Re: Capacitor help

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: Bart Anderson <classi6-at-classictesla-dot-com> 

Hi John,

Tesla list wrote:

>Original poster: "John H. Couture" <couturejh-at-mgte-dot-com>
>
>Bart -
>
>Do you take capacitor charging time into consideration when selecting a
>primary capacitor?

Yes. I allow the user any cap size desired (cover's all "topology's" that 
way) but I calc the charge time in relation to the bps, time constant at 
break, percent charged, and of course the effective cap voltage. This is 
all available for the user to view and should be considered when a cap size 
is selected.

>The calculations below using the standard capacitor
>charge equation indicates that the TC pri cap is not being charged to full
>voltage when the NST is the power supply. I have been researching this
>problem and have reached an impasse.
>
>For example the charging time for each half cycle of 60 Hz (120 BPS) is
>
>  1/4x60 = 4.17 ms. The capacitor charging time to 98% of 15000 is 4 time
>constants.
>
>    t = 4(-RC)(ln(V2/V1))
>
>For a 15KV/60 ma NST the R=Z=V/I= 15000/.06 = 250000 ohms
>
>     .00417 = 4(-250000xC)(ln(1/15000))
>
>      C = .00417/(4(-250000)(-9.62)) = 433 pf max size pri cap.

All good.

>This is saying that a 15KV/60 ma NST cannot charge the pri cap to anything
>near the 15000 volts if the cap is larger than 433 pf and the charging time
>is 4.17 ms.

No, it's not saying that. It's simply showing you the cap size 433pF can be 
charged to 98% in the time allotted.

>This cap is 24 times smaller than the resonant cap! What is
>wrong with these calculations?

Nothing is wrong. The calcs are correct for the simple transformer model 
shown. For more exacting science as we move toward or away from the 
resonant case, the transformer reactances must be known or at least 
approximated for a complex analysis. But for the what we have here, they 
are correct.

The charge curve is by no means linear. The cap charges very quickly at 
first and "gradually" slows it's rate of charge. By the time it's nearing 
99%, it's current is only "trickling" in. Kind of like pouring a cup of 
coffee (fast at first  then gradually slowing near the top, well, sort of).


Vcap = V*(1-e(-t/zc)
    e = Eulars constant (2.7182818)
    -t = (1/bps)*1000 (8.333ms for 120 bps)
    V = Vout ( 15000)
    z = impedance (250000)

Cap voltage with 346pF cap
15000(1-2.7182818(-.00833/(250000*346pF) = 14999 rms volts = 99.99%

Cap voltage with 433pF cap
15000(1-2.7182818(-.00833/(250000*433pF) = 14993 rms volts = 99.95%

Cap voltage with resonant cap size 11nF cap
15000(1-2.7182818(-.00833/(250000*11nF) = 14275 rms volts = 95.17%

Cap voltage with srsg LTR 28nF cap
15000(1-2.7182818(-.00833/(250000*28nF) = 10439 rms volts = 69.57%

Note the difference in voltage of 0.04% between 346pF up to the resonant 
cap size of 11nF.
Because of the charge curve for the cap  size and transformer current, and 
for the changes in BPS for our systems, I have choosen to keep the user 
aware by showing these numbers.

Take care,
Bart