# Re: Primary Q's and Spark Gaps

• To: tesla-at-grendel.objinc-dot-com
• Subject: Re: Primary Q's and Spark Gaps
• From: ed-at-alumni.caltech.edu (Edward V. Phillips)
• Date: Wed, 6 Dec 1995 19:39:37 -0800
• >Received: from tybalt.caltech.edu (root-at-tybalt.caltech.edu [131.215.139.100]) by uucp-1.csn-dot-net (8.6.12/8.6.12) with ESMTP id UAA04375 for <tesla-at-grendel.objinc-dot-com>; Wed, 6 Dec 1995 20:40:24 -0700

```Malcom:
The resonant frequency of the secondary (before discharge
starts) is about 319 kHz, as measured with a signal generator.
The "hump" phenomenon is indeed a "beating" between the two peaks
in amplitude response of a double-tuned transformer when the
coupling is well above critical.  I was going to send you a note
on this, but haven't had the time to compose it.  If you happen
to have a copy of "Radiotron Designer's Handbook", Third edition,
November, 1941 you will find appropriate equations on page 123.
This was a product of Amalgamated Wireless in Sydney, reprinted
in the US by RCA.  It is an excellent small book, and the section
on double-tuned transformers is a condensatation of Aiken's original
publication of 1937.  Make that condensation without so many at's.
Anyhow, the two peaks in the response have a separation of about
delta f=k*fo*sqr(1-1/k^2*Q^2), where fo is the resonant frequency
k is the coupling factor, and Q is the Q of either primary or
secondary (assuming identical tuning and Q for both circuits).  This
equation is good for k*Q of 3 or greater, which I suspect is the
case for a typical Tesla coil BEFORE the discharge starts and the
secondary has become heavily loaded.  If you manipulate the equation
you can find the time between peaks or zeros of the "humps".  It is
t=1/(delta f)=1/(k*fo), subject to the same approximations of
equal tuning and Q's.  I have tested this with a P spice simulation,
and find the results to be as close as I can read the output.
Of course, once the discharge starts the Q of the secondary
changes and becomes a non-linear function of time, as does the
Q of the primary as the spark cools off.  If you looked at the
spectrum of the output, averaged over time, you would get something
which wasn't necessarily representative of what you would measure
if you could look as each time segment of the discharge separately.
The Corum's mention some of this in their publications.  Anyhow,
you should be able to guess at your operating k by measuring the
time between peaks (zeros would maybe be easier to measure) of
the response and inverting the above expression to get the
equivalent value of k.  Note that, as long as k*Q is much above 3,
the timing depens on k only, and not on Q.  By the way, running the
same SPICE simulation made it obvious that one would like much
higher values of k than you might expect from critical coupling,
which gives the maximum gain when the primary is fed from a current
source such as a vacuum tube.  The simulation I ran charged the
capacitor to a fixed voltage and then discharged it into the primaryh
winding.
By the way, as of this evening I am getting 24" streamers
(one or two at a time only) and white arcs to a grounded door knob
when the streamers "come its way", with the coil I mentioned earlier.
To repeat its parameters, the secondary is 16.4" long, close wound
with #28 wire.  Resonant frequency with the 9" x 3" toroid is about
320 kHz.  Primary uses three 0.003 mfd ceramic doorknob capacitors
for energy storage, while primary coil is wound on a 7.25" diameter
paper tube and is 2.5" high.  Transformer is a 12 kV, 60 ma unit
and spark gap is 5 two inch sections of 1" copper pipe with
axes parallel and total gap of somewhat under 1/4".  How do these
results sound to you?  By far the best performance I have ever
gotten here.  Forgot to mention line current is between 5 and 6
amps at 120 volts.
One last thing.  I took some pictures of the streamers
with my camcorder this evening, and on playing them back slow
motion got the impression (it might have been due to stroboscopic
beats between spark frequency and camera frame rate) that I could
streamers grow, disappear, and reappear in some other place.  Any