RE: Tesla Coil Blunders

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "John H. Couture by way of Terry Fritz <twftesla-at-uswest-dot-net>" <couturejh-at-worldnet.att-dot-net>


Malcolm -

It appears the resonant frequency equation is beginning to reveal some of
it's secrets. Most coilers take this equation for granted not realizing that
it has some interesting properties for the Tesla coil. One of those
properties is that if the R is large enough you will end up with a square
root of a negative number. As I say in the TCC Guide that shows this
equation when the R is large enough there will be no resonant frequency.
This would probably never occur with TC operation, however, some R value is
always present in the TC system when operating. The R is normally small
enough and can be ignored with signal generator low power tests. But how
about the R when the TC is operational? Are coilers blundering in this
matter.

With the operational secondary circuit the R includes all losses plus the
load. The load during operation includes streamers, corona, radiation, etc.
It is obvious that the load can present a large variety of conditions during
operation. Researching these conditions could help obtain better output from
the TC system. One exception is when sparks to ground occur which is a
direct shorting of the secondary circuit to ground. This means that tests
would be made only with (small streamers?) and not strikes to ground.

For the above to have any significance the following question must be
answered. Does the resonant frequency reduce when the TC is operational
compared to the low power signal generator measurements?  If it does how
does it affect the R of the resonant frquency equation? These are difficult
tests to make with resonable precision (+/- 1%?) and maybe standard test
methods should be set up so the test results are more coordinated. In the
past the few tests of this type that have been made have given conflicting
results.

John Couture

--------------------------


-----Original Message-----
From: Tesla list [mailto:tesla-at-pupman-dot-com]
Sent: Tuesday, April 03, 2001 12:20 PM
To: tesla-at-pupman-dot-com
Subject: RE: Tesla Coil Blunders


Original poster: "Malcolm Watts by way of Terry Fritz <twftesla-at-uswest-dot-net>"
<m.j.watts-at-massey.ac.nz>

Hi John,

On 2 Apr 01, at 21:26, Tesla list wrote:

> Original poster: "John H. Couture by way of Terry Fritz
> <twftesla-at-uswest-dot-net>" <couturejh-at-worldnet.att-dot-net>
>
>
> Malcolm -
>
> Sorry - the two R's are shown in the following equations:
>
>    Q = Xl/Rq  Rq = Xl/Q

>    F = .159 sqrt(1/LC - (Rf/2L)^2)
>
>    Rf = 2L sqrt(1/LC - (6.283F)^2)

I think I detect an error in this last equation? Plug some typical
figures in and try it. I did and ended up having to square root a
negative number.

> The Rq in the Q factor equation is the one to which you are referring.
> The other Rf is the one in the Resonant Frequency equation and is a
> different resistance. This resistance affects the resonant frequency
> of the RLC circuit.

Actually, both will because they are one and the same and are defined
as the equivalent series resistance of the circuit.

Let's assume a secondary with an unloaded Q of 200 and an inductance
of 20mH and resonates at 200kHz. The first equation shows that ESR
(Rq in your nomenclature)= 125.7 Ohms roughly.  To resonate at this
frequency, the equivalent capacitance (ignoring that loss for the
moment) will be about 31.7pF.

I now plug that resistance, inductance and capacitance into your
second equation to find F. The change in frequency is absolutely
trifling. If you don't believe me, do it.

Now let's change to a loaded Q of 10. The first equation shows that
ESR has risen to 2.5kOhms approx.

Plugging this new figure for R into equation 2 shows the frequency
now to have dropped less than half a percent, not exactly a
convincing argument that R is responsible for a massive drop in
frequency.

> The meager TC operating test data (scope/antenna probe) I have been
> able to collect from coilers indicates this Rf may be involved in
> reducing the resonant frequency compared to the low voltage, low
> current Wheeler/Medhurst/Freq meter test.

If anything is dropping the frequency significantly it has to be
streamer capacitance.

> This resonant frequency reduction has resulted in coilers and TC
> programers having to make an adjustment in the calculation of the
> resonant frequency compared to the operating test. Apparently you
> haven't noticed this reduction.

My work coil shows no significant change in resonant frequency
according to waveforms I've captured on the storage scope as compared
with low power sig gen measurements.

Regards,
malcolm