Introduction to Auto-transformers
An autotransformer is an electrical transformer with only one winding. The auto prefix refers to the single coil rather than any automatic mechanism. In an autotransformer portions of the same winding act as both the primary and secondary. The winding has at least three taps where electrical connections are made. An autotransformer can be smaller, lighter and cheaper than a standard dual-winding transformer however the autotransformer does not provide electrical isolation.
At first sight, an autotransformer appears to be similar to a resistance potential divider. But this is not so. A resistive potential divider can’t step up the voltage, whereas it is possible in an autotransformer.
Operation
An autotransformer has a single winding with two end terminals, and one or more terminals at intermediate tap points. The primary voltage is applied across two of the terminals, and the secondary voltage taken from two terminals, almost always having one terminal in common with the primary voltage. The primary and secondary circuits therefore have a number of windings turns in common. Since the volts-per-turn is the same in both windings, each develops a voltage in proportion to its number of turns. In an autotransformer part of the current flows directly from the input to the output, and only part is transferred inductively, allowing a smaller, lighter, cheaper core to be used as well as requiring only a single winding.
One end of the winding is usually connected in common to both the voltage source and the electrical load. The other end of the source and load are connected to taps along the winding. Different taps on the winding correspond to different voltages, measured from the common end. In a step-down transformer the source is usually connected across the entire winding while the load is connected by a tap across only a portion of the winding. In a step-up transformer, conversely, the load is attached across the full winding while the source is connected to a tap across a portion of the winding.
As in an ordinary transformer, the ratio of secondary to primary voltages is equal to the ratio of the number of turns of the winding they connect to. For example, connecting the load between the middle and bottom of the autotransformer will reduce the voltage by 50%. Depending on the application, that portion of the winding used solely in the higher-voltage (lower current) portion may be wound with wire of a smaller gauge, though the entire winding is directly connected.
As shown in the figure current I2 flows through the load and current I1 is taken from the source. Neglecting losses, Input power = Output power Or V1I1cosθ1 = V2I2cosθ2 If internal ( or leakage) impedance drops and losses are neglected, then cosθ1 = cosθ2.N2 N1
Hence V1I1= V2I2
Or V2/V1= I1/I2=N2/N1 = k
Here , k is less than unity. The above expressed relation is identical with a two winding transformer. Applications Autotransformers are frequently used in power applications to interconnect systems operating at different voltage classes, for example 138 kV to 66 kV for transmission. It is used in industry to adapt machinery built (for example) for 480 V supplies to operate on a 600 V supply. A special form of autotransformer called a zig zag is used to provide grounding (earthing) on three-phase systems that otherwise have no connection to ground (earth). A zig-zag transformer provides a path for current that is common to all three phases (so-called zero sequence current). In audio applications, tapped autotransformers are used to adapt speakers to constant-voltage audio distribution systems, and for impedance matching such as between a low-impedance microphone and a high-impedance amplifier input.

Advantages Reduced core length that is the weight of the autotransformer core is decreased. Owing to the reduction in conductor and core materials, the ohmic losses in conductor and the core loss are lowered. Therefore, an autotransformer has higher efficiency than a two winding transformer of the same output. Reduction in the conductor material means lower value of ohmic resistance. A part of the winding being common, leakage flux and therefore, leakage reactance is less. In other words, an autotransformer has lower value of leakage impedance and has superior voltage regulation than a two-winding transformer of the same output.
Limitations
An autotransformer does not provide electrical isolation between its windings as an ordinary transformer does. A failure of the insulation of the windings of an autotransformer can result in full input voltage applied to the output. This is an important safety consideration when deciding to use an autotransformer in a given application. Furthermore, if the neutral side of the input is not at ground voltage, the neutral side of the output will not be either.
Because it requires both fewer windings and a smaller core, an autotransformer for power applications is typically lighter and less costly than a two-winding transformer, up to a voltage ratio of about 3:1; beyond that range, a two-winding transformer is usually more economical.
In three phase power transmission applications, autotransformers have the limitations of not suppressing harmonic currents and as acting as another source of ground fault currents. A large three-phase autotransformer may have a "buried" delta winding, not connected to the outside of the tank, to absorb some harmonic currents.
In practice, transformer losses mean that autotransformers are not perfectly reversible; one designed for stepping down a voltage will deliver slightly less voltage than required if used to step up. The difference is usually slight enough to allow reversal where the actual voltage level is not critical. This is true of isolated winding transformers too.
Like multiple-winding transformers, autotransformers operate on time-varying magnetic fields and so cannot be used directly on DC.

Experimental analysis and working
In our project we have designed an autotransformer of 400 turns. We have observed the voltages at different terminals by giving it a supply of 15 volts. The different voltages observed at different number of turns are mentioned on the below table.

S.no No. Of turns Observed volatge
1. 0-400 8
2. 0-300 6.27
3. 0-200 3.39
4. 0-100 1.13

From the table we can observe that the result obtained is as per the principle of the autotransformer. Since the core was chosen randomly, some losses can be observed.