A real transformer is modeled by adding resistors and
noncoupled inductors to the ideal transformer.
Z
1
N
1
N
2
2
Z
2
⋅
=
An impedance Z
2
on the secondary of an ideal transformer
reflects to the primary side as:
Ratio of input and output Impedances of Ideal Transformer
Z
2
V
2
I
2
=
V
1
a
I
1
a
⋅
=
V
1
a
2
I
1
⋅
=
Z
1
a
2
=
Current Ratio as a Function of Turns Ratio of Ideal Transformer
I
1
I
2
N
2
N
1
=
1
a
=
Voltage Ratio as a Function of Turns Ratio of Ideal Transformer
V
1
V
2
N
1
N
2
=
a
=
V
1
I
1
⋅
V
2
I
2
⋅
=
P
1
P
2
=
From the equations above the power balance follows:
I
1
I
2
N
2
N
1
=
considering the balance of excitation N
1
I
1
=N
2
I
2
we get:
V
1
V
2
N
1
N
2
=
Given a transformer with turns N
1
and N
2
with common mutual flux:
Let's start with the basic equations for an ideal transformer:
VN
t
Φ
Mutual
d
d
⋅
=
The basic equation describing induction of a voltage in a transformer coil is:
A transformer consists of 2 or more windings on a common magnetic core:
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 Spring '08
 GIESSELMANN
 Alternating Current, Flux, Magnetic Field, Inductor, ideal transformer

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