# Re: K Quiz

```Subject:   Re: K Quiz
Date:    Wed, 21 May 1997 07:58:08 -0400 (EDT)
From:    tesla-at-america-dot-com (Bob Schumann)
To:    Tesla List <tesla-at-pupman-dot-com>

>Subject:  K Quiz
>  Date:   Tue, 20 May 1997 14:14:03 -0400 (EDT)
>  From:   msr7-at-po.cwru.edu (Mark S. Rzeszotarski, Ph.D.)
>    To:   tesla-at-pupman-dot-com
>
>
>Hello coilers,
>        Here is a little food for thought.
>     "K" is the term applied to the degree of magnetic coupling between
>the
>primary and secondary coils of a conventional tesla coil (or the primary
>and
>driver
>coil in the magnifier configuration).  Typically, we aim for values
>between
>0.1 and
>0.25 or so for a conventional tesla coil, and 0.4 or higher for
>magnifier
>primary/driver coil systems.  "M" is the amount of mutual inductance
>between the
>primary and secondary coil.  We define:
>K = M / SQUARE_ROOT [ Lp x Ls ]
>where Lp is the primary inductance, Ls is the secondary inductance,  M
>is the
>mutual inductance, and K is the coefficient of coupling between the two
>coils.
>
>Consider the following scenarios:
>
>Primary coil A:
>     flat pancake coil, 10 turns, inside diameter = 12", outside
>diameter=22"
>     Lp=56.6 uH
>
>Primary coil B:
>     flat pancake coil,  5 turns, inside diameter = 12", outside
>diameter=22"
>     Lp=15.8 uH
>
>Secondary coil #1:
>     solenoidal coil, 24" tall, 8" diameter, 888 turns #22 wire, Ls=45.8
>mH
>
>Secondary coil #2:
>     solenoidal coil, 24" tall, 8" diameter, 566 turns #18 wire, Ls=18.7
>mH
>
>Secondary coil #3:
>     solenoidal coil, 24" tall, 8" diameter, 288 turns #12 wire, Ls= 4.8
>mH
>
>where: uH is microhenries, mH is millihenries and dimensional units are
>in
>inches.
>
>     Assume the bottom turn of the secondary coil is aligned with the
>plane
>of the flat
>pancake primary coil for all cases.  For primary coil A used with
>secondary coil
>#1, I experimentally measure K=0.23 with M=375.2 uH.
>     My question is this, what happens to K as we try the different
>combinations
>of primaries and secondaries above?  Think about it.  (BTW, I know what
>the
>
>Primary   Secondary        K
>   A              #1               0.23
>   B              #1                  ?
>   A              #2                  ?
>   B              #2                  ?
>   A              #3                  ?
>   B              #3                  ?
>
>Regards,
>Mark S. Rzeszotarski, Ph.D.
>
>

I do not have enough data to make a determination
to fill in missing K values. Though you have
stated M for the first setup, it is missing for
all the others. I can not solve for K without
the known value of the variable M. When using
different value coils, the measurements for
fields aiding and fields bucking will change
for each substitution therefore changing the
value of M, a critical value needed in the
determination of K. You said assume the primary
and secondary coils aligned on a flat plane.
If there is a way to calculate M from this
geometry, I am not aware of it. IMO as soon as
you change out 1 coil for another, the field
interaction changes and M must be re-calculated
prior to solving the coefficient of coupling.

I've got my flame-proof suit on so have at it! Heheh

Bob Schumann

tesla-at-america-dot-com
http://www.america-dot-com/~tesla

```