An auto transformer is a type of transformer that uses a single winding to transfer electrical energy between its primary and secondary circuits. The primary and secondary circuits are connected by a common winding, with a tap or taps placed along the winding to provide different voltage levels.

　　The working of an auto transformer is based on the principle of electromagnetic induction. When an alternating current flows through the primary winding, it induces a voltage in the secondary winding. The voltage induced in the secondary winding is proportional to the ratio of the number of turns in the primary winding to the number of turns in the secondary winding.

　　Auto-transformers are typically used to step up or step down voltage levels in a power distribution system. For example, an auto-transformer can be used to step down the voltage level from a high-voltage transmission line to a lower voltage level used in a distribution system. The advantage of an auto-transformer over a traditional two-winding transformer is that it is less expensive and more efficient because it uses less copper.

　　However, it should be noted that the disadvantage of an auto-transformer is that it does not provide galvanic isolation between the primary and secondary circuits. This means that the electrical potential between the primary and secondary circuits is not completely isolated, which could cause a safety hazard in certain applications.