**Document**

**Name**

# The Voltech Handbook of Transformer Testing

**Description**

## 1.2 B-H Curves

When the primary of a transformer is energized with the secondary unloaded, a small current flows in the primary.

This current creates a 'magnetizing force' that produces the magnetic flux in the transformer core.

The magnetizing force (H) is equal to the product of magnetizing current and the number of turns, and is expressed as Ampere - Turns.

For any given magnetic material the relationship between magnetizing force and the magnetic flux produced can be plotted, and this is known as the B-H curve of the material: -

H (Magnetizing force - ampere turns/metre or Oersteds) |

Figure 2

From the B-H curve it can be seen that as the magnetizing force is increased from zero, the flux increases up to a certain maximum value of flux.

Above this level, further increases in magnetizing force result in no significant increase in flux. The magnetic material is said to be 'saturated'.

A transformer is normally designed to ensure that the magnetic flux density is below the level that would cause saturation.

The flux density can be determined using the following equation: -

E = 4.44 NBAf

Where..

E represents the rms value of the applied voltage.

N represents the number of turns of the winding

B represents the maximum value of the magnetic flux density in the core
(Tesla)

A represents the cross sectional area of the magnetic material in the core
(sq. metres)

f represents the frequency of the applied volts

Note

1 Tesla = 1 weber/metre^{2}

1 weber/m^{2}; = 10000 gauss

1 ampere-turn per meter = 4x10^{-3} Oersteds

In practice, all magnetic materials, once magnetized, retain some of their magnetization even when the magnetizing force is reduced to zero.

This effect is known as 'remanence' and results in the B-H curve for the material exhibiting a response to a decreasing magnetizing force that is different to the response to an increasing magnetizing force.

In practice then real magnetic materials have a B-H curve as follows :-

Figure 3

The curve shown above is termed the 'hysteresis' loop of the material, and represents the true B-H response of the material. (The B-H curve shown in figure 2 represented the average or mean of the true B-H loop response).

The slope of the B-H curve, the saturation level and the size of the hysteresis loop are dependent on the type of material used, and on other factors. This is illustrated using the following examples: -

Figure 4 |
Low-grade Iron core High saturation flux density Large loop = Large Hysteresis loss Suitable for 50/60Hz |

Figure 5 |
High grade iron core High saturation flux density Medium loop = Medium Hysteresis loss Suitable for 400Hz transformers |

Figure 6 |
Ferrite core - no air gap Medium saturation flux density Small loop = Small Hysteresis loss Suitable for high frequency transformers |

Figure 7 |
Ferrite core - large air gap Small loop = Small Hysteresis loss Suitable for high frequency Inductors with large dc current. |