# 'Exact' Transformer Model

## Ideal Transformer

To start off lets review the Ideal Transformer model with this illustration.

From this and using the fact that in an Ideal Transformer power input is equal to power output we are able to derive a very useful set of identities. Namely:

$V1 / V2 = N1 / N2 = I2 / I1$

## Exact Transfromer

Now this model does not take into account several things such as resistance in the windings and losses in the core. If we add these in where:

R1 = Winding resistance on the primary side X1 = Leakage inductance on the primary side

Rc = The real portion of the core losses Xm = Is used to maintain mutual flux in the core

R2 = Winding resistance on the secondary side X2 = Leakage inductance on the secondary side

We are left with what is often referred to as the Exact Transformer model, illustrated below. File:Exact transformer.jpgâ€Ž

## Lumped Circuit Transformer Model

Using what we know about an ideal transformer, we are able to apply a transformation (multiplication by an Impedance Scaling Factor) to the impedance located on the secondary side effectively moving them to the primary side. This will allow us take out the Ideal Transformer from the exact model and leave us with a Lumped Circuit model. File:Lumpedtransformer.jpgâ€Ž