Re: Parallel and Series LCR Circuit Qs

["Richard Kircher" <richard.kircher-at-worldnet.att-dot-net> (by way of Terry Fritz <twftesla-at-uswest-dot-net>)]

Hi All,
	It sure sounds like a lot of things are important in TC design.  Maybe the
prime question is "what's most important".  I suggest the key to that
answer is $$$'s (component cost) and your source of energy.  Certainly,
without a high Cp/Cs ratio there won't be much voltage or possibly a
decline in voltage as an extreme.  Voltage is squared in the Energy
equation while capacitance is not.  I did not mean to say that a high Cp/Cs
ratio should be obtained by making Cs small.  I agree with all that say Cs
should be large, but that only means that Cp also has to be large in
proportion to maintain the high Cp/Cs ratio.

	I really don't know where the compromise should be made when Cp size is
limited by $$$'s for the primary capacitor and power source (AC Transformer
or DC Supply).  I would take my hat off to anyone that has that answer
nailed down taking all variables and non-linearities into account.  Of
course, we all learn quickly that it is not just dollars and Cp that limits
a TC's performance, there are other factors like Lp (primary coil) physical
limitations, proportion, silver plated copper, efficiency, voltage
break-down ratings, cost, cost, cost, etc. too.

	Efficiency and Impedance matching are also intriguing and important
subjects.  I still think efficiency, (aka Q) is of prime importance FOR THE
OVERALL COIL.  The secondary dissipative losses are not that important
because the reactive impedance levels are high by comparison, so who care
about 100 ohms.  On the primary side, losses in the coil, spark gap, and
capacitor are very important.  The 10,000 amp primary current also flows
thru the capacitor and makes me a little concerned about the MMC made from
the interconnection of a lot of "thin" (compared to copper tubing) wire
leads.  MMC's are very popular these days so the thin wire lead worry and
internal construction may not be valid - another "don't know" for me.

	Most confusing to me is impedance matching to the load/streamer.  Some
folks think that the most power transfer occurs when the source impedance
is matched to the load impedance.  Don't try that idea with your car
battery.  The most power transfer occurs when the source impedance is ZERO
ohms and this applies to all lumped component circuits.  Of course,
absolute zero is not achievable especially when the Cp/Cs ratio is high in
the world of realizable coil parameters.  Given that the streamer impedance
can't be changed or matched, it would seem the only thing left to do is to
make the coil output resistance as low as possible (high efficiency) and
match the reactive component.  

	Terry's work indicates that the streamer impedance is capacitive (1pF per
foot)  Therefore it sounds like the coil should be inductive to tune it
out.  Alternately, it would seem that the streamer de-tunes the coil and
lowers the secondary resonate frequency.  So, I guess the primary should be
tuned lower in frequency than the secondary to start with (?).  I wonder
how much lower?  Maybe the answer is to just tune the coil by trial and
error until the maximum streamer length is reached and forget about the
grid dip meter.  Any ideas about this (or any ramblings) would be welcome.

Dick (K2YZ)


At 10:22 PM 8/8/00 -0600, you wrote:
>Original poster: 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:
>