Hysteresis Loop: What is it (And What is its Significance)?

What is a Hysteresis Loop?

A hysteresis loop, also called a B-H loop or hysteresis curve, is a plot of magnetic flux density B against magnetizing force H as the field is taken through a full cycle. The loop gives retentivity, residual magnetism (residual flux), coercive force, permeability and reluctance of the material.

The figure below is one B-H hysteresis loop.

Picture a magnetic core wound with insulated wire. That is the circuit used to trace the loop.

The winding is fed from a DC supply through a variable resistor so the current I can be changed. Magnetizing force H is proportional to I:

N is the number of turns and l is the mean magnetic path length of the core, not the wire length. Flux density B follows B = μH while permeability μ is roughly constant. After saturation B barely rises with further H.

The terms below are the ones a hysteresis loop is read for.

Definition of Hysteresis

Hysteresis is the lag of flux density B behind magnetizing force H as the field is changed.

Definition of Coercive Force

Coercive force is the reverse magnetizing force (−H) that brings residual flux density back to zero.

Residual Flux Density

Residual flux density is the magnetic flux per unit area left in the material when H = 0 after the field has been removed.

Definition of Retentivity

Retentivity is how strongly the material keeps that residual magnetism after H is reduced to zero.
The steps below walk around one hysteresis loop.

• Step 1:
  When the supply current (I) is 0, there is no flux density (B) or magnetizing force (H). This is represented by point ‘O’ in the graph.
• Step 2:
  When current is increased from zero value to a certain value, magnetizing force (H) and flux density (B) both are set up and increased following the path o – a.
• Step 3:
  For a certain value of current, flux density (B) becomes maximum (B_max). The point indicates the magnetic saturation or maximum flux density of this core material. All element of core material get aligned perfectly. Hence H_max is marked on H axis. So no change of value of B with further increment of H occurs beyond point ‘a’.
• Step 4:
  When the value of current is decreased from its value of magnetic flux saturation, H is decreased along with decrement of B not following the previous path rather following the curve a – b.
• Step 5:
  The point ‘b’ indicates H = 0 for I = 0 with a certain value of B. This lagging of B behind H is called hysteresis. The point ‘b’ explains that after removing magnetizing force (H), magnetism property with little value remains in this magnetic material it is known as residual magnetism (B_r). Here o – b is the value of residual flux density due to retentivity of the material.
• Step 6:
  If the direction of the current I is reversed, the direction of H also gets reversed. The increment of H in reverse direction following path b – c decreases the value of residual magnetism (B_r) that gets zero at point ‘c’ with certain negative value of H. This negative value of H is called coercive force (H_c)
• Step 7:
  H is increased more in negative direction further; B gets reverses following path c – d. At point‘d’, again magnetic saturation takes place but in opposite direction with respect to previous case. At point‘d’, B and H get maximum values in reverse direction, i.e. (-B_m and -H_m).
• Step 8:
  If we decrease the value of H in this direction, again B decreases following the path de. At point ‘e’, H gets zero-valued, but B is with finite value. The point ‘e’ stands for residual magnetism (-B_r) of the magnetic core material in opposite direction with respect to previous case.
• Step 9:
  If the direction of H again reversed by reversing the current I, then residual magnetism or residual flux density (-B_r) again decreases and gets zero at point ‘f’ following the path e – f. Again further increment of H, the value of B increases from zero to its maximum value or saturation level at point a following path f – a.

The path a – b – c – d – e – f – a forms hysteresis loop.
[NB: The shape and the size of the hysteresis loop depend on the nature of the material chosen]

Significance of Hysteresis Loops

What a hysteresis loops plot is used for:

1. Smaller hysteresis loop area symbolizes less hysteresis loss.
2. Hysteresis loop provides the value of retentivity and coercivity of a material. Thus the way to choose perfect material to make permanent magnet, core of machines becomes easier.
3. From B-H graph, residual magnetism can be determined and thus choosing of material for electromagnets is easy.