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

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    Air gap Transformer
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Discussion Overview

The discussion revolves around the analysis of magnetic field intensity in an inductor with an air gap, particularly focusing on the effects of the air gap on the BH curve and the discrepancies in formula derivations from a referenced paper by Roshen. The scope includes theoretical derivation and technical clarification related to magnetic circuits in switching power supplies.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • BlackMelon describes the impact of an air gap on the BH curve in transformer design, noting that increasing the gap length leads to fringing flux and unexpected reluctance behavior.
  • BlackMelon identifies a mismatch in the scalar potential function between their derivation and Roshen's paper, specifically questioning the absence of the variable y in a particular term.
  • Some participants suggest that the discrepancy may be a typo in Roshen's work, but express uncertainty about the details of the expansion.
  • BlackMelon seeks clarification on which part of their expansion is confusing to others, indicating a lack of expertise in LaPlace expansions and inviting further discussion on the topic.

Areas of Agreement / Disagreement

There is no consensus on the nature of the discrepancy in the formulae, with some participants suggesting it may be a typo while others express uncertainty about the derivation process. The discussion remains unresolved regarding the correct interpretation of the terms involved.

Contextual Notes

Participants express varying levels of expertise in mathematical techniques relevant to the discussion, which may influence their understanding of the derivations and the specific terms in question.

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.
 
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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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