Flat Primary Winding - next question

From:  Mark S. Rzeszotarski, Ph.D. [SMTP:msr7-at-po.cwru.edu]
Sent:  Thursday, June 18, 1998 2:49 AM
To:  Tesla List
Subject:  Re: Flat Primary Winding - next question

Hello All:
Steve Young said in part:
>I am wondering just how
>primary diameter affects coupling to the secondary.  I envision the
>magnetic flux from a larger diameter primary will intercept more of the
>secondary than will a more compact primary, but I don't know the practical
>significance of such an effect.  I would assume we should couple to as much
>of the secondary as possible to even out the secondary volts per turn
>distribution (implies large diameter primary).

Consider three flat spiral primaries:
System A: inside diameter 12", outside diameter 23.34", N=15.125 turns
(Terry Fritz's primary)
System B: inside diameter 12", outside diameter 36.00", N=15.125 turns (match N)
System C: inside diameter 12", outside diameter 36.00", N=14.000 turns
(match Lp)
        Assume each is coupled to a secondary which is 1000 turns of .02"
wire on a 10.25 inch diameter by 30 inch tall secondary, positioned such
that the bottom turn of the secondary is in the same plane as the flat
spiral primary.

Results of mutual inductance calculations:
System A:  Lp=131 uH   Ls=76.3 mH   M=636 uH   K=.20
System B:  Lp=151 uH   Ls=76.3 mH   M=614 uH   K=.18 (same # turns as System A)
System C:  Lp=132 uH   Ls=76.3 mH   M=569 uH   K=.18 (tried to match Lp of
System A)
        Conclusion: you get slightly better coupling with the smaller
diameter primary.  The current in the secondary is directly proportional to
M, so the small diameter primary may be advantageous.  Of course, you could
wind a solenoidal primary and get even higher M, if you can hold off the
higher voltages.....

>This leads to another thought.  If the primary effectively couples mainly
>to the lower part of a 1000 turn secondary (e.g. the first 100 or so
>turns), then do we in effect have a 100 turn secondary feeding a 900 turn
>third coil?
        One can examine the degree of coupling between the primary and
secondary by looking at the mutual inductance M between the primary and a
one inch tall segment of the secondary.  In the example below, I looked at
the coupling between the primary and a secondary 10.25" diameter, 1" height
with 33.33 turns.  The secondary coil is moved from 0" above the primary to
28" above the primary, near the top of the actual secondary.  Here are the
results for System A and System C (which have the same Lp and Ls):

Position        M for System A          M for System C
    0"          93 uH   (100%)          64 uH   (100%)
    2"          71 uH   ( 76%)          53 uH   ( 83%)
    4"          50 uH   ( 54%)          42 uH   ( 66%)
    6"          35 uH   ( 38%)          32 uH   ( 50%)
    8"          25 uH   ( 27%)          25 uH   ( 39%)
   12"          13 uH   ( 14%)          15 uH   ( 23%)
   16"           7 uH   (  8%)           9 uH   ( 14%)
   20"           4 uH   (  4%)           6 uH   (  9%)
   24"           3 uH   (  3%)           4 uH   (  6%)
   28"           2 uH   (  2%)           3 uH   (  5%)
        It is clear that the larger diameter primary bathes the secondary a
little higher up than the smaller diameter primary.  Still, most of the
coupling is accomplished in the lower 1/4th of the coil height or so.  So,
to answer your question, no, not 100 turns, more like 200 turns!
        There are striking similarities between the magnifier configuration
and the conventional two coil system.  Unfortunately, you generally lose
with the magnifier, unless you can build a really fast quenching series type
rotary spark gap to handle the higher coupling coefficient.

Mark S. Rzeszotarski, Ph.D.