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Re: capacitor charge rate/power

Hi Pholp,
	This is the same question that I myself about a month ago.  When the
driving source is anything but a constant voltage, such as a sinusoidal AC
waveform, then the simplest way to solve the problem is with a simulation.
I did this to determine the optimum capacitor size for a particular size
transformer.   I have attached a JPG file that shows results and can send
you the simulation in Excel if you are interested.  It assumes a pure
sinusoid driving waveform.  I understand that the "real" waveform is
distorted due to non-linearities in the NST.  The simualion works for any
input waveform, so if someone can help with characterizing the
non-linearities, then an exact and more useful solution can be computed.
Here is text that was sent to another Coiler as we discussed the simulation
and resulting graphs that are attached.  

Look at the jpg graph first.  It combines results obtained from the Excel
worksheet and shows how I was trying to select the optimum capacitor for my
NST.

http://1071737050/site/misc/CHRGSIM1.jpg
<<Since the Tesla list cannot accept file attachments, I posted it - Terry>> 

The graph can be verified by simulating the charging of a capacitor as I
have done or by direct measurement.  It is based on a 60 cycle, 15000 volt
rms, 30 ma NST sinusoidal charging source, however the results are
scaleable to any size transformer and matching capacitor.  The top and
bottom graph both use time in milliseconds along the same scale x-axis.  A
full cycle of 60 Hertz is 16.7 milliseconds while a 1/4 cycle is 4.17
milliseconds.

         The top graph (on jpg file) shows the capacitor voltage without
spark gap (no discharges).  The C00375 curve is the voltage for a 0.00375
uF capacitor, C0053 curve is the voltage for a 0.0053 uF capacitor, C0075
curve is the voltage for a 0.0075 uF capacitor.  As expected, the smallest
capacitor charges to the highest voltage (not energy) and follows the
charging waveform most closely, while the larger capacitor lags most behind
in voltage.  That's because Vcap is the integral of 1/C i dt.  Also notice
that the cap keeps charging beyond a 1/4 cycle until the driving
transformer drops below the cap voltage.  Since the larger capacitor has
the lowest voltage, it has the longest charge time.  You may benefit from
this because you have a synchronous spark gap that can be made to fire at
any time.  Hopefully this could be used to select the optimum firing angle.


          The bottom graph is the energy stored in the capacitor and is
what is really important.  The spark gap determines the time and therefore
the energy that is released into the primary circuit.  This is why one of
the final tuning tweaks is to increase the primary spark gap and release as
much energy as possible.  The J00375 curve is the Energy (in Joules) as a
function of time for a 0.00375 uF capacitor, J0053 curve is the Energy for
a 0.0053 uF capacitor, J0075 curve is the voltage for a 0.0075 uF capacitor. 
          Several interesting conclusions can be drawn from these curves:

1.  If the spark gap is set at a low voltage or an async SG is used such
that the charging time is short (less than 4 ms in a 60 cycle system), then
there is a slight advantage in using a capacitor that is a little smaller
than the size that matches the impedance of the transformer.

2.  All else staying the same (not optimizing design of the cap size),
changing to a larger transformer leads to longer sparks because its higher
charging current capacity increases the charging rate - same as having a
smaller capacitor in voltage, but more energy because the capacitor size
stays the same (J = .5 * C * V^2)

3.  There is a slight advantage in the 6 to 7 ms region in energy stored
and spark length if the discharge gap size could be set to fire in this
time range.  For this 15/30 NST example, the spark setting should be around
13,000 volts.  Note the same final tuning tweak rule applies.  You'll know
if the gap firing voltage is too high because it won't fire at all with the
larger cap.  Yeh, I admit this is tricky tuning but is something to shoot
for while squeezing out the longest spark length out.
The results shown by the jpg graph were done to try and optimize the
capacitor size and determine the best firing voltage or time.

Hope this helps, Dick


At 06:33 PM 7/29/00 -0600, you wrote:
>Original poster: "Pholp Smiff" <kawanze-at-hotmail-dot-com> 
>
>can anyone give me a formula as to how long it takes to charge a capacitor 
>depending on size and power? i.e.: using a 12kv-at-60mA transformer, how long 
>would it take to charge a .1mF capacitor? Can someone tell me and show me 
>the math behind it? And how much power is actually stored and let out in a 
>discharge. Also i'd like to know how to determing the size of a bleeder 
>resistor for capacitors.
>
>thanks
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