Re: [TCML] Question for solid-staters

```Hi Ken,

```
It looks like you could also use coaxial stacked or coplanar single-turn primaries in your system and still achieve the desired multiplication of ampere-turns. It looks to be quite difficult to achieve coupling coefficients much above 0.85 using single-turn air-core coils without resorting to things like bifilar winding.
```
```
To quantify this, I used Antonio's Inca program to solve for the individual winding inductance, mutual inductance, and coupling coefficient between a pair of identical primary windings. Looking at the photo of your coil's 24" x 24" base, I estimated that the diameter of your primary is about 12". I also assumed #4AWG (about 0.20" diameter) insulated primary wire with 1/16" thick insulation. I also assumed two identical single-turn primary windings, one stacked above other the other (configuration 1) and one tucked outside the other (configuration 2). Windings were assumed to be separated just by their two layers of insulation (assumed to be a total of 1/8", for a center-to-center turn separation of 0.325". All primaries were assumed to be about 6" above the floor.
```
Configuration 1 (vertically stacked):
L2 (upper winding) = 0.759 uH
L2 (lower winding) = 0.754 uH
M = 0.574 uH
k = 0.759

Configuration 2 (nested planar):
L1 (inner winding) = 0.759 uH
L2 (outer winding) = 0.811 uH
M = 0.595 uH
k = 0.758

```
The coupling coefficient is relatively insensitive to primary diameter at 12" or above. For example, doubling the primary winding to 24" only increases k to ~0.79 for either configuration. If we reduce the insulation thickness to about 30 mils (between 24" turns), k increases to about ~0.85 - higher, but still below 0.90.
```
```
So, it looks like you have a wide degree of latitude for either stacking or nesting primary turns while still achieving the desired ampere-turn scaling. No need for using partial turns.
```
Bert
--
Bert Hickman
Stoneridge Engineering, LLC
http://www.capturedlightning.com
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Ken Herrick wrote:
```
```Hi, Greg (et al)-

seem to refer to, and the SLAC 76-primary design shows, a coaxial set of
primaries.  But I am referring to a set of primaries that are co-planar
and not coaxial.  That is, in my case, each of the 4 primaries is to
occupy 1/4 of the cross-section of the adjacent secondary.  And, as I
indicated, all 4 are to be driven synchronously, resulting in 4
synchronized flux paths.

My reasoning is this (but see next par.): if the primaries were to be of
nominally identical shape, coaxial and adjacent, with each driven by the
same amount of p-p voltage, the result would deliver no more
ampere-turns than if just a single driving electronics were to be used,
with a single primary having 1/4 the dc resistance. That's because of
transformer action between the primaries.  Whereas with, say, 4
primaries that are co-planar but not coaxial, there would be minimal (or
at least, markedly reduced) magnetic coupling between them.  Each would
generate its own flux path through the secondary and it would be the
flux paths that would add.  The only other way I can see to do it would
be as I had done before: daisy-chain multiple driving sources into one
equivalent primary coil.  But that is more complex since all but 1 of
them must float with respect to the one, so the h.v. sources of the
other 3 must be choke-isolated.  (In any case, of course,
transformer-coupling for each l.v. drive is required, to
galvanically-isolate the l.v. from the mains.)

So...it has just belatedly occurred to me to computer-simulate it; piece
of cake!  Driving a simple 3-coil transformer from 2 identical
sources--one to each of 2 primaries which have respective ("perfect") k
of 1 and with the secondary:primary k of 0.95, I get only about 15%
difference in the rms secondary currents with one of the drives
connected, then unconnected  (proving my surmise).  But when I reduce
the primary:primary k only to 0.9 rather than the 0.95, I get a 2:1
difference, within a few %.  Interesting...it takes only a _small
reduction_ in that k to bring the current gain right up to 2!

So...(once again): which would be best?  Stacked, identical and coaxial
primaries or co-planar, identical and non-coaxial ones?  If the former,
it appears necessary that they not be too closely situated.  But perhaps
just a rather short spacing would result in a respective k less than
0.95.  Although...would there not be resultant flux leakage out from
between the primaries in that case?

I'm getting way too old for this...

Ken
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```

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