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RE: Matching capacitor size to transformers

Hi All,

I have a bit more time now so I'll explain how I came up with this.


The energy stored in a capacitor just before the gap fires is:

	E = 1/2 C Vf^2  (joules)

Since the firing voltage should be SQRT(2) of the RMS transformer voltage: 

	Vf = SQRT(2) Vo  (volts)

Also the power of the system is the capacitor energy multiplied by the
break rate:

	Pc = C Vo^2 BPS  (watts)

The power available from the transformer is it's rated voltage and current
less the power lost in protection filters (L):

	Pt = Vo Io - L  (watts)

These two powers must be equal:

	C Vo^2 BPS == Vo Io -L

Solving for C:

	C = ( Vo Io - L ) / ( BPS Vo^2 )  (farads)

When I compared this value for C to my coils, I found that there was a
consistent factor of 0.92  Therefore:

	C = 0.92 ( Vo Io - L ) / ( BPS Vo^2 )   (farads)

This is the capacitor size required for an LTR coil driven by a current
limited transformer running from a sync gap.  This is the largest known cap
a given transformer can charge properly. 

I use this equation in MMCCalc2 to find a good cap size for a specific
transformer.  If the coil has a static gap or is  not as "refined" as a
good LTR coil a string or two less capacitance can be selected easily with
an MMC.  However, this equation does keep one from making the capacitor too
large to every be used.

Cheers,

	Terry


>Hi All,
>
>I was pondering how to best predict what size capacitor would go with what 
>size NST.  Also, given a NST and capacitor size, what would be the break rate.
>
>I have come up with the following two equations based on many things:
>
>	0.92 x ( Vo x Io - L ) / ( BPS x Vo^2 ) = C
>
>	0.92 x ( Vo x Io - L ) / ( C x Vo^2 ) = BPS
>
>Vo = Transformer RMS output voltage (volts)
>Io = Transformer RMS output current (amps)
>L = known system loss (mostly protection filter resistors) (watts)
>BPS = Breaks Per Second
>C = Capacitor value in Farads
>
>The second equation is just a slight rearrangement of the first.
>
>C is the largest cap size that a fine tuned LTR coil can charge.  Static gap 
>and other systems would be less but at least this provides an upper limit.  
>The BPS equation my predict what the BPS of a static gap system with say 
>resonant charging might be.  
>
>This equation is meant to fill a void in my MMC program.  The MMC program is 
>good at arranging small caps to make a given capacitor, but many people 
>don't know what value of capacitor they need...
>
>The equation comes from how much energy a transformer can deliver and how 
>many times per second it can charge a cap of a given value.  The 0.92 factor 
>comes from my observations of my coils and basically is adjusting for system 
>loss.
>
>Comments??
>
>Cheers,
>
>	Terry