Re: Recycled: Measuring Coupling Coefficients

From: 	John H. Couture[SMTP:couturejh-at-worldnet.att-dot-net]
Sent: 	Sunday, December 07, 1997 1:22 AM
To: 	Tesla List
Subject: 	Re: Recycled: Measuring Coupling Coefficients

At 05:41 AM 12/6/97 +0000, you wrote:
>From: 	Mark S. Rzeszotarski, Ph.D.[SMTP:msr7-at-po.cwru.edu]
>Sent: 	Friday, December 05, 1997 6:57 AM
>To: 	Tesla List
>Subject: 	Re: Recycled: Measuring Coupling Coefficients
>Hello All,
-------------------------------- snip
>        K depends only on geometry.  M, Lp and Ls depend only on geometry.
>The equation above considering the two Q factors is the value of K one
>should strive for for maximum energy transfer between the primary and
>secondary.  Of course, you also want that to be equal to one of those nice K
>values where all of the energy happens to be transferred to the secondary
>when the gap turns off (1st, 2nd or 3rd notch, generally).  In addition, you
>may want to match Qp to Qs under full firing conditions.  To do this you
>must measure the load Q of both circuits during spark production.
>        You can precalculate M and K quite easily using Neumann's formula.
>It is a slow numerical integration, but yields accurate results.  The power
>series approximation described in Grover's Inductance text is inaccurate for
>typical tesla coil geometries.  I have written the numerical integration
>code, and it is fairly straightforward.  It has worked well for me for
>solenoidal and flat spiral primaries, and gives an approximate solution for
>inverted cones.  (M is accurate, but Lp is approximated.)  I plan to post
>the program to the net after some more fine tuning.  It is in beta testing now.
>Mark S. Rzeszotarski, Ph.D.


  Mark -

  As I mentioned in an earlier post the K factor appears to be related only
to the physical characteristics and geometry of the coil. However, this
appears to be contrary to    K = 1/sqrt(QpQs)    and    Q = 6.283 F L
where the K factor is related to the frequencies, unlike the other K
equations where the frequencies cancel out. Do you have a an explanation for
this apparent contradiction ?

  The transfer of energy between the two coils is always 100% and purely
inductive. The K factor only affects the time for the total transfer. There
are, of course, losses due to currents in the windings. These losses do not
affect the transfer which is inductive and reactive with no losses. 

  The JHCTES TC computer program determines the mutual inductance from the
physical characteristics and geometry of the coils. It also calculates the
Lp and Ls using the Wheeler equation so the K factor can be found. This
method has been found to closely agree with K factor tests when properly
performed. The program also calculates and coordinates 46 of the major Tesla
coils parameters while keeping the complete system in tune.

  The Tesla List will be looking forward to your Neumann numerical
integration computer program.

  John Couture