1
Summary of Lecture #33
11/10/2010
Magnetically coupled circuits
•
Mutual inductance
M
12
,
M
21
and
M
•
Dot convention
•
tdomain
VI
characteristic
•
sdomain
VI
characteristic
•
Examples
1
•
VI
chara. of an isolated inductor with
i(0

) = 0
•
VI
characteristic of coupled coils in time domain,
with
i
1
(t)
and
i
2
(t)
going into
dotted terminals
•
VI
characteristic of coupled coils in s domain,
assuming
i
1
(0

) = i
2
(0

) = 0
dt
di
L
dt
di
M
)
t
(
v
dt
di
M
dt
di
L
)
t
(
v
2
2
1
21
2
2
12
1
1
1
+
=
+
=
)
s
(
I
s
L
)
s
(
I
s
M
)
s
(
V
)
s
(
I
s
M
)
s
(
I
s
L
)
s
(
V
2
2
1
21
2
2
12
1
1
1
+
=
+
=
di(t)
v(t)
L
,
V(s)
LsI(s)
dt
=
=
+
_
v(t)
i(t)
L
L
1
, L
2
: Self inductance
M
12
= M
21
= M
Mutual inductance
If one of currents goes into a dotted terminal
and
the
other
current
goes
into
the
undotted terminal, then
•
In time domain
•
In s domain, assuming
i
1
(0

) = i
2
(0

) = 0,
dt
di
L
dt
di
M
)
t
(
v
dt
di
M
dt
di
L
)
t
(
v
2
2
1
2
2
1
1
1
+

=

=
)
s
(
I
s
L
)
s
(
I
Ms
)
s
(
V
)
s
(
I
Ms
)
s
(
I
s
L
)
s
(
V
2
2
1
2
2
1
1
1
+

=

=
OR
Dot convention
The voltage drop across a coil, arising from the
magnetic coupling with
the other coil, from the
dotted terminal to the undotted terminal, equals
M
times the time derivative of the current through
the other coil, going from the dotted terminal to
the undotted terminal.
A part of
v
1
is due to coil 1 itself
and that part is
.
A part of
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 Spring '06
 Inductor, dt, DI

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