Undergrad Magnetic Field Intensity At the Inductor's Air Gap (+Fringing Flux)

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The discussion focuses on the impact of an air gap in a transformer's core on magnetic field intensity and core saturation in switching power supply design. The participant shares their derivation and references a paper by Roshen, noting a discrepancy in the scalar potential function related to the air gap term. They question why Roshen's equation lacks a variable present in their own derivation, suggesting it may be a typo. Additionally, there are inquiries about the clarity of their expansion and a lack of expertise in LaPlace expansions. The conversation highlights the complexities of magnetic field calculations in transformer design.
BlackMelon
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Hi there!

Sorry for the unclear images in the previous post. This time I upload pdf files for my derivation and the reference paper.

So, when I design a switching power supply, usually I make an air gap at the transformer's core. This will alter the BH curve, preventing the core saturation. However, as I increase the gap's length, the fluxes fringes. So, the reluctance of the air gap is not high enough to alter the BH curve as I expected.

To solve the problem, I read a paper by Roshen (file Roshen2007.pdf) and derive formulae inside that paper (file Formulae Derivation... .pdf).
I got a mismatch of scalar potential function (equation II.6 in both files).

On the last page of my derivation, I got a term Hg*y/2.
On the second page of Roshen's paper, this term is Hg/lg

I would like to know why Roshen did not put the variable y on that term?

Best Regards,
BlackMelon
 

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Looks to me like a typo in Roshen, but I couldn't follow the expansion completely.
 
Charles Link said:
Looks to me like a typo in Roshen, but I couldn't follow the expansion completely.

May I know which part of my expansion is confusing?
 
BlackMelon said:
May I know which part of my expansion is confusing?
I don't have much expertise at doing the LaPlace expansions, both the integer one, and the continuous one. I'm somewhat familiar with the Legendre type method of solution, and I think this one is similar to that, but I have little expertise with it.
 
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