Re: Cap resonant value.

["Barton B. Anderson" <tesla123-at-pacbell-dot-net> (by way of Terry Fritz <twftesla-at-uswest-dot-net>)]

Hi Ed, Kamil, 

Tesla list wrote: 
>
> Original poster: Esondrmn-at-aol-dot-com 
>
> << Original poster: "Kamil Kompa" <czlonek-at-polbox-dot-com> 
>  > I have 13kV 400mA transformer , but I have to limit current to 200mA 
>  > because my power line is 220V 12A only. 
>  > Which value schould i use to find capacitor size that will be resonant 
>  > (200mA or 400mA) ? 
>  > 
>  > Kamil Kompa 
>
>  It's my understanding you should use the "rated" value (400mA) for
> impedance. 
>  The matched size is based on it and it doesn't change. But the limited 
> current 
>  means you will only turn up Vin to about 2600W or 170V max. But if I'm 
> mistaken 
>  here, I hope someone will correct me. 
>
>  Bart 
>   >> 
> I thought our inductive ballast in the primary circuit effectively increasd 
> the inductance of the transformer and essentially produces the same as rated 
> voltage (less some resistive loss) at a lower current - thus you should 
> calculate based on the reduced current figure. 
>
> Ed Sonderman

Yes, our inductive ballast is series connected with our primary transformer
winding, and the total inductance is in parallel with the applied voltage (this
should be taken into account). 

I pulled out my calculator and here's what I came up with: 

The transformer (5000W, 13000V,400mA) match size is 1 / (2 * pi * F * Z): 
C = 1  / (377 * (13000/400mA)) = 81.6nF 

A 5200W transformer with 170 V applied will overkill your 12A limitation by 6
amps (sorry about that), so you would have to apply an input voltage of 110V
which will put you right at 11.8A (200mA on L2). The transformers output
voltage will be down to 6500V (6500 x 200mA = 1300W). 

Now, (1300W, 6500V, 200mA): 
C = 1 / (377 * (6500/200mA)) = 81.6nF 

This works out the same as using the rated transformer values. Now "no"
external ballast has been applied here and would change the value. Assuming you
externally ballast the transformer using a variac or welder that can apply the
same inductance as L1 (xfmr), then you will have twice the inductance
effectively reducing the resonant condition to half the rated value, so 40.8nF.
This works out identical to "pretending" the transformer is 200mA at 13000V: 

(13kv / 200mA = 65000 ohms) so, 

C = 1 / (377 * 65000) = 40.8nF. 

The only thing to note, is that the reason the transformer would be resonant at
this value is due to the ballast in series with L1 and capable of applying the
same amount of inductance. You could actually pick any size cap you want and
make it resonant as long as you have the ballast set appropriately. If your
ballast could only apply say half the inductance of L1, then the resonant cap
size would change to 52.7nF. 

Obvisouly, the two ways to do this is to first know the ballast and transformer
values then work out the cap size OR first know the cap size and transformer
values then work out the ballast. 

If the transformer is internally ballasted, then the rated transfomer values
are the ones to use for a resonant cap size. 

Take care, 
Bart