Re: Parallel and Series LCR Circuit Qs

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

Hi Antonio,

At 10:49 AM 8/9/00 -0300, you wrote:
>Tesla list wrote:
>> 
>> Original poster: Terry Fritz <twftesla-at-uswest-dot-net>
>
>>         "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.
>
>Can you explain better this? 

See the following page that explains basically how I find the output
impedance of a coil.  Usually, I do "trial and error" into the expected
equivalent static load to find the best power to the arc.

http://users.better-dot-org/tfritz/impedance/impedance.html

The impedance matching does not seem to be critical at all, but one does
not want to be super far off.  I assume the gap does not quench during the
firing cycle since that how "my" coils are designed and operate.  Another
timed switch would do this however...

I never have though much about the complex conjugate view or dynamic
streamer impedance changes during the firing cycle.  I was happy just to
get this far! :-))  However, one can add such functions to the model and do
sensitivity analysis to see if the effect is worth worrying with (I have
never done this).

No doubt, finer detail in the model would get more accurate results.  What
is not known is how much difference that would make.  If a "truly optimal"
coil gets say another foot, then it would be worth the trouble.  If you
gain another millimeter, well then it's probably not worth warming the CPU
over :-))  Since coils with "not so great" matching still do fairly well, I
suspect "perfect" matching is not that important as long as you are
somewhat close.  I would guess, from playing with models for hours on end,
that an error factor or 2 or 3 is pretty good.  The streamer may indeed
"match itself" to the coil somewhat too.  Equal length streamers can have a
wide variety of visual forms, so there is something going on there...  The
coil can also produce multiple streamers and such to radically change things...

Impedance matching is intriguing and useful, but one should not get "too"
detailed.  Too many other things can affect the coil and streamers too.
The art is too young here to expect more than a general guide.  Much more
would have to be known about streamers before trusting such calculations
past the first digit of accuracy.  But at least you can get close enough to
avoid those "real dog" coils we all have hidden in the closet :-))

Cheers,

	Terry



>What do you consider to be Zsource?
>I see two possibilities, considering the primary circuit connected, and
>in this case the "equivalent linear resistance" of the gap will be
>important, and just the impedance seen at the top of the secondary
>after quenching, what would result in matching conditions involving
>the resistance of the secondary winding. Note that matching conditions
>apply only to the resistive parts of the impedances, and that the
>reactive parts are to be cancelled, so the equations would be:
>Re(Zsource(jw))=Re(Zstreamer(jw))
>Im(Zsource(jw))=-Im(Zstreamer(jw))
>w would be the frequency where the total system appears to resonate.
>Note that all this is just an approximation, even assuming linearity,
>because everything occurs during a transient, and not at sinusoidal 
>steady state.
>Matching to a particular streamer length may result in interesting
>behavior, if this really works, because a streamer would dissipate
>more an more power as it grows to the designed length, and less
>power if it tries to exceed it. The resulting feedback would tend
>to keep the streamers at a constant length. Multiple streamers would
>result in different matching conditions, and lengths.
>
>Antonio Carlos M. de Queiroz
>
>