Download Coupled circuit

Coupled circuit
Alternating current circuits
Corcoran
Coefficient of coupling
1
1’
2
2’
The coefficient of coupling between circuit
11’ and circuit 22’ will be defined as:
k 
Z 12
Z 11 Z 22

Z 21
Z 11 Z 22
Where, Z12=Z21=mutual inductance between circuit 1 and circuit 2
Z11’= impedance seen looking into terminals 11’ with terminals 22’ open circuited
Z22’= impedance seen looking into terminals 11’ with terminals 22’ open circuited
Magnetically coupled circuit
If a portion of the magnetic flux established by one circuit interlinks with a
second circuit, the two circuit are coupled magnetically and energy may be
transferred from one circuit to other by the way of the magnetic field which is
common to the two circuits.
Self Inductance
LN
d
di
Self inductance
Mutual inductance
M 21  N 2
M 21  N 2
v1  N1
d21
d di
di
 N1 21  2  M 21 2
dt
di2 dt
dt
d21
di2
d21
N N
k 2 1
di2
 21
v1  M 21
di2
dt
Mutual inductance
v 2  N1
d12
d di
di
 N1 12  1  M 12 1
dt
di1 dt
dt
M 12  N1
v 2  M 12
di1
dt
M 12  N1
d12
di1
d12
NN
k 1 2
di1
12
12=  21
Coefficient of magnetic coupling
The quantity of coupling between two coils is sometimes referred to as the Coefficient
of
Coupling.
The
formula
for
Coefficient
of
Coupling
is:
 M 12i1

 12    21 
N2
 
  
k  
 L1i1
 1    2 
N1

k
 M 21i2


N1 


L
i
 2 2

N2 

L1 L 2
M
M 12 M 21
L1 L2
Example 3, Problems 5,6
Circuit directions and the sign of M
If the induced voltage of mutual inductance acts in the same direction as
the induced voltage of self inductance, the sign of M is considered positive.
If it opposes the induced voltage, the sign of M is considered to be
negative.
Dot convention
Dot convention
Dot convention
Direction of M
Dot convention
Direction of M
Dot convention
Circuit direction and the sign of M
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