Re: Parallel and Series LCR Circuit Qs

["Antonio Carlos M. de Queiroz" <acmq-at-compuland-dot-com.br> (by way of Terry Fritz <twftesla-at-uswest-dot-net>)]

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? 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