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An autotransformer does not normally use any capacitors as it is a transformer with one winding and the lower voltage is taken from a tap part-way up the winding. A capacitor could be added if there is a concern about the power factor presented by the autotransformer to the supply.
An autotransformer is a transformer with at least two windings where a part of one winding (the common winding) is shared between both primary and secondary outputs.
A true autotransformer consists of one, tapped, winding. For a step-down transformer, part of the winding is in series with the supply and the other part is common to both the supply and the load. For a step-up autotransformer, part of the winding is in series with the load, while the other part is common to both supply and load.But you can also use a mutual transformer as an autotransformer, by connecting the two windings in series and, then, described as above.
"Auto" refers to the single winding used an auto transformer.