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Re: Power in a TC System

Hi Gavin,

At 05:31 PM 05/21/2000 +0100, you wrote:
>Hi Terry,
>
>Tesla List wrote:
>
>> Original Poster: Terry Fritz <twftesla-at-uswest-dot-net>
>>
>> Hi Gavin,
>>
>> At 11:17 PM 05/19/2000 +0100, you wrote:
>> >Hi John,
>> >I know a bit about coiling, but tend to get lost with definitions (I only
>> >learnt
>> >the other day what an MMC was, but had been using them for the last few
>> >years!).
>> >
>>
>> Really!  The first use of today's modern MMCs with high current
>> polypropylene caps has been credited to Reinhard in the summer of 1998, so
>> far...  We are kind of wondering who was the first to use them?  Not that
>> there is any great pot of gold for being the "first" but if you have used
>> them before all of us you should get some kind of honorable mention...
>> Other mini caps have been used for a decade plus but only the modern poly
>> caps have really worked well.
>>
>
>Hmmm, not sure now you said that, I'll tell you what I did, when I did it and
>leave it to your better judgment.
>I connected five 2.5nF/30kV capacitor sub-banks in parallel to give me a
>12.5nF/30kV capacitor bank. Each sub-bank was made up from four 10nF/7.5kV
>cylindrical (1 inch diam. by 2.5 inches long) capacitors, don't know what the
>gunk (dielectric) inside was. So does this constitute an MMC? This was all
done
>in probably late 1998.....I think, Reinhard can keep the glory, I have 
>something
>else, but no web site to stick it on. The use of an MMC (if I've got the
>definition right) was not some stroke of genius, more an act of laziness. 
>Winding
>a secondary was bad enough, but rolling my own capacitor was too much like
hard
>work.

People have been using ordinary caps for a decade plus at least.  But those
tended to blow up all the time.  MMC caps specifically use polypropylene as
the dielectric and the caps are made for high-voltage high-current use.

>
snip...>
>O.K. they say mathematics is the universal language, could you post a 
>formula for
>an LTR and a resonant matched primary capacitor, 

Using a 15000 volt 60 milliamps NST.

for the resonant case:
The output impedance of the NST is 15000 / 0.060 = 250000 ohms

We want a cap that will have that impedance at 60 Hz

Zc = 1 / (2 * pi * F * C)  

so  

C = 1 / (2 * pi * F * Zc) 

Putting in the numbers we get

C = 1 / ( 2 * pi * 60 * 250000 ) = 10.61nF 


For the LTR case, I use energy equations:
The power available from a 15/60 NST in the LTR case is V x I or

15000 x 0.060 = 900 watts

C capacitor stores energy according to the equation:

E = 1/2 C V^2

The power is equivalent to the energy expended per second so in the case of
Tesla coils this is:

P = 1/2 C Vm^2 x BPS

Where Vm = 15000 x SQRT(2) so you can say P = C V^2 BPS

So   V I = C V^2 BPS  

or 

C = I / (V * BPS)

 C = 0.060 / (15000 x 120) = 33.33nF

Since I loose about 10% in protection resistors that value is 10% less or 30nF.

The actual value when some other losses are added is about 93% of this so I
get 28nF in a real 15/60 system.

I use

C = 0.84 I / (V x BPS) 

with good results.

I did this from memory while eating lunch so if any thing seems wrong... ;-))

Simply, in a resonant system you are trying to cancel the inductance of the
NST with the capacitance so you can reach resonance and pull power out of
it without current limiting.  You need to run these systems at high BPS
(Bangs Per Second) to discharge the cap before the voltage gets too high.
If the gap does not fire, the voltage will skyrocket and blow the NST or
caps instantly.

Synchronous rotary gap LTR coils are more complex.  They have a cap that
loads the NST so that its output voltage is lower than the rating.
However, by carefully adjusting the gap timing, the inductance can be made
to "kick" and supply enough current to charge the cap to full voltage.  If
the gap stops firing in and LTR coil, the NST voltage drops.  You can also
use LTR caps about 1.5 times the resonant value in static gap coils too and
get more energy storage at lower BPS this is far less likely to blow an NST.

That is basically it.  It can get far more messy but this all works fine...

Cheers,

	Terry

 




>
>This may eventually sink in! Please be patient, thanks again.
>
>Kind regards
>
>Gavin, U.K.
>
>
>