[TCML] charging reactors

bartb bartb at classictesla.com
Fri Mar 6 20:23:57 MST 2009

```Hi Kurt and All (thanks for all your replies),

I looked at all the formula's given and they all appear to be Wheeler
from an air core inductance derivation. The formula that I used, I'm not
sure of it's nature, but it is far off. However, the proline calculator
is still significantly off as well from these Wheeler formula's by about
1H for the coil example I used. In my spreadsheet, layers are an input
and used to determine total turns. Although the calculators turns and
layers match my own, the Wheeler formula shows 3.95H where proline shows
5H. So, there is something else proline is looking at. However, the
Wheeler formula (however you use it), is an air core multilayer coil
formula.

A magnetic mass such as ferrite, iron, or various composites will vary
permeability substantially. While researching this aspect, the following
formula was predominant:
L=(0.4*pi*µ*N^2 *A*10^-8 )//l/
where:
L=inductance (henries)
µ=core permeability
N=number of turns
A=core across section (cm^2 )
/l/=magnetic path length(cm)

The permeability of cores can vary widely, so one has their work cut out
for them using a magnetic core.

But as Kurt mentioned, maybe an air core inductor would suffice. This
would certainly make the coil design far easier and L far more
manageable. Considering the low current, it just might be the way to do it.

Take care,
Bart

Kurt Schraner wrote:
> Hi,
>
> Bart, I apparently seem using the same formula as the guy on
> http://www.pronine.ca/multind.htm
>
> The formula seems to stem from the radio amateurs handbook. I took
> mine from:
>
> ARRL Handbook 1957 / p27
>
> a=avg.diameter in inches = (Di+Da)/2
> b=length of winding in inches
> c=radial depth of winding in inches = (Da-Di)/2
>
> L[uH]=(0.2*a^2*n^2)/(3*a+9*b+10*c)
>
> I've verified it's results on my induction coils (without core, of
> course), and it works well, i.e.:
> My 26k turns induction coil secondary: measured 15.15H; calc. 15.09H;
> Error 0.42%
> My 48k turns induction coil secondary: measured 49.8  H; calc. 47.7
> H; Error 4.22%
>
> More precise methods could probably been taken from NBS circular 74,
> but the above is about within the precision of my LCR meter.
>
```