# Re: Primary Q's and Spark Gaps (and magic formula)

• To: tesla-at-grendel.objinc-dot-com
• Subject: Re: Primary Q's and Spark Gaps (and magic formula)
• From: mrbarton-at-ix-dot-netcom-dot-com (Mark Barton)
• Date: Wed, 6 Dec 1995 19:11:16 -0800
• >Received: from ix9.ix-dot-netcom-dot-com (ix9.ix-dot-netcom-dot-com [199.182.120.9]) by uucp-1.csn-dot-net (8.6.12/8.6.12) with ESMTP id UAA00505 for <tesla-at-grendel.objinc-dot-com>; Wed, 6 Dec 1995 20:11:48 -0700

```Hi Malcolm,

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))

These observed frequencies arise because of the trading of energy back
and forth from primary to secondary and back.  A good analogy is as
follows:  Imagine a 6 foot length of stout rope stretched horizontally
between two supports.  Suspended from the rope are two child's swings
which are equal in length and are side by side.  If you set one swing
a'swingin, the other swing will absorb the energy because some (K) is
being coupled to it via the horizontal rope.  It will also absorb this
energy efficiently because both swings have the same natural period
(frequency).  After several cycles the first swing will stop completely
and the second swing will be at its maximum.  This process will reverse
with each swing actually stopping as energy is traded completely to the
other.  Of course the process eventually dies out.  If the coupling is
tight between the swings, it will take fewer cycles to completely
transfer the energy each way, and vice versa.  This action is EXACTLY
what happens in a Tesla coil and with the magic formula for the output
waveform, you can see it live and in color.

The rate at which energy is traded = f2 - f1

Zap,
Mark

======================================================================

You wrote:

>     On a slightly related topic....
>a cursory glance at the formula Mark Barton posted describing
>the secondary output waveform suggests that the "hump" phenomenon
>was actually the split frequencies beating. I haven't done the maths
>on it yet but it is going to be very revealing as he says. I already
>had a look at frequency relationships but rather hastily and without
>a great deal of solid measurement.
>
>Malcolm

```