# Re: Primary-Secondary Coupling (Renamed)

• To: tesla-at-grendel.objinc-dot-com
• Subject: Re: Primary-Secondary Coupling (Renamed)
• From: MSR7-at-PO.CWRU.EDU (Mark S. Rzeszotarski, Ph.D.)
• Date: Thu, 7 Dec 1995 14:53:41 -0500
• >Received: from slc5.INS.CWRU.Edu (slc5.INS.CWRU.Edu [129.22.8.107]) by uucp-1.csn-dot-net (8.6.12/8.6.12) with ESMTP id MAA17679 for <tesla-at-grendel.objinc-dot-com>; Thu, 7 Dec 1995 12:20:03 -0700
• Cc: msr7-at-slc5.INS.CWRU.Edu

```><liberal snipping here>
>From mrbarton-at-ix-dot-netcom-dot-com Thu Dec  7 01:12 MST 1995
>
>What do mean here by "hump" phenomena?  (and my name's NOT Igor!)
>The formula shows that as K goes up the two observed frequencies get
>wider apart (given that pri and sec have equal resonant frequencies.
>As K approaches 1.0 the two frequencies tend toward 0 and infinity.  By
>shorting the spark gap and using a signal generator on the primary, the
>two freqs are readily observed on the secondary, and from their split,
>K can be calculated directly...
>
>    K = 1 - 2 / (1 + (f2^2 / f1^2))
>
>where f1 and f2 are the lower and higher frequencies.
>
>These frequencies relate to the natural frequencies (f0) of both
>circuits (which should be equal):
>
>    fo = sqrt(2 / (1 / f1^2 + 1 / f2^2))
>
<really good analogy stuff deleted>

Conventional tesla coils are coupled rather loosely with coupling
coefficients (K) less than 0.2 or so.  (The coupling coefficient (K) is
defined as the mutual inductance between the primary and secondary divided
by the square root of the product of the individual primary and secondary
inductances.)  With small values of K we usually do not observe much if any
frequency splitting.  Where it really becomes a factor is if you use tight
coupling.  This is what Tesla employed with his extra coil (magnifier)
configuration at Colorado Springs.  Richard Hull (TCBOR) has a nice video
showing this (I think magnifier tape #2?), where he uses a coupling
coefficient around 0.4 to 0.6 between the primary and a secondary coil which
is referred to as the "driver" coil.  The output of the driver (secondary)
coil then base feeds a third "extra" coil, (with excellent results I might
add).  In one of Richard's experiments he tunes the primary to the lower
split frequency component and couples energy to the extra coil quite
efficiently.  The system performs well because now more of the primary
energy is delivered to the extra coil (due to increased K) than in
conventional tesla configurations.  Because of the frequency splitting and
tight coupling, the primary-driver coil pair act more like a conventional
transformer than a helical resonator.  Standing waves on the driver coil can
form, and additional insulation between the primary and secondary must be
employed to prevent arcing.  In addition, high coupling values require that
the spark gap conduction time be very short.  Hence, a rotary spark gap is a
must, with additional stationary gaps in series to aid in the quenching
process.  BTW, the math is described pretty well in the Corum brothers
TCTUTOR computer program documentation, available from I.T.S. (Hope you like
transmision line theory!)
Regards,
Mark Rzeszotarski, Ph.D.

```