Schematicaly, a transformer is composed of two windings with some of their flux in common :
In the case we are interested in, a high permeability core is used as
common support of those windings and concentrate magnetic
flux. Faraday's law allows voltages at the first and second windings
to be written as a function of the flux 
and 
thru them :
In previous formulas, 
and 
stand for the respective
resistances of the windings 1 and 2. In applications, the input
winding is called the primary of the transformer, while the ouput one
is called the secondary (this naming is application dependent: a
single phase transformer can be loaded from any of its windings). We
will admit in the following the primary has index 1 and secundary
index 2. In the previous system of equations it is possible to
decompose flux and in common and proper part. This
yields to the following notation :
with 
and 
respective numbers of turns of the windings,
commun flux and 
proper flux (called
leakage flux). The system of equations becomes :
Leakage flux 
is generated only by primary current 
,
and we can associate to it a self-inductance 
such that
(strictly speaking, since an iron core is
ferromagnetic, this is not true, but the high permeability of the core
implies that the reluctance of the induction tubes giving
is dominated by the reluctance of the air part of it). Likewise, we
will put 
. Inductances and 
are
called primary and secundary leakage inductances. When the secundary
circuit is open, a current 
flows thru the primary : it is called
the magnetizing current. Bu putting 
, we have :
or equivalently with 
:
In other words, a real transformer can be modelled as a perfect
transformer (with leakage or resistance) with parasitic elements
(resistances and inductances) connected to it. For a perfect
transformer, one has the relation 
, the
quantity 
beeing the transformation ratio. In
a loaded iron core transformer, the magnetizing curre will be
negligible with respect to other currents and we will have 
. Those two relations show that a perfect transformer loaded
on the primary by an impedance Z will show an impedance 
at the secundary. With this, we can make three equivalent schemas of a real transformer :
Note that since leakage inductances are in series, they will tend to limit response at high frequencies while the finite permeability of the core will limit it at low frequencies.