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Registered Member #1527
Joined: Mon Jun 09 2008, 05:00PM
Location:
Posts: 4
Comrades,
If the primary capacitance of an AC spark gap Tesla coil is found through:
V/I=1/(j*2*pi*f*C)
where V and I are the rated values of the transformer, a problem arises in terms of power calculations, as the charge on the capcitor doesn't seem to furnish the full power rating of the tranformer. Behold:
Energy=0.5*C*V^2
but C=I/(2*pi*f*V) [From the first equation]
hence, Energy=0.5*I*V/(2*pi*f)
In one second the spark gap should fire (2*frequency) times (e.g. 100 for a 50Hz frequency), hence the power delivered by the capacitor:
Power = Energy*2*frequency = I*V/(2*pi) = Rated transformer power /(2*pi)
This 2*pi seems to be ruining the elegance of the putatively correct primary capacitance value. The transformer seems to be delivering (1/2*pi) or (1/6) of its full power rating.
Registered Member #1232
Joined: Wed Jan 16 2008, 10:53PM
Location: Doon tha Toon!
Posts: 881
That equation just gives you the capacitor size that cancels the leakage inductance of the NST at the operating frequency. And it isn't even a good idea to do that for a number of reasons.
In practice the spark gap typically fires somewhat faster than twice per cycle. The capacitor also charges resonantly after every firing to a voltage higher than the PEAK voltage of the transformer alone. Both of these things mean that you can draw more power out of the NST than the rating plate would suggest.
Registered Member #1527
Joined: Mon Jun 09 2008, 05:00PM
Location:
Posts: 4
Many thanks Geordie...but how do you go about finding the optimum capacitance then? Is there an upper limit for the primary capacitance you can calculate? You seem to view the equation I mentioned with great contempt.
Registered Member #135
Joined: Sat Feb 11 2006, 12:06AM
Location: Anywhere is fine
Posts: 1735
There are limits, current limits in fact due to the capacitor shorting your AC source during the charging cycle. If you want more info check out the many threads on capacitence calculations, "Calculating LTR", and transformer related threads. There's a lot of information around.
The short answer from me is 1.5x resonant from the transformer. And there's a bit of extensive work on that one. Or if you want to check out Terry Fritz's work, that's around too.
Registered Member #1232
Joined: Wed Jan 16 2008, 10:53PM
Location: Doon tha Toon!
Posts: 881
Different people prefer to build their systems differently. I haven't built a conventional Tesla Coil in many many years now, but my personal preference at the time was to size the capacitor to around 70% of the "matched" value given by your calculation. Then I set up the system to run with a synchronous rotary gap giving 4 presentations per mains cycle (200bps in 50Hz countries.) That gives total power throughput around the faceplate rating of an NST, whilst at the same time keeping peak voltage under control and achieving good power factor.
That seemed to work well for me, although it was not arrived at by guesswork. I did quite a lot of investigations into both DC and AC resonant charging in TC applications. Most of the info is on my website.
Registered Member #135
Joined: Sat Feb 11 2006, 12:06AM
Location: Anywhere is fine
Posts: 1735
I didn't guess either Richie, its all documented with calculations in my paperwork, with simulations, measurements, And calculated values to back up the simulation!
I even invested ~3k in doorknob caps to see how the performance changed at different values, hence the need for a decade capacitor. I had the best results at 120 BPS and 1.5x resonant, and the simulation shows best power density in that ballpark.
I would also say that as the break rate increases you will see shorter arc lengths, so if you're looking for maximum arc length try to stay around 100 bps for 50Hz and 120 bps for 60Hz
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The Occult 2 pi - Primary Capacitance Muddle
