# Re: Recycled: Measuring Coupling Coefficients

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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,
I have just returned from a business trip to Chicago and am sorry to
have missed out on the following discussion, appropriately snipped from several:
>  Your comments prompted me to go back and review the K factor again. I
>think you are correct (K related only to geometry) because as I pointed out
>in another post the frequencies (F) cancel out in the test equations.
>However, this does not happen in the following:
>
>      K = 1/sqrt(Qp x Qs)       Q = 6.283 F L / R
>
>  Regarding your other comment on "you can't pre-calculate K either" I would
>point out that the JHCTES TC computer program will first calculate "how many
>turns you will be using on that 15 turn primary" and then will determine the
>K factor. In other words the program is doing what you say is necessary to
>calculate the K factor.

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.
Regards,
Mark S. Rzeszotarski, Ph.D.

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