# B-H Curve Hysteresis Loop in Transformers

The relationship between induced magnetic flux density (B) and magnetizing force (H) helps us to understand  B-H curve Hysteresis loop in transformers . In simple words, this relation determines the behavior of ferromagnetic materials (used in transformers core) when magnetic field passes through them.

Basically, magnetizing force “H” is the magnetic field which magnetizes a material whereas the value of magnetic flux density (B) represents how much the material is magnetized. The area of B-H curve is actually the energy loss occur in the core of transformers.

### B-H Curve in Transformers: In the above fig, B-H Hysteresis loop curve shows the value of magnetic flux density (B) varies with respect to the magnetic field intensity(H). At starting, transformer core is unmagnetized with both B and H is at point A (shown in the above graph). When the applied current in primary coil starts to increase, magnetic field intensity (H=NI)  increases and so does the flux density in the core will increase (transformer core starts to magnetize). Flux density in the core keeps on increasing with the increase of magnetic field intensity up to certain value.

After a particular value of magnetic flux density (B), flux in the core will not increase any further with the increase of magnetic field intensity. Any further increase in magnetic field intensity doesn’t result in the increase of magnetic flux density. At that point, the core will starts to lose its electromagnetic property and gradually saturate. The point (B) shown in the above graph is the saturation point.

Now, if we reduce the magnetic field intensity (By decreasing the primary current in the coil), it can be observed that the magnetic flux density doesn’t come back along the same path as it exhibits hysteresis. When magnetic field intensity is zero (means external magnetizing field is removed) at point A, there is still some amount of residual magnetic flux remains in the core material (point A-C in the graph). This is known as Retentivity (residual flux density). This lagging of flux density(B) with respect to magnetic field intensity (H= NI) is known as hysteresis loss ↗.

In order to remove the residual magnetic field, we have to apply magnetizing field in the reverse direction (by reversing the current) so that the flux in the core (point C-D) is totally removed. The negative value of magnetic field intensity required to remove the residual magnetic flux is known as coercivity (Point A-D).

If we keep on increasing magnetic field intensity (by increasing current) in the negative direction, flux in the core now starts to increase in the negative direction. After a particular value of flux density, flux in the core again doesn’t increase any further with the increase of magnetic field intensity and saturates (point E) in the opposite direction.

If we bring magnetic field intensity again in the positive direction (by increasing the primary current), flux density (B) again exhibits hysteresis nature. Point F in the graph shows that there is some value of flux density (residual flux density) since the magnetic field intensity is zero at that point. To get residual magnetic field  back to zero, again we have to apply extra magnetizing force (point F-G) until it is removed.

Moreover, further increasing the value of field intensity makes the flux density to move towards saturation point(B). This makes the whole complete B-H curve known as hysteresis loop B-H curve. All the magnetic materials used in transformer core exhibit this kind of hysteresis nature.

##### Conclusion:

Hysteresis loss occur in the transformer core is directly proportional to the area of the hysteresis loop. Hence hysteresis losses can be reduced by using core material having less hysteresis loop area. Silicon and steel used for the manufacturing of transformer core generally have less hysteresis loop area. In the above fig, we can analyze that hysteresis loop having large area required large coercive force while small hysteresis loop required small coercive force. Small coercive force means less energy (hysteresis) losses while large coercive force required results in high energy losses in the core of transformers.

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