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

#### NatsuNatsume

Joined Aug 3, 2023
2
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 fluxe 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).
However, I got a mismatch between scalar potential functions in both papers (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?

#### Attachments

• 1.1 MB Views: 6
• 1.6 MB Views: 4

#### sgodblacktechy

Joined Jul 27, 2023
6
As for the mismatch in Roshen's paper, it's always a good idea to double-check these things. It's possible that the variable y was omitted in the term for simplicity or might be hidden in other parts of the derivation.

#### MrAl

Joined Jun 17, 2014
10,881
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 fluxe 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).
However, I got a mismatch between scalar potential functions in both papers (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?

Hello there,

Are you really saying that you cannot make the gap large enough to alter the BH curve enough for your application?
That sounds really hard to believe because the permeability drops really fast with even a small gap.
If you really can't get it down low enough, then maybe you are starting with the wrong core material to begin with.
I assume you know that you may have to add more wire turns as you increase the gap length.

What is the shape of the core, and what are the dimensions of the core, and what kind of material is it, and what is the typical permeability of the material?
Also, what is the application.

Last edited:

#### NatsuNatsume

Joined Aug 3, 2023
2
Hello there,

Are you really saying that you cannot make the gap large enough to alter the BH curve enough for your application?
That sounds really hard to believe because the permeability drops really fast with even a small gap.
If you really can't get it down low enough, then maybe you are starting with the wrong core material to begin with.
I assume you know that you may have to add more wire turns as you increase the gap length.

What is the shape of the core, and what are the dimensions of the core, and what kind of material is it, and what is the typical permeability of the material?
Also, what is the application.
Sorry. I mean I have reached my intended limit of how wide the gap should be. Otherwise, the power loss I calculated will be too high and the efficiency of the whole power supply will fail the specification.

The core shape is ETD29/16/10
https://www.tdk-electronics.tdk.com/inf/80/db/fer/etd_29_16_10.pdf

The material is N87

The permeability is around
3750 at 200mT (See page 3 of N87). The initial permeability is 2200 +-25% (see page 2)

For the circuit below, I have shown just only the important part. For more details, please read INN3679C's datasheet.
https://www.power.com/products/innoswitch/innoswitch3-ep/inn3679c-h606-0

This IC has the feature: the higher the current of its drain pin is, the higher the switching frequency will be.
So, this will reduce the peaks of the drain pin's current and the magnetization current, iLm, of the transformer. So, we don't need to use a giant core just only to handle with the high magnetic flux density at low input voltage (120Vdc).
From figure 6 of the datasheet, this plots the normalized drain current ( ID/ILIM = ID/2.13A) vs the switching frequency

#### MrAl

Joined Jun 17, 2014
10,881
Hello again,

Yes your efficiency can suffer that's a drawback.

Did you try using a core with lower permeability to begin with?

This looks much (although not exactly) like a modern wall wart circuit. Perhaps you can find more design details by looking up one of those simpler controllers that have maybe 4 pins. They pulse the primary just like you are doing and use a similar regulation method with feedback through an opto coupler. You have probably seen these around too. The DC output regulator is often a TL431 type chip.
If you have trouble finding this type of application I'll look around in my own older notes.
If I remember right, they might slow the transformer construction details also.

#### Janis59

Joined Aug 21, 2017
1,781
General formula for any core containing airgap is n*I=B(hcore/μ0μrel+Hair0). All the units - SI basic.