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Re: Sizing capacitors

Original poster: "Dr. Resonance" <resonance@xxxxxxxxxx>
Another interesting formulation is matching the transformer to the capacitor size.
Imagine if you have a variac to adjust the voltage and another variac to adjust the current, ie, an adjustable series inductor on the primary side of your pole xmfr / PT xmfr.
For initial testing you might set the xmfrs impedance equal to the impedance of the capacitor bank. Use a climbing arc to set the current to a certain value, ie, perhaps 30 Amperes. Knowing the 30 amp current value on the primary side using 220 volts you can calc. the power in the system The, using the 14,400 volt sec xmfr value you find the sec. current value. You then use this value to match the capacitive reactance value and you have the resonant match value for the xmfr - cap bank. Go slightly above this value to prevent undesireable xmfr to cap resonance, usually 1.3 to 1.4 times the capacitive match value at resonance. 

Now, here is where the interesting part begins.
Set up a current meter on the primary side and monitor the primary amps. Increase the voltage control variac to 89-90% and then adjust the current control (series variac) for 25-30 amps. As power is applied to the coil system, at some point, you will notice the current actually begin to decrease even as you increase the voltage control variac. In ham radio, tuning linear amps, this was referred to as "dipping the plate current at resonance". The current will decrease as the voltage variac (power into the system is increased). There is a "tuning dip" on the ammeter at this point.
This tuning point is the most efficient operating point for a classic spark gap Tesla coil system. As you increase the power into the system the amps will again start to rise. Slightly above the "tuning dip" point is the point at which the sparks will be their longest with a reasonable minimum of input power for any given system. Longer sparks can be produced above this current input point, however, a lot more power is required and the system is not operating in an efficient mode, ie, you have increased the power factor above the unity point and this is an area where classic Tesla coils do not operate very smooth. They become current hogs and try to saturate the current controller and produce audio "thumps" in the current and voltage variacs.
This is what I refer to as "tuning the power supply to the system" and will give you a reliable indication of the most efficient power input (current level especially) for your given system. It's an experiment worth doing at least once to determine where the "resonant current dip" point is for your system. Then you can adjust the number of turns on your series power reactor to prodvide this proper level of current just as your voltage variac reaches 100% on it's scale.
Up to approx 35 Amps a single variac provides voltage control for this experiment while a single variac in series with the pole xmfr pri provides the current control. If you are running a 0.1 uF to 0.2 uF cap bank then you will need a dual variac for the voltage control and another dual variac for the current control to determine this tuning point. After this experiment is conducted you will know the best current for your system and the second current control variac is eliminated and the turns are adjusted on the primary series reactor to provide this "dip current" or slightly above (10% is usually very good for performance). This is the best way to determine the proper amount of current your current reactor / pole xmfr system should be providing to your system.
Then, matching the impedance to determine the resonant value capacitance, and increase this value by 1.3 x Cres and you will have a very nice performing system. Values up to 1.6 Cres do work but they produce sparks with more of a "capacitive discharge" and don't seem to be as active as the sparks off a toroid at 1.3 x Cres value. 

Dr. Resonance





Original poster: "J. Aaron Holmes" <jaholmes@xxxxxxxxxxxxxxxxxx>

Thanks, Terry!  Very helpful as usual.  I suppose my
doubts about the transformer <==> capacitor
formulation come about because it seems to me that a
capacitive load on the transformer is going to have a
crummy power factor, thus rendering the transformer VA
incompatible with the coil Watts value.

Is that true?  In other words, to use 290nF would mean
200W effective power from the transformer, but the VA
would be higher, right?  If I'm way off, just shut me
up! :-))  Otherwise, what I guess I was asking was
this:  How would one go about choosing a cap for a
given VA, or otherwise so as to avoid exceeding some
rated peak current.  Again, this is a PT and probably
can take a few times its rated 200VA...guess I'm just
interested in "getting the math" instead of surviving
on "rules of thumb" as I have for years now.

Regarding "resonance" and "DC"...duh!  My brain was
obviously already in bed when I went off on LTR/STR.
I'd actually *love* to know how those values were
computed for NSTs, etc., but if you recall sending it
to the list or posting it somewhere, I'll just look
harder :-)

Good night (for me!) -
Aaron, N7OE

--- Tesla list <tesla@xxxxxxxxxx> wrote:

> Original poster: Vardan
> <vardan01@xxxxxxxxxxxxxxxxxxxxxxx>
>
> Hi,
>
> At 10:14 PM 6/16/2006, you wrote:
> >I've built coils before using caps that were
> obviously
> >"way STR" (e.g., 30nF on a 15kVA pig), and so never
> >bothered to really understand how one sizes a cap
> to
> >take maximum advantage of one's transformer (didn't
> >have room in my garage to do that with a pig
> anyway!),
> >but now I'm working on a coil based on a tiny 200VA
> PT
> >and find myself wondering how much cap the thing
> can
> >really take.  I know how to compute the cap size
> >needed to deliver, say, 200W to the coil based on a
> >particular firing voltage, however I'm guessing
> this
> >doesn't corelate well to the rated VA of the
> >transformer, which is based on the rated RMS
> voltage.
>
> The coil's power is:
>
> P = 1/2 x C x V^2 x BPS
>
> Where:
> P is the power in watts
> C is the primary capacitance
> V is the firing voltage
> BPS is the breaks per second
>
>
> >The output voltage of my PT is 2400VAC (Yes,
> >2.4kV--this is for a SISG coil), so the peak
> voltage
> >would be 2400V x SQRT(2) = 3390V.  If I limit my
> >transformer to 200VA, how much cap can I charge to
> >this voltage in a half cycle?
>
> 200 = 1/2 x C x 3390^2 x 120      C = 290nF
>
> >As this is a
> >non-shunted transformer, I'm thinking LTR and STR
> have
> >less to do with the cap and more to do with the
> >ballast, yes?
>
> Yes.
>
> >So if I compute the maximum cap size I
> >can charge in a half cycle at 200VA, then ballast
> for
> >300VA, I'm running STR, and if I were to ballast
> for
> >100VA, I'd be running LTR...?  How far off of
> >resonance does one have to be to meet the
> definitions
> >of STR and LTR?
>
> Since you have control over the ballast, you can do
> anything you want.
>
>
> >If I go the LTR route, I'd like to know how much
> >voltage I can expect to develop on the cap in a
> half
> >cycle (less than 3390V, obviously) so that I know
> how
> >many SISG sections must be used.
>
> LTR coil charge to the "same" firing voltage, they
> just charge larger
> cap values.  However, since SISG coils are DC, the
> inductive kick
> effects are not present.  You can't resonate "DC" so
> LTR has no
> meaning for DC coils.
>
> >I know how I'd do
> >this for DC, but how about for 60Hz AC?
> >
> >Lastly (in case Terry is reading this):  Is there
> any
> >reason why one wouldn't want to use fewer SIDACs in
> >one SISG section than in another within the same
> >"stack"?  For example, if my firing voltage divided
> by
> >900 has a 300V remainder, can I just use one SIDAC
> in
> >the last SISG section to take advantage of this
> >straggling 300V, or am I better off making all the
> >sections the same.  Can't think of why that'd be
> >critical, but just in case...
>
> I have not tried it specifically but it "should" be
> fine.  In my new
> coil, I just lowered all of them...  I have just
> jumpered across the
> heatsinks for lower voltage effectively shorting
> them out and that
> works fine.  It is a series charger so there should
> not be any timing problems.
>
>
> >Sorry for any repeat Q's (I'm sure they all are!),
> but
> >while I see tables of STR and LTR values floating
> >around for NSTs and pigs, I'm afraid I simply have
> no
> >idea how those numbers were established!
>
> You probably really don't want to know ;-))
>
> Cheers,
>
>          Terry
>
>
>
> >Thanks for reading all this :-)
> >
> >Regards,
> >Aaron, N7OE
>
>
>