- It consists of only single winding which is common to both primary and secondary winding.
- It has two end terminals ( PR) acts as primary and one end terminal ( either P or R ) and inter mediate terminal Q acts as a secondary winding ( Figure A ).
- The position of the intermediate terminal Q determines whether auto – transformer works as step down transformer or step up transformer.
- The theory and operation of the auto-transformer is similar to that of conventional two winding transformer.
- The auto transformer is cheaper than the ordinary transformer because of single winding uses less copper than the two winding. Since the voltage / turn is equal in both winding, the voltage develops across each winding depends on number of turns.

- Figure B shows a step down transformer in
which PQ winding acts as a primary having N
_{1}turns and QR winding acts as a secondary winding consists of N_{2}turns. - If the supply
voltage V
_{1}is given to primary winding.

Induced emf per turn ( E

_{t}) = V_{1}/ N_{1}
As we know that the value of E

_{t}is same for both windings.
Secondary voltage V

_{2}= E_{t }× N_{2}_{}

**Saving of copper in auto transformer as step down transformer**

- The weight of winding material ( copper ) is proportional to the length and area of cross section of the conductors.

W a Volume of material

W a ( a × L )

- The cross section of the conductor depends on current ( I ) and length of conductors is proportional to the number of turns ( N ).
- Therefore the weight of copper is directly proportional to ampere - turns ( NI ).

Weight of the copper in the ordinary
transformer ( W

_{O}) = N_{1}I_{1}+ N_{2}I_{2}
Weight of copper in the auto transformer ( W

_{a}) =
Weight of copper in part PQ a I

_{1}( N_{1}– N_{2}) +
Weight of copper in part QR a ( I

_{2}– I_{1}) N_{2}
Weight of copper in the auto
transformer a I

_{1}( N_{1}– N_{2}) + ( I_{2}– I_{1}) N_{2}
a ( I

_{1}N_{1}+ I_{2}N_{2}– 2N_{2}I_{1})- Weight of copper in auto transformer ( W
_{a}) / Weight of copper in ordinary transformer ( W_{O}) = ( I_{1}N_{1}+ I_{2}N_{2}– 2N_{2}I_{1}) / ( I_{1}N_{1}+ I_{2}N_{2})

= ( I

_{1}N_{1}+ I_{1}N_{1}– 2N_{2}I_{1}) / 2N_{1}I_{1}( As N_{1}I_{1}= N_{2}I_{2})
= ( 2I

_{1}N_{1}/ 2I_{1}N_{1}) – ( 2N_{2}I_{1}/ 2I_{1}N_{1})
= ( 1 ) – ( K ) ( As K = N

_{2}/ N_{1}= I_{1}/ I_{2})
= 1 – K

Therefore W

_{a }= ( 1 – K ) W_{O}
Saving in copper = W

_{O}– W_{a}
= W

_{O }– ( 1 – K ) W_{O}
= KW

_{O}- Therefore the saving in copper material depends on the value of K ( Voltage transformation ratio ).
- Higher value of K, more saving in copper material

**Saving of copper in auto transformer as step up transformer**

Weight of the copper in the ordinary
transformer ( W

_{O}) = N_{1}I_{1}+ N_{2}I_{2}
Weight of copper in the auto transformer (
W

_{a}) =
Weight of copper in part PR a I

_{2}( N_{2}– N_{1}) +
Weight of copper in part RQ a ( I

_{1 }– I_{2 }) N_{1}
Total weight of copper in the auto
transformer a I

_{2}( N_{2}– N_{1}) + ( I_{1 }– I_{2 }) N_{1}
a ( I

_{1}N_{1}+ I_{2}N_{2}– 2N_{1}I_{2})
Weight of copper in auto transformer ( W

_{a}) / Weight of copper in ordinary transformer ( W_{O}) = ( I_{1}N_{1}+ I_{2}N_{2}– 2N_{1}I_{2}) / ( I_{1}N_{1}+ I_{2}N_{2})
= ( I

_{1}N_{1}+ I_{1}N_{1}– 2N_{1}I_{2}) / 2N_{1}I_{1}( As N_{1}I_{1}= N_{2}I_{2})
= ( 2I

_{1}N_{1}/ 2I_{1}N_{1}) – ( 2N_{1}I_{2}/ 2 N_{1}I_{1})
= ( 1 ) – ( 1 / K ) ( As K = N

_{2}/ N_{1}= I_{1}/ I_{2})
= ( 1 – 1 / K )

- Therefore W
_{a }= [ ( 1 – 1 / K ) ] W_{O} - Saving in copper = W
_{O}– [ ( 1 – 1 / K ) ] W_{O}

= [ 1 – 1 + 1 / K ] W

_{O }
= ( 1 / K ) W

_{O}- Therefore the saving in copper material depends on the value of 1 / K.
- Lower value of K, more saving in copper material

**Application**

- The auto transformer is used for starting of synchronous motor and induction motor. Its winding is used only during starting period of the motor for a few seconds.
- It is used as a furnace transformer for getting suitable supply voltage for furnace winding from 230 V supply.
- It is used as laboratory equipment to get suitable supply voltage as per requirement.
- To compensate the small voltage drop in a distribution cable by giving small voltage boost.
- It may be used as interconnecting transformer in 132 kV / 66 kV supply system.

**Connection of two winding transformer into a auto transformer**

- The winding connection diagram of an auto transformer from two winding transformer may be as ( I ) Step down transformer ( II ) Step up transformer

- Conversion of two winding transformer into step down auto transformer

- Conversion of two winding transformer into step up auto transformer

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