# Auto Transformer

An **auto transformer** has one winding only Part of this winding being common to both primary and secondary. Primary and secondary windings are not electically isolated as in the case of a two winding transformer. Because of one winding. It uses less copper and hence is cheaper. It is used where transformation ratio differs little from unity. In Figure 1 step up and step down auto transformers are shown.

**Figure 1. Auto Transformer (a) Step Up (b) Step Down**

In Figure 1(a) AB is primary winding have N_{1} turns and BC is secondary winding having N_{2} turns. Neglecting losses, we can write:

V_{2} / V_{1} = I_{1} / I_{2} = K

Where current in section BC is (I_{2} - I_{1})

## Saving of Copper

Volume and hence weight of copper is proportional to the length and area of cross-section of the conductors, but length of conductor is proportional to the number of turns and cross-section of conductor depend on current. Hence weight of conductor is proportional to the product of current and number of turns.

**Considering the Figure 1:** Weight of copper in section AC is α (N_{1} - N_{2}) I_{1} weight of copper in section BC is α N_{2} (I_{2} - I_{1}). Total weight of copper in auto transformer is proportional to (N_{1} - N_{2}) I_{1} + N_{2} (I_{1} - I_{1}). Now consider a two winding transformer performing the same duty, weight of copper on its primary is proportional to N_{1}I_{1} and weight of copper on its secondary is proportional to N_{2}I_{2}.

Total weight of copper is α (N_{1}I_{1} + N_{2}I_{2})

Thus

Dividing and multiplying by N_{1}I_{1} we get:

Weight of copper of in auto transformer:

Wa = (I - K) weight of copper in 2-winding transformer, W_{2}

Saving = W_{2} - W_{a}

= W_{2} - (I - K)W_{2}

= W_{2} - W_{2} + KW_{2}

= KW_{2}

Saving = K (Weight of copper in 2-winding transformer. Hence saving will increase as "K" approches unity.

## Uses of Auto Transformer

- As a booster: The voltage drop occurring in transmission lines can economically be compensated by the use of auto transformer.
- In an induction motor starter, it is used to lower the applied voltage of motor at the starting.
- It is used in furnaces for getting convenient supply.
- It is used in electrical laboratories for having low voltages.