transmission Line Transformer
(7200 V to 240 V or 120 V)
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Center Tapped Transformer
(power distribution,
microphone, automobiles,
AC-to-DC rectifiers)
Ignition Coil (12 V to 40000 V)
EE 1270 Introduction to Electric Circuits
Suketu Naik
2
Mutual Inductance
Mutual inductance is the ability of one inductor to induce a voltage
across a neighboring inductor [unit=H].
M  M 21  M 12  N 2 N1  k L1 L2 ;0  k  1
L1  N1 ; L2  N 2
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Where, μ=magnetic constant=magnetic permeability [N/A2]
N1=number of turns in left coil
N2=number of turns in right coil
ϕ11=magnetic flux produced by current i1 through N1 turns
ϕ21=magnetic flux produced by current i1 through N1 and N2 turns
ϕ22=magnetic flux produced by current i2 through N2 turns
ϕ12=magnetic flux produced by current i2 through N1 and N2 turns
M=M21=M12=mutual inductance [H], k=coefficient of coupling
EE 1270 Introduction to Electric Circuits
Suketu Naik
Mutually Coupled Coils: Dot Convention
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 When the current enters the dotted terminal in one coil, the polarity
of induced voltage in other coil is positive at its dotted terminal
 When the current leaves the dotted terminal in one coil, the polarity
of induced voltage in other coil is negative at its dotted terminal
EE 1270 Introduction to Electric Circuits
Suketu Naik
Analysis using Mesh Current Method
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di1
di2
 v g  i1 R1  L1
M
0
dt
dt
di2
di1
i2 R2  L2
M
0
dt
dt
EE 1270 Introduction to Electric Circuits
Suketu Naik
Example 6.6: Current in Magnetically Coupled Coils
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Write Mesh-current Equations
EE 1270 Introduction to Electric Circuits
Suketu Naik
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P6.45: Design of Transformer
Check out the transformer design for Switching Mode Power Supply:
http://www.digikey.com/en/pdf/w/wurth-elektronik/cookbook-transformer-design
EE 1270 Introduction to Electric Circuits
Suketu Naik