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Re: [TCML] charging reactors - Inductance formulas



Stephen Hiscock wrote:
<snip>
as you can see no-one seems to be consistent with terms they use, or letters that assign to variables...eg why is "a" the radius?, why is "b" the length?, they swap radius for diameter and vice versa for no apparent reason and it doesn't make the formulas anymore accurate or easy to use..

If we all started from first principles and derived the inductance formulas from scratch there wouldn't be much of an issue - and I believe Dr. Antonio Carlos M. de Queiroz has written a program to derive the inductance for any coil....

Regards
Stephen

P.s I will post some more general formulas tomorrow on inductance and calculating the Coil of Maximum Inductance - as I'm due to do some work which I have to rush of to...

Hi Stephen,

Your correct, there is a lot of inconsistency out there and inaccuracy. The formula I originally posted, I found again listed and there is no mention to average radius's. As a matter of fact, it distinctly calls out inner radius and outer radius (pictorially as well) which for the particular formula, is absolutely wrong. For example, take a look at this:
http://microblog.routed.net/wp-content/uploads/2008/10/pancakewheel.pdf

If you follow that paper, L will be roughly 1/2 of the real deal, because it is a hack job of the Wheeler approximation.

What is correct and should be used here are Wheeler approximations such as:
L(uH) = (0.8 * a^2 * n^2) / (6*a + 9*b + 10*c ) inputs in inches.
L(uH) = (31.6 * a^2 * n^2) / (6*a + 9*b + 10*c) inputs in meters.
Both assume:
a = average radius of coil
b = length of windings
c = difference between outer and inner radii

The single layer air core that you showed is also what the Proline Calculator used (except they are calling out d as average diameter) which is also a nice try but another example of a hack job.
L(uH) = (d2 * n2)/(18*d+40*l)

Regarding maxL. I look forward to seeing what you have there. Max L is very useful in these type of multilayer inductor designs because as it should minimize DCR and maximizes L for the least wire length (which should be a goal with this type of design).

Take care,
Bart
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