# Re: [TCML] Cap and transformer matching: math

```I'm not sure I follow your logic - tau is for R-C circuits, and this is
predominantly an L-C circuit.  But beyond that, trying to mathematically
model an NST charging a cap unfortunately is just not the best approach.
NST's become non-linear as the core saturates and no one to my knowledge in
the TC community has a satisfactory model to accommodate the non-linear
effects, which are extremely significant.  The good news is that such core
saturation provides a free and welcome boost to the current able to be
pulled from an NST,

I performed and published a study that measured the actual power processed
from a variety of NST's over a range of capacitor values, and the results
corroborate the referenced spreadsheet.  My report is at:

Regards, Gary Lau
MA, USA

On Tue, Aug 30, 2016 at 6:08 PM, Brian Hall <brianh4242@xxxxxxxxxxx> wrote:

> Thanks Gary and Matt, after reading your replies that does make a lot of
> sense now.
>
> I bookmarked the link for the mmc cap to transformer value table.
>
> (Please correct me if I'm wrong in the rest of this, but I would like to
> make sure I understand what's happening in the circuit).
> I actually have a 15/30 NST and the chart tells me that a good LTR value
> is 0.0077 uF.
>
> A cap charges in 5 tau were tau = R times C, and hopefully Resistance in
> the tank circuit is low enough to be ignored.
>
> Thus 0.0077 uF = C = tau, and 5 tau is about 0.0385 microseconds.  A full
> charge and discharge cap cycle is 10 tau which in this case is 0.077
> microseconds.
>
>
> For a 15/30 NST at 60 Hz, 15kv is actually reached in 1/4 of the sine wave
> cycle, in the positive direction, 0 to 90 degrees.  The cap discharge also
> takes 5 tau were the voltage goes from 15kv to 0v at angles 90 to 180
> degrees as the vector rotates.  From 180 to 360 degrees of course the same
> thing happens but in the opposite direction of current flow.
>
>
> 60 Hz means that 1/2 cycle occurs in 1/30th of a second = 0.03 seconds.
>
> Converting to microseconds the decimal is moved six places to the right,
> giving us 30,000 microseconds per half cycle.
>
> This gives us a ratio of 30,000 half cycle microseconds / 0.077 charge and
> discharge microseconds (bangs of the spark gap)  which is about 389,610
> bangs per half cycle...
>
>
> Where is my math wrong?  That really doesn't sound right.
>
>
> ----------------------------------
> Brian Hall
>
>
>
> ________________________________
> From: Tesla <tesla-bounces@xxxxxxxxxx> on behalf of Gary Lau <
> glau1024@xxxxxxxxx>
> Sent: Tuesday, August 30, 2016 5:18 PM
> To: Tesla Coil Mailing List
> Subject: Re: [TCML] Show and tell first SGTC
>
> Getting a Tesla coil to operate at peak efficiency is a balancing act
> across many parameters.  That the primary and secondary circuits are tuned
> to roughly the same frequency is the prime directive here, but other things
> matter as well.
>
> The primary cap is not tuned to the NST in a resonant-sense, but it does
> need to be "matched", at least in the ballpark, to extract as much power
> from the NST as possible.  The best way to understand this is to consider
> extreme examples.  Let's say your NST was a 15/30 and the primary cap was
> tiny, say 100pF.  Your NST could charge that cap from zero to 15kV in
> practically no time.  The gap would try to fire hundreds (thousands?) of
> times per mains half-cycle, and with the capacitance so low, each "bang"
> would have very little energy.  This is not what we want - we want there to
> be one to a dozen or so as-big-as-possible bangs per half cycle.
>
> Now consider the other extreme.  Let's say your primary cap was huge, let's
> say 0.1 uF (one would normally want to use a cap on the order of .006-.01
> uF with a 15/30 NST).  With such a too-huge cap, the NST would be unable to
> charge the cap to 15kV in a single mains half-cycle.  What would actually
> happen is that the cap would charge higher and higher on successive
> half-cycles until the spark gap breakdown voltage is achieved. You'd get
> big bangs, but very infrequently, and it would be murder on your NST.
>
> There is not a simple formula that one plugs in your NST parameters and out
> pops the matched cap value.  Instead most coilers use a look-up table that
> has proven to be accurate.  There are probably other copies floating around
> the web - one can be found here:
> http://www.classictesla.com/hot-streamer/temp/MMCcapSales.gif
>
> Regards, Gary Lau
> MA, USA
>
>
>
> On Sun, Aug 28, 2016 at 7:35 PM, Brian Hall <brianh4242@xxxxxxxxxxx>
> wrote:
>
> > This brings up a general question I have, given what I've read here over
> > the years on this list vs. what I have learned about LC resonance in a
> > recent college circuit theory class.
> >
> > If the resonant frequency F = 1/(2pi(sqrt(LC))) then why does the
> > capacitance of the primary circuit need to be matched to the transformer?
> >
> >
> > Or is it that the primary capacitor has two attributes: voltage and
> > capacitance.  The capacitor voltage needs to handle what the transformer
> > voltage can deliver, (or 1.5 to 2x the transformer max out volts)  and
> the
> > primary coil L and primary capacitance C need inductive and capacitivie
> > values such that F = 1/(2pi(sqrt(LC)))   holds true, and match with the
> > same resonant frequency F of the secondary LC circuit?    Is that all we
> > need to change when we swap out a transformer in the primary circuit,
> just
> > the voltage max on the capacitor?
> >
> > And Adam, yes I too would like to see a link to the video of your coil,
> > always fun to demonstrate your first one!  So satisfying to see those
> > sparks fly.
> > ----------------------------------
> > Brian Hall
> > <snip>
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