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

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SUMMARY

The discussion centers on the design of switching power supplies, specifically addressing the impact of air gaps in transformer cores on magnetic field intensity and core saturation. The user, BlackMelon, references a paper by Roshen (2007) to derive formulae related to the scalar potential function, noting a discrepancy between their derivation and Roshen's equation II.6. The key issue is the presence of the variable 'y' in BlackMelon's formula, which is absent in Roshen's, leading to questions about potential typographical errors in the reference material.

PREREQUISITES
  • Understanding of magnetic circuits and core saturation principles
  • Familiarity with the BH curve and its implications in transformer design
  • Knowledge of LaPlace expansions and their application in electromagnetic theory
  • Experience with scalar potential functions in magnetic field calculations
NEXT STEPS
  • Review the paper "Magnetic Field Intensity in Air Gaps" by Roshen (2007) for detailed derivations
  • Study the principles of core saturation and its effects on transformer efficiency
  • Learn about LaPlace transformations in electromagnetic applications
  • Explore advanced techniques for analyzing magnetic circuits, such as the Legendre method
USEFUL FOR

Electrical engineers, power supply designers, and researchers in electromagnetic theory seeking to deepen their understanding of transformer core design and magnetic field analysis.

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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