# Pitch Factor and Distribution Factor | Winding factor in Alternator

The product of pitch factor K_{p} and distribution factor K_{d} is called as winding factor.

i.e., K_{w }= K_{p} K_{d}

## Pitch factor

Before getting to know about the pitch factor and distribution factor in detail, you need to know about the armature winding in the alternator and its types.

Now, What is pitch factor?

The ratio of phasor sum of induced EMFs per coil to the arithmetic sum of induced EMFs per coil is known as **pitch factor K _{p} or coil span factor K_{c}**. Its value is always less than unity.

Let us consider, the coil has a pitch short by an angle α electrical degrees from the full pitch. The induced emf in each coil side be E. Now, if the coil is said to be full pitch, then total induced emf in the coil would be 2E.

For a coil, that is short-pitched by α electrical degrees, the resultant induced emf E_{R} is the phasor sum of two voltages α electrical degrees.

The formula for pitch factor is given by

The pitch factor in the above equation is for fundamental component of emf.

If the coil span is reduced by one slot, then the phase angle α between the induced EMFs in the two sides of the coil is given as

## Distribution factor

If all the coil sides of any one phase under one pole are bunched in one slot, the winding obtained is known as concentrated winding.

The ratio of the phasor sum of the EMFs induced in all the coils distributed in a number of slots under one pole to the arithmetic sum of the EMFs induced(or to the resultant of EMFs induced in all coils concentrated in one slot under one pole) is known as **breadth factor K _{b} or distribution factor K_{d}**. Its value is always less than unity.

Let n be the number of slots per pole.

m be the number of slots per pole per phase.

E_{c} be the induced emf in each coil side.

Angular displacement between the slots

The EMFs induced in different coils of one phase under one pole are represented by side AC, CD, DE, EF,… which are equal in magnitude but differ in phase.[Say the magnitude be E and phase difference be 180 degrees]

If bisectors are drawn on AC, CD, DE, EF, they would meet at a common point. This point would be the center of the circle having AC, CD, DE, EF as the chords. They represent the EMFs induced in the coils in different slots.

The resultant emf can be obtained from the below equation,

Thus the distribution factor can be obtained as

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