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

```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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