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

[BlackMelon]

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

 

[Charles Link]

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

 

[BlackMelon]

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?

 

[Charles Link]

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.