B-H curve of core with air gap

Thread Starter

mothermohammad

Joined May 17, 2014
69
Hi,

As you know, with the air gap in the core, we reach a core whose B-H curve is linear. In addition, The Hgap is more than Hcore, and Bgap is lower than Bcore.
My question is the new B-H curve belong to what area of core, the gap region or the inside the core?
If the new B-H curve is for the total of the core, why the Bgap and Bcore are different? as a consequence, why we have different H?


Thanks
 

wayneh

Joined Sep 9, 2010
17,496
The new B-H curve is for the entire magnetic circuit including the gap. The core and the gap both contribute since they are both part of the magnetic circuit.
 

Thread Starter

mothermohammad

Joined May 17, 2014
69
Thank you so much.
In the Lecture of the University of California Santa Cruz, there is an example of a magnetic circuit containing air gap, in which the magnetic density, B, in the air gap is 0.25 T, and the B in the core is 0.36 T (according to BeAe=BgAg). Further, the H (magnetic intensity) in the air gap is much more than the H in the core.
Indeed, although the air gap B is lower than B in the core, the air gap H is much more than the core H!
How can it be? How can we show these two points on the same B-H curve?
Please see the attachment
 

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Thread Starter

mothermohammad

Joined May 17, 2014
69
I calculated the new permeability of the core and it became 67.7 rather than 6000. Further, the ratio permeability of the air gap became 0.98 rather than 1.
 

Attachments

wayneh

Joined Sep 9, 2010
17,496
The core is a good conductor of the magnetic field lines, just as a wire is a good conductor and will have a low voltage drop across it compared to the high resistance of the air gap.
 

MrAl

Joined Jun 17, 2014
11,396
Hi,

As you know, with the air gap in the core, we reach a core whose B-H curve is linear. In addition, The Hgap is more than Hcore, and Bgap is lower than Bcore.
My question is the new B-H curve belong to what area of core, the gap region or the inside the core?
If the new B-H curve is for the total of the core, why the Bgap and Bcore are different? as a consequence, why we have different H?

Thanks
Hi,

The general view is that the core has a certain BH curve, and if you look at that curve it extends a certain distance horizontally until the core material reaches some particular level of saturation.
Now if we introduce a single air gap, the BH curve is now extended to a higher value along the horizontal axis until that same particular level of saturation is reached. Since the horizontal axis is considered to be proportional to current in the winding, that means that the construction with the air gap can handle a higher level current before the core material saturates. Once the core material saturates, the entire inductance of the construction drops and that can have the effect of causing the construction to draw more current which in turn pushes it deeper into saturation.

The simplest view of what the air gap does is it acts the same as the core material, except with a much wider length than the actual air gap, and the increased length is approximately proportional to the ratio of the permeability of the core material to the permeability of the gap material. Since the gap is usually air and usually considered to have relative permeability of 1, that means that the air gap begins to look like a construction made up entirely of core material with no air gap but with the magnetic path length increased by the length of the core times the permeability of the core. In other words, the air gap makes the core look much longer than it really is if it did not have an air gap.
So for a quick example, if the core magnetic path length is 10 and the permeability is 100, then with the introduction of an air gap of 0.1 units of length the construction will behave similar to a construction that is made up of core material only with no gap but with length of 10+10*100*0.1=110 units of length.

The whole ball game is how the construction behaves from an external view point because we introduce a gap so that we get more favorable electrical qualities out of the inductor.

To understand how we can have a higher H in the air gap, we'd have to see the exact construction, and the exact original problem statement along with any original drawings. The description as given so far seems too random to be able to explain because the H is different for the air gap than in the core material.
 
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Thread Starter

mothermohammad

Joined May 17, 2014
69
Thank you for your attention and answer.

I think when we want to consider the B or H of the air gap, we should not use the amended B-H curve.
 
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