Re: Parallel and Series LCR Circuit Qs

[Terry Fritz <twftesla-at-uswest-dot-net>]

Hi Dick,

	"i" have always gone by the assumption that the streamer is a load that
needs to be feed with as much 'power' as possible.  I have measured the
streamer impedance of my small coil and Greg Leyh as taken data off his BIG
coil that have both have given fairly consistent results for streamer
impedance.  That being 220K ohms in series with 1 pF per foot of streamer.
So the Tesla coil "source" basically needs to be impedance matched to
supply this "load", optimally.  

	Of course, TCs are nasty non-linear messes that are hard to quantify and
the above 220K +1pF/foot thing is a "average equivalent" of a much more
complex thing.  But you see the point.  I have made TCs that "should" give
fantastic voltages, but the streamer load bogs them right down (I use it as
a door stop now ;-)).  One can also make a TC that can supply a LOT of
current but the voltage is too low to get good streamers.

	Most TCs made to the typical dimensions today have managed to naturally
get pretty close to the component values need to give a good impedance
match.  The fancy measurements and models are really only playing high-tech
catchup (but they have managed to extend the art in some ways too! :-))

So "i" would consider Zsource = Zstreamer to be more important than the Cp
to Cs ratio.

1/2 of a coil's power is typically lost in the spark gap.  That is a giant
efficiency killer.  There are little tricks that can improve this but spark
gaps eat a lot of streamer length (~40%).  People have hinted at better
solutions, but so far, the old spark gap has beaten them all... 

"i" don't take Q too seriously unless it is a CW coil where long term
heating may be a meltdown problem.  Once you add a streamer load to a spark
gap TC, the Q goes WAY down and it just does not count...

My 'little coil' took me two months to work out all the impedance match and
other issues.  And "i" am sposta know what I am doing :-))  Unfortunately,
for the average guy, the high-tech computer modeling stuff is a bit too
messy.  The computer tools are all there but they are not really user
friendly and "easy"...  I can sort of envision the "perfect" program that
would take the usual equations and also incorporate the "magic" of
E-Tesla5, MathCad models, Malcolm's ruler and Robert Jones' theory, John
Freau's equation and the work of Dr. Rzeszotarski to give a really
comprehensive view of a Tesla coil before it is made (not to mention the
skill of Bill Wysock in putting the darn thing together!) Marco's Thor
project should help with some finer details of what streamers "really"
do...  However, ALL the variables are daunting!  Such a program would have
to really suggest the "best way" to go and what would give the most
"streamer per buck"...  

The "basic" tools really are all there...  However, another "leap forward"
is needed to really bring it all together into the rev 1.0 of the "perfect"
TC design program...  Then there is the "how much risk are you willing"
(MMC vs. EMMC) factors...  

We are fairly far from the "perfect" knowledge of this hobby (profession
for a few).  But we are closer than we were....

Cheers,

	Terry
 
	

At 11:16 PM 8/8/00 -0400, you wrote:
>Hi Jim,
>	Your questions about Q are interesting and seem to be 
>founded in a lot of thought.  Assuming the criteria for a good 
>TC is spark length, then the design goals should be to 
>achieve a high terminal voltage (without that there is no spark 
>or descent spark length.  Therefore coil design goals are:
>
>1.  High Efficiency
>2.  Large ratio Cp to Cs
>
>I do not agree with the following statement made:
>
>     "However, from what I have read (and understand) the design 
>      dictates a large top capacity and relatively small inductance; 
>      this resulting in white streamers showing a relatively
>      substantial current."
>
>Instead, the top capacity should be large compared to secondary
>coil self-capacitance.  There is a design compromise that has 
>to be made with efficiency, coil, and secondary inductance.
>
>All energy headed towards the secondary comes from what is 
>stored in the primary capacitance (Cp) at the time the spark 
>gap fires.  That energy is:
> 
>Jp = .5 Cp Vp^2  (Joules)
>
>At the secondary, the same equation applies:
>Js = .5 Cs Vs^2 
>
>Jp = Js Eff
>
>Therefore we have an algebraic equation to solve:
>0.5 Cp Vp^2 = .5 Cs Vs^2 Eff
>
>Vs = Vp Eff sqrt( Cp/Cs )
>
>For maximum Vs, secondary voltage we need high 
>efficiency and a large Cp, and a small Cs.  To get that 
>voltage to the top terminal, it would be best to have 
>Cs = Ctop or as nearly so as possible.  Voltage in 
>Cself contributes to coil destruction and less to 
>spark length.  I agree that a large Cs contributes to 
>white hot sparks, but the Cp has to increase by the
>same factor.
>
>If Eff = 1.0 then the above equation indicates the 
>highest secondary voltage that is possible.
>
>Problem 1:  A large Cp is difficult to charge to a high
>voltage during the time of a 1/2 60 cycle period without
>a very high voltage and high current transformer or 
>power source.  Just putting in a large Cp is not the 
>answer because Vp won't be very high due to the 
>limited charging power source and short charging time.
>
>Problem 2:  A small Cs requires a high Ls, secondary 
>inductance to tune at a reasonably low frequency where 
>losses like skin effect are minimized.  High Ls for 
>achievable Q's means high resistive losses Rloss = Ls/Q.
>Kiss high efficiency good-bye with high losses.
>
>All Coilers are trying to achieve the highest Vs and do 
>this by modelling and experimenting with the components 
>that go into a TC.  It's a self arresting activity because 
>of parts destruction caused by high voltages and currents
>that result as one achieves the long spark goal.  Physics
>dictates that efficiency is the price paid for a hardy TC and 
>in the end when design is optimized the limiting factor is 
>the strength and cost of materials that go into a TC.
>
>Compounding the problem is non-linearities and the 
>accuracy of models.  Pure experimentation is not the 
>answer either because results don't necessarily indicate 
>clearly the limiting cause for perfection and guide to 
>further experimental changes.
>
>Lot's of fun, yes???  You bet it is.  Sorry for the long 
>winded spiel and I hope this helps answer your questions.
>
>Dick (K2YZ)
>
>
>At 06:51 PM 7/22/00 -0600, you wrote: