# Auto Transformer Calculations With Formula

### Auto Transformer calculations:

Autotransformers are the single winding transformer which has output and input will be in the same winding. Hence another winding can be eliminated, this is the major advantage of the autotransformer.

### Transformation ratio calculations:

Transformation ratio k is equal to the ratio between secondary output voltage V2 in Volts to primary input voltage V1 in volts or ratio between primary current I1 in amps to Secondary output current I2 in amps or the ratio between secondary turns N2 to primary winding N1.

Transformation ratio = primary input voltage / secondary output voltage = Primary current /secondary current = Secondary turns / primary turns

k = V1 / V1 = I1 / I2 = N2 / N1

Also using above formula you can find the unknown value of the auto transformer.

### Power transformation formula:

The total power S(Con-VA) in VA is conducted from the autotransformer is equal to the transformation ratio times of the product of the secondary voltage and secondary current.

S(Con-VA) = k x V2 x I2

At the same time,

Power transformed in VA = V2 x I2 x (1 – k) Volt-Amp

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### Relationship between the autotransformer and two winding transformer:

Autotransformer and two winding transformer can be used in place of each other. But auto transformers are having wide advantage such as low copper consumption, less voltage regulation, reduced VA rating and low losses.

### Conductor Weight Calculation:

Conductor Weight of the autotransformer is equal to the difference between the conductor weight of the two winding transformer to transformation times of the conductor weight of the two winding transformer.

Autotransformer Conductor = (1 – k) x two winding transformer conductor

### kVA rating calculation:

kVA rating of the autotransformer is equal to the kVA rating of the two winding transformer divided by one minus transformation ratio.

kVA Autotransformer = kVA of two winding transformer / (1 – k)

### Loss Calculation:

Loss of the autotransformer is equal to the difference between the loss of the two winding transformer to transformation times of the loss of the two winding transformer.

Autotransformer loss = (1 – k) x loss of the two winding transformer

### Impedance drop calculation:

Impedance of the autotransformer is equal to the difference between the impedance of the two winding transformer to transformation times of the impedance of the two winding transformer.

Autotransformer impedance = (1 – k) x impedance of the two winding transformer

### Voltage regulation calculation:

Autotransformer voltage regulation is equal to the difference between the voltage regulation of the two winding transformer to transformation times of the voltage regulation of the two winding transformer.

Auto transformer voltage regulation = (1 – k) x two winding transformer voltage regulation