Hello, folks!

Long story here. I need to wind about a dozen of inductances for driving 8W CFL UV lamps for UV lightbox. I did a small research on the topic and came to a conclusion, that using Iron powder or MPP cores is to expensive in that particular case. On the other hand, there are many types of regular toroidal ferromagnetic cores that are dirt cheap and widely available. They come with initial permeability of 1000 to 2500, making them useless for relatively high current (in my case 0.7-0.8 A according to rough calculations) application due to core saturation. As everybody knows, this problem can be solved by introduction of an air gap into the magnetic path. So, I decided to go that way and wind some gapped inductances. To do so, I need some kind of solution-finding tool to calculate core and winding parameters. The software for such calculations is mostly stick to the E-shaped cores and some standard EPCOS types of core materials like N30, N27, N87. I did some research and wrote a simple program (see the attached file) that can calculate inductance specification from arbitrary toroid size/shape, desired inductance, initial permeability, wire turns and diameter, current, core saturation, fill factor, current density and any combination of this parameters. Not a rocket since, actually, just an implementation of standard inductance related equations with some validity checking. This program let me punch in just any combination of parameters and immediately see the result.

But this not even a half way to the solution! The real problem starts right at the point where the Air Gap break the core (and magnetic path) in two pieces. I fount, that the well known reluctance equation, that can be found in famous Wm. T. McLyman's "Transformer and Inductor Design Handbook 4th Ed" is not accurate enough cause of fringing flux effect and it's impact on the final reluctance. The calculation of the fringing flux effect is simplified, giving lower results in compare to what is really measured. Sure, I can get away with that result and than adapt calculated parameters to what I get on practice by experimenting (furthermore I have a good RLC-meter and can build a rig for measuring saturation current), but this is not a true engineering way (as I will not be able to distribute the result if I need to produce just s slightly different inductance) and currently I have a plenty of time for analytical solution before my home lab will became functional back again.

Fortunately, after a long and hard search, we found a recent article that describes a modern approach for calculation air gap reluctance with improved fringing flux effect calculation. This is achieved by dividing air gap to typical sections and treating the whole thing as a sum of several pre-defined elements, rather than a simple gap. See the attached document: "A Novel Approach for 3D Air Gap Reluctance Calculation" by J.Muhlethaler, J.W.Kolar and A.Ecklebe. Accidentally, I found that Mr. Jonas MÃ¼hlethaler is the chair man at the Gecko Simulations - the developer company of the GeckoMAGNETICS simulation tool, implementing that method for core calculations, meaning some serious math and since is involved here.

The problem with the method above is in two basic things. First of all, I was not able to figure out how to use it even for described cases. This is due to my math. It is more than a decade since I did math and physics in university. It seems, that I'm way to stupid for this to be implemented in code and I need help in calculation chain to be implemented in code. The other problem is in core shapes. The described cores are... yap, orthogonal/rectangular: O, E and E-I cores and I, from initial point of view, see no way how to use this methods on toroidal cores. Another dead end. In my opinion, the solution is somewhere near to "Air gap type 1", described in section II (Fig. 4), but I have no clue how to handle the 'high' of the affected core side and it's shape on sides as they are round.

Here is the toroidal core with a gap and magnetic flux for such core. It is a little bit rainbowish, but hope this will help.

Dimensions in Fig. 1:

Cw - core width

Ch - core heigh

Lg - gap length

Ho - affected heigh of the outer side of the core

Hi - affected heigh of the inner side of the core

OD - core outer diameter

ID - core inner diameter

So, help needed.

P.S. In case the solution will be found, I will make the program and source code available under something like GPLv2, so everybody can use this method for accurate gapped toroid inductance calculations.