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

```On Tue, 30 Aug 2016 22:08:36 +0000
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.

++++++++++++
60 Hz means that 1/2 cycle occurs in 1/120th of a second = 0.0083
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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>
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