RE: Tesla Coil Blunders

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

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