Re........ Measuring Coupling Coefficients

From: 	terryf-at-verinet-dot-com[SMTP:terryf-at-verinet-dot-com]
Sent: 	Sunday, December 07, 1997 7:01 PM
To: 	Tesla List
Subject: 	Re........  Measuring Coupling Coefficients

        Mark's program will be a major benefit to those who do Tesla coil
modeling.  The mutual inductance between the primary and secondary coils has
always been a very difficult factor to predict. This will provide one of the
last factors we need to do full Tesla coil analysis completely from scratch
with little need for trial and error testing.  Computer modeling of input
circuits, primary to secondary relationships, electrostatic fields, are all
now becoming very well understood (the secondary sparks are still a
frontier).  In the next few years this will have a dramatic impact on how we
all build coils.  It will also lay to rest some of the long standing
traditional mistakes we all make just because we didn't understand the true
nature of the circuits we were building.  This is a very exciting time for
Tesla coils and their construction.  There are many possibilities for
improvements and increased output, efficiency, and reliability.  After
studying neon transformers and the conditions they deal with, I am surprised
that they work at all.  I'll say more on this when all the numbers are
Additional comments follow:

>>From: 	Mark S. Rzeszotarski, Ph.D.[SMTP:msr7-at-po.cwru.edu]
>>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
>>Mark S. Rzeszotarski, Ph.D.
>From: 	John H. Couture[SMTP:couturejh-at-worldnet.att-dot-net]
>  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 equation Q = 6.283 F L does not sound correct.  The equation 6.283 F L
is equivalent to the inductive reactance of a single coil, not it's Q.
There is a Q factor associated with inductors.  The formula is Q = Xr/Rs
where Xr is the reactance and Rs is the series resistance.  I assume this is
what you meant because this is the equation in your "Tesla Coil Notebook".
It needs to be pointed out that this equation assumes a specific model of a
single inductor and the equation can only be applied to those cases.  I do
not see how this factor is useful for finding the mutual inductance in a
Tesla coil.  It is not correct to take these equations out of context and
use them in other situations without explaining what they represent.
        For example:  Suppose I have a primary with a Qp of 12 and a
secondary with a Qs of 30.  Using the equation Q = Xr/Rs this can be easily
measured (If you have ~$3000 worth of test equipment).  The equation ( K =
1/sqrt(QpQs) ) will predict a K of 0.0527 but does not take into account
that the two coils are separated by 150 feet and thus have a K of zero.
Such equations need very specific definitions so that they can be
understood, verified, and measured by anyone. 

>  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. 

I disagree that the energy transfer is 100%.  Resistive losses, as you point
out, are at work and the losses as sparks emit from the coil disrupt the
circuit and can cause heavy losses of efficiency.  Models take such
additional factors into account.  The real target of my original post was to
find accurate ways to measure or calculate the mutual inductance of Tesla
coils.  I was not interested in rules of thumb or approximations based on
observation (although they are more interesting :-)).  I wanted, and found,
a good solid method that could be used by anybody that would produce
accurate and reliable results.  Some other methods may be inaccurate or be
easy to mess up.  Equations like K = 1/sqrt(QpQs) may look good but are not
useful unless they are defined, easy to measure, and can be verified.  A
solid theoretical foundation is also nice.

>  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 great thing about Mark's program is that is should be able to handle any
configuration.  I believe that the JHCTES program is based on coil testing
of a limited number of coils in limited configurations and numerical
predictions are based on those data points.  This should give good results
as long as the coils in question are similar to the original coils.  Mark's
program should even be able to do the non-linear coils I play with (needs
slight modification).  The JHCTES program cannot predict these coils at all.

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

        I have seen the program.  Needs some polish but looks very good.  I
haven't had time to test it to any great degree but it is very promising.
Hopefully, it will be ready to release to the sharks soon and we'll see how
well it floats :-))