An *auto-transformer *is a transformer with only one winding wound on a laminated core. A part of winding is common to the both primary and secondary circuits.

In a two winding transformer, primary and secondary windings are electrically isolated, but in a auto-transformer the two windings are not electrically isolated.

**Construction**

The winding is wound on laminated silicon steel. Laminations are used to reduce the eddy current losses, whereas, hysteresis loss is reduced by using silicon steel.

According to construction point of view, auto-transformer is divided into two types. In one type of transformers, there is a continuous winding with taps brought out at convenient points determined by the designed secondary voltage. And in other type of auto-transformer, there are two or more different coils which are electrically connected to form a continuous winding. **Enamelled copper **is used for winding.

A simple arrangement of a step-down auto-transformer is shown in figure, where N_{1 }and N_{2 }are the number of turns between winding AC and winding DC respectively.

**Working**

**At no-load**

When we apply a AC voltage to the primary side of a auto-transformer, the exciting current flows from A to C and it establishes a working m.m.f. directed vertically downward in the core.

**At load**

When switch S is called, the current in winding BC must flow from C to B, in order to create an m.m.f. opposing the exciting or working m.m.f. , according to Lenz’s Law. Since the working m.m.f. in a transformer remains substantially constant at its no-load value, the primary must draw additional current I, from the source, in order to neutralize the current of I_{CB}. In winding AC, I flows from A to C, whereas in winding BC I_{2 }flows from C to B.

I_{3 }= I_{2 }– I_{1}

m.m.f. of winding AB = I_{1 }(N_{1 }– N_{2})

= (I_{2 }– I_{1}) N_{2}

= I_{3}N_{2 }= m.m.f. of winding CB

Transformed VA = V_{AB}I_{AB }= (V_{1 }– V_{2}) I_{1}

Total input VA to transformer = V_{1}I_{1 }= output VA

Conducted VA = total input VA – transformed VA

= V_{1}I_{1 }– (V_{1 }– V_{2})I_{1 }= V_{2}I_{1}

Neglecting internal impedance drops and losses

**Saving of Copper Cu**

Volume and hence weight of Cu, is proportional to length and area of the cross-section of the conducting materials or conductors. Now, length of the conductors is proportional to the number of turns and cross-section depends on current. Hence weight is proportional to the product of the current and number of turns.

∴ Weight of conductor for winding AB ∝ (N_{1 }– N_{2}) I_{1}

Winding BC carries a current (I_{2} – I_{1}) and has N_{2 }turns

∴ Weight of conductor for winding BC ∝ (I_{2 }– I_{1}) N_{2}

_{}Hence, total weight of conductor in an auto-transformer is

∝ I_{1}(N_{1} – N_{2}) + N_{2} (I_{2 }– I_{1})

∝ 2 (I_{1}N_{1 }– I_{1}N_{2})

∝ 2 (N_{1 }– N_{2}) I_{1}

If two winding transformer were to perform the same duty, then

Weight of copper on its primary ∝ N_{1}I_{1}

Weight of copper on its secondary ∝ N_{2}I_{2}

∴ Total weight of conductor in a two-winding transformer

∝ N_{1}I_{1 }+ N_{2}I_{2}

∝ 2 N_{1}I_{1}

Weight of conductor in auto-transformer = (1-k)(weight of conductor in two-winding transformer)

Saving of conductor material if auto-transformer is used = k X Conductor weight in two-winding transformer.

If k = 0.1, saving of conductor material is only 10% and for k = 0.9, saving of conductor material is 90%. Hence the use of auto-transformer is more economical only when the voltage ratio k is more nearer to unity.

**Advantages of Auto-transformers**

- As discussed above, an auto-transformer require less copper than a two winding transformer of the same ratings.
- An auto-transformer has smaller size than a two winding transformer.
- An auto-transformer has better efficiency than a two winding transformer of the similar rating.
- Auto-transformer requires less exciting current than a two winding transformer of the same rating.
- An auto-transformer has better voltage regulation than a two winding transformer of the same rating.

**Disadvantages of Auto-transformers**

- It can be operated on light loads.
- The short circuit current is much larger than that for the two winding transformer of the same rating.

**Applications of auto-transformers**

- Auto-transformer are used to give a small boost to a distribution cable to the correct voltage drop.
- These transformers are used as auto-starter transformers to give upto 50 to 60% of full voltage to an induction motor during starting.
- Auto-transformers are used in control equipment for 1-phase and 3-phase electrical locomotives.
- These transformers are used as interconnecting transformers in 132KV/400KV system.