Transcript The Concept of Mutual Inductance ECE 201 Circuit Theory 1 1

The Concept of Mutual Inductance
ECE 201 Circuit Theory 1
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Magnetically -- Coupled Coils
Non – Magnetic Core
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Magnetically-Coupled Coils
• Number of turns on each coil are N1 and N2
• Coil 1 energized by a time-varying current
source (Primary)
• Coil 2 in not energized and has open circuited
terminals (Secondary)
• Polarity of voltage v2 is assigned by the dot
convention
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Flux Components
Flux produced by i1 has 2 components, Φ11 (links only N1
turns) and Φ21 (links the N2 turns and the N1 turns).
Φc,i
coil
current
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1  11  21
Total flux linking coil 1
1  P1 N1i1
11  P11 N1i1
21  P21 N1i1
P1 N1i1  P11 N1i1  P21 N1i1
P1  P11  P21
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Use Faraday’s Law to find voltages
d 1 d ( N11 )
d (11  21 )
v1 

 N1
dt
dt
dt
  PNi
 d (P11 N1i1 ) d (P21 N1i1 ) 
v1  N1 


dt
dt


di1
di1
di1
2
2
v1  N1 (P11  P21 )
 N1 P1
 L1
dt
dt
dt
d 2 d ( N 221 )
d (P21 N 2i1 )
v2 

 N2
dt
dt
dt
di1
di1
v2  N 2 N1P21
 M 21
dt
dt
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Excite coil 2 and leave coil 1 open
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2  22  12
Total flux linking coil 2
2  P2 N 2i2
22  P22 N 2i2
12  P12 N 2i2
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Use Faraday’s Law to find Voltages
d 2
di2
di2
2
v2 
 N 2 P2
 L2
dt
dt
dt
v1 
d 1 d ( N112 )
di

 N1 N 2 P12 2
dt
dt
dt
M 12  N1 N 2 P12
P12  P21
Mutual Inductance
For non-magnetic materials
M 12  M 21  M
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