EE201
Transformers
Oct. 9, 2007
Denard Lynch
Page 1 of 7
The inductance we have studied previously is correctly know as the
self inductance
of a
coil, commonly called just
inductance
.
Mutual inductance
is the inductive effect (the reaction to a changing flux predicted by
Faraday’s Law) in
one
coil due to the flux created in
another
.
(Refer to notes on mutual
inductance in previous notes on “Inductance”.)
This mutual inductance is used to
advantage in a device called a transformer, which is used extensively in the electrical and
electronics industries.
A transformer is a device in which two coils are deliberately arranged so that the flux
from one coil is maximally coupled to a second coil, usually on the same core.
Assume for the moment that there is a flux established in one of two closely coupled
coils,
Φ
p
, then the voltage induced in this coil, e
p
, is given by:
e
p
=
N
p
d
Φ
p
dt
=
L
p
di
p
dt
Similarly, the voltage induced in the second coil would be:
e
s
=
N
s
d
Φ
s
dt
If we define a coefficient of coupling,
k
, as
k
=
Φ
s
Φ
p
, where
Φ
p
is the originally induced
flux and
Φ
s
is the portion of the flux which couples the second coil.
Clearly
Φ
s
can never
be greater than
Φ
p
, so
k
max
≤
1.
Modern transformers are “tightly coupled”, with
k
≈
1.
Most of the useful formulas describing transformer behaviour are developed here
assuming that
k
= 1, but they could easily be modified to reflect the performance of a
“loosely coupled” coil (
k
< 1).
The first useful operational formula:
if k = 1,
Φ
p
=
Φ
s
=
Φ
e
p
=
N
s
d
Φ
dt
, and
e
s
=
N
s
d
Φ
dt
and
e
p
e
s
=
N
p
N
s
, where
N
s
N
p
is called the turns ratio,
n
therefore,
e
s
=
ne
p
(1)
Note that a turns ratio, n > 1 is called a stepup transformer, a turns ratio < 1 is called a
stepdown transformer, and an n = 1 is called an isolation transformer.
While the voltage depends on
changing
flux, the flux depends only on the
current
(Ampere’s Law for magnetic circuits).
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
EE201
Transformers
Oct. 9, 2007
Denard Lynch
Page 2 of 7
Recall
ℑ
=
NI
=
Φℜ
or
Φ
=
NI
ℜ
.
The primary flux:
Φ
p
=
N
p
I
p
ℜ
p
, and the secondary flux
must be:
Φ
s
=
N
s
I
s
ℜ
s
.
Since we have assumed
k
= 1,
Φ
p
=
Φ
s
=
Φ
, and since they are wound
on the same core,
ℜ
p
=
ℜ
s
.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '10
 Linch
 Flux, Inductor, turns ratio, Denard Lynch

Click to edit the document details